Factors associated with treatment costs in patients with coronary artery disease in India: Comparison of linear regression, gamma regression and quantile regression methods

Factors associated with treatment costs in patients with coronary artery disease in India: Comparison of linear regression, gamma regression and quantile regression methods | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Factors associated with treatment costs in patients with coronary artery disease in India: Comparison of linear regression, gamma regression and quantile regression methods Saba Abidi, Shridhar Dwivedi, Vinod Sharma, Anoop Kumar, Sushama Talegaonkar, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7890011/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 15 You are reading this latest preprint version Abstract Introduction : There is no uniformly agreed regression model for analysing cost data. The objective of the current study was to compare the performance of linear regression, gamma regression, and quantile regression and predict a better model using costs among patients with coronary artery disease (CAD). Methods A cross-sectional survey was conducted on CAD patients at a tertiary care hospital in New Delhi between May and October 2023. Descriptive statistics for direct and indirect costs were estimated, and their association with demographic and clinical variables was explored using linear, gamma and quantile regression along with prediction errors. Results 560 CAD patients were interviewed (mean age 62 ± 10.50years). 182 patients were found to be on medical therapy only, and 378 patients underwent any procedure along with medical treatment. The highest and lowest costs were observed for patients who underwent coronary artery bypass graft (US $ 3323/per patient) and received only medical therapy (US $ 220/per patient). According to linear regression, gender, distance to the hospital and type of intervention significantly affected the expenditure. In gamma regression, only the type of intervention was statistically significant. In quantile regression, being male, living away from the hospital and having a high SES score positively affected the expenditure. Quantile regression was found to have fewer prediction errors. Conclusion Establishing an appropriate statistical model is fundamental for predicting the costs, which could be affected by several factors, and the final choice of the regression model should be made after careful assessment of predictive ability and tailored to specific data. Cost analysis coronary artery diseases health expenditure regression Figures Figure 1 Figure 2 Figure 3 Introduction Cardiovascular diseases (CVDs) continue to be the prominent reason for premature mortality across the world, and the most prevalent CVD in India is coronary artery disease. [ 1 , 2 ] Coronary artery disease (CAD) is a condition when the heart does not get sufficient blood and oxygen due to obstruction in the coronary arteries. [ 1 ] In 2022, globally, CAD affected 300 people, with a prevalence and mortality rate of 3610.2 and 108.8 per 1,00,000 population, respectively. [ 2 ] In 2016, CAD was the most prevalent type of cardiovascular disease, with a prevalence of 11% in India, contributing to a high economic burden. [ 3 ] Recent evidence has suggested that CVDs are implicated in poverty due to cataclysmic health spending and mounting out-of-pocket expenditure (OOPE). (4–6) CVDs are responsible for the increased financial burden on the household budget and, ultimately, the national economy. Cost of Illness (COI) study provides evidence of the economic burden of disease on a country’s economy and offers insights to decision-makers to utilise the limited resources efficiently. COI is defined as the value of the resources that are expended or forgone due to a health problem, and includes health sector costs (direct costs), the value of decreased or lost productivity by the patient (indirect costs), and the cost of pain and suffering (intangible costs). [ 6 – 8 ] In India, COI studies have been conducted for CVDs [ 9 , 10 ], but not specifically for CAD. Previous studies have estimated the overall healthcare costs and OOPE for CVDs [ 11 , 12 ]. However, the use of regression models has been limited. Propensity Score matching [ 13 ] and logistic regression [ 14 , 15 ] methods have been widely used to estimate the effect of predictors on healthcare expenditures. Studies conducted in settings other than India have used different regression models to ascertain the relationship between expenditure on CVDs and covariates. Studies published from Finland, the United Kingdom and New Zealand used machine learning prediction models to conduct the regression analysis. [ 16 – 18 ]. Lu et al (2023) used quantile regression to estimate the effect of independent variables on the expenditure of CVD for China. [ 19 ] Other generalised linear models were used in different countries, such as gamma regression in England and Japan [ 20 , 21 ] and logistic regression in the USA [ 22 ] In health economics, estimating the population mean costs is widely accepted as a statistic of interest to policymakers. [ 23 ] The non-negative nature of healthcare costs data most often exhibits substantial positive skewness, with heavy tails and is often multimodal. Estimating the mean cost and establishing a relationship between the costs and the predictor variables are the main challenges in developing regression models in healthcare. [ 24 ] As mentioned above, in healthcare systems, various statistical models are commonly used in predicting expenditure based on explanatory variables. Generalised Linear Models (GLMs) are regression models used to identify relationships between a dependent variable and predictor variables, including linear, logistic, Poisson, and exponential relationships. GLMs enable us to perform regression for non-normal distributions of the dependent variable. [ 25 ] The application of these models shows that they are robust to the placement of covariates and random effects. [ 26 ] Gamma regression is a type of GLM that is commonly used for analysing health expenditure for patients incurring costs greater than zero. Gamma regression models are flexible and do not require data transformation or removal of outliers to accommodate many outcome distribution shapes. [ 27 , 28 ] Similar to gamma regression, quantile regression also works well in the presence of outliers and non-normal data. Quantile regression predicts the effect of a change in the defined quantile of the dependent variable with a change in the unit of the independent variable. [ 29 ] This approach has been found to be superior to linear regression and provides an inclusive presentation of factors that affect health expenditure. [ 29 ] The current study aimed to apply more commonly used linear, gamma and quantile regression models in medical literature for analysing cost data in a cohort of patients receiving treatment for CAD to assess the consistency of findings regarding the significance of the clinical variables. It was hypothesised that the different models would result in different conclusions about the impact of demographic and clinical factors on the cost of treatment. The different models would have different abilities to correctly predict patient costs for CAD treatment in tertiary care healthcare facilities in India, and similar geographical settings. Methods This study was based on a cross-sectional survey conducted at a cardiac-specific tertiary care hospital in New Delhi from May-October 2023. Sample Size Calculation The sample size was calculated based on the estimated average costs, regardless of age and comorbidity. A previous study [10] shows that the standard deviation of average costs is approximately $ 2,400, and the average cost is $979. Expecting a precision of 20% on either side and estimating the average cost with a 95% confidence level, the sample size calculated was 555 subjects. Therefore, a total of 560 samples were taken for the study. N= (Z 1-α/2) 2 * (SD) 2 E 2 N=( 1.96) 2 * (2400) 2 (200) 2 553≅555 Z=Z score at 95% confidence interval, value=1.96 SD= Standard deviation from Gupta et al. (2020) E=Margin of error (calculated as E=mean x precision, E=979*0.2=195.8≅200) Eligibility criteria Patients were directly recruited during their visits for regular check-ups in the hospital's cardiac OPD. Written informed consent was obtained prior to starting any interview with the patient. The template of informed consent, as per guidelines by ICMR, has been included in the supplementary material (Supplementary 1). Patients above 18 years of age, both genders, visiting the hospital, and suffering from coronary artery diseases were included in the data collection. Patients having diseases other than coronary artery diseases like rheumatic heart disease, heart failure, congenital heart diseases, etc., patients not continuing the treatment at the hospital, and patients who were unwilling to participate in the study were excluded. Data Collection Two experts (ST & AK) designed the case record form (CRF) and two cardiologists (SD and VS) validated it (Supplementary 1). Firstly, the CRF was used to collect data from 20 patients in May 2023 and the collected data was checked for its adherence with the objectives. Changes suggested at this step were incorporated in the final CRF. The final CRF was used to collect information on socio-demographic characteristics, medical history, and treatment costs. Patients were selected using convenience sample and the information collected from May-October 2023. Cost calculation Participants were inquired if they received either medical therapy (MT) or any invasive procedure for CAD in the previous 12 months. The patients were divided into four groups, namely, only MT, MT+CAG (Coronary angiography), MT+ PTCA (Percutaneous Transluminal Coronary Angioplasty) and MT+CABG (Coronary Artery Bypass Graft). Participants were asked if they had received either an outpatient (OP) or inpatient (IP) hospitalisation treatment (invasive procedure) for CAD in the previous 12 months. If affirmative for only MT, participants were asked to report the number of visits and medical expenditures for each category: medications, consultation fees, and laboratory or radiological tests. If the participant was hospitalised for any procedure, then the information about the procedure, length of hospital stay, and hospital costs was obtained from the hospital medical records. Data on direct non-medical expenditures, including expenses on travel to and from the clinic/hospital, whereas indirect costs included the time duration the patient spent at the hospital, and the number of days the patient was hospitalised. The cost of illness was calculated by considering both direct and indirect costs. Direct medical costs included the costs of medications, laboratory tests, consultations, procedures, and hospitalisation costs. Direct non-medical costs included travel costs, and indirect costs were productivity losses by the patient. The final cost data were converted into USD 2023 using the conversion rate of 1 US$ = 83.1164 INR [30]. The costs of medicines for CAD patients were identified from the CIMS (Current Index of Medical Specialities) website for branded drugs and the Jan Aushadhi website for generic drugs. For the patients who underwent any invasive intervention at the hospital, the total costs for their treatment, length of stay, laboratory costs, and consultation costs were obtained from their medical records and corroborated with payment receipts. The distance between the patient's point of origin and the hospital was calculated using the address present in the medical records. The average travel cost was used to calculate INR 30 (US$ 0.4) for 1.5 km and INR 11 (US$ 0.1) per kilometer[1]. The cost was calculated for the patient's arrival and departure from the hospital. The number of visits done in one year multiplied by the travel cost per visit. Regarding the CAD patients on medical therapy, those who need to visit the OPD for regular check-ups were asked how many hours they spend at the hospital during each visit. If the number of hours was 4 hours on every visit, it was considered a full-day loss of productivity. The number of days lost due to hospital visits or hospital stays was multiplied by INR 176 (minimum wage per day) in India (US$ 2). The minimum wage was 176 Indian rupees, as reported by the Ministry of Labour in the wage floor index. [31] Independent variables Socio-economic status was calculated using the Kuppuswamy scale [33], presented in the Supplementary material (Supplementary 3). This scale is based on a cumulative score-based on education, occupation, and income variables. Based on this scale, patients were classified into five socio-economic status categories: Upper (I), Upper Middle (II), Lower Middle (III), Lower (IV), and Very Lower (V). However, socioeconomic status (SES) was taken as a continuous variable for the analysis, using the Kuppuswamy score as the SES score. Other variables included age, gender, distance to hospital, and type of intervention undergone by the CAD patients Statistical Analysis The descriptive statistics were used to calculate the measure of central tendency and measures of dispersion (Mean, median, Standard deviation and interquartile range) using MS Excel. Appropriate statistical tests were used to measure the significance level between the mean values. The costs were presented as mean, standard deviation, median and interquartile range (IQR) values. The socioeconomic class was calculated based on the Kuppuswamy scale [32]. First, simple linear regression was used to identify the factors associated with annual cost. The dependent variable was the total expenditure. The explanatory variables, which could explain the dependent variable, were identified as age, gender, distance to the hospital, socioeconomic status score, and type of intervention the CAD patients underwent. Then, a multiple regression analysis was performed to determine the factors affecting the total expenditure, and adjusted coefficients with a 95% confidence interval (CI) were calculated. The best-fit model was identified using multiple regression. Next, gamma regression models were conducted to estimate the healthcare expenditure associated with explanatory variables and the model with the lowest AIC (Akaike information criterion) score was considered. In most conditions, the gamma regression model effectively estimates population means of healthcare costs. [34] The generalised linear model with log link and gamma distribution was found be appropriate, and age, gender, distance to hospital, SES score and type of intervention were the independent variables. Age, distance to hospital and SES score were taken as continuous variables and gender and type of intervention were taken as categorical variable. Quantile regression for expenditure was performed at intervals of 50 th , 75 th , 90 th and 95 th percentile, and the coefficients (95% CI) were checked for positive or negative impact of expenditure [30]. The ability to predict costs was assessed using root mean squared (RMSE) and mean absolute errors (MAE) were calculated for all the regression models used to identify a better model. The errors for quantile regression were calculated for 50th percentile (by default quantile regression is a median regression) [34]. R software v4.4.2 (R Foundation for Statistical Computing, Vienna, Austria) was used to analyse the data, and a p-value of <0.05 was considered statistically significant. All costs were converted into US$ per 2023 values (1 INR= 83.1164 US$) based on December 29, 2023)[2]. Ethical Approval The study protocol has been approved by the Institutional Ethics Committee of Delhi Pharmaceutical Sciences and Research University (DPSRU-BREC/2022/A/041) and the National Heart Institute (3/9/002/EC/2023). Patients were administered with informed consent form and consent was obtained prior to data collection. Results The mean age (SD) of the 555 respondents was 62 (± 10.50) years, with two-thirds of the respondents being males (Table 1). About 85% of the participants were married and 61% were retired. More than half (67%) of the participants belonged to upper middle class, followed by lower middle (17.3%) and upper (14.1%) classes. Of the participants, 32.5% underwent only medical therapy, and the remaining 67.5% either PCI or CABG in addition to MT in the last year. (Table 1) The distribution of cost data was positively skewed, with a small minority of patients having very high costs (Figure 1). The median (IQR) annual illness cost for patients who only took medical therapy was [US$ 220(US$166-US$290)] (Table 2). For patients who underwent coronary angiography and received medical therapy, the median (IQR) cost of illness was estimated to be US$ 445 (US$380-US$500) per year. For patients who underwent percutaneous intervention or CABG in conjunction with medical therapy in the previous year, the median cost of illness was calculated to be US$ 2,420 (US$ 2,334-US$ 2,741) and US$ 3,323 (US$ 3,246-US$ 3,782), respectively. For patients on MT, almost half (48.5%) of the cost of illness was attributed to medications. In the case of invasive interventions, the cost of interventions dominated the cost of illness. The median (IQR) annual direct costs for only medical therapy were US$ 214(US$156-US$279). For patients on medical therapy and an invasive intervention, the median direct costs were US$ 430(US$370-US$487) for CAG, US$ 2409(US$2323-US$2729) for PTCA and US$ 3297(US$3219-US$3756) for CABG. The highest indirect costs (US$ 25(US$22-US$29)] were observed for CAD patients undergoing CABG, and the lowest for only MT [US$ 7(US$5-US$11)]. (Table 2) Most of the costs were statistically insignificant (p>0.05). The mean cost of treating CAD without procedures and with CAG in lower middle socio-economic status was statistically significant compared to the upper middle group with p values of 0.02 and 0.04, respectively. Similarly, the mean cost of CAG was reported to be statistically significant when compared between males and females (p=0.01). (Table 3) The R 2 value for the linear regression was 95.53% indicating the variation in the outcome variable expenditure explained by the predictors. The adjusted R 2 is almost equal to the multiple R-square, thus highlighting that the model has good cross-validity. The effect of the type of intervention was found to be statistically significant. The coefficient for age was -58.41, gender 4359.18, distance 136.48, and SES score -23.85, with the intercept at 300776.13. Gender and distance to the hospital had a statistically significant impact on the expenditure for managing CAD, with p values of 0.0389 and 0.0169, respectively. (Table 4) Gamma regression with the logarithmic function was identified as the appropriate model because it had the lowest AIC. Gamma regression found that only the type of intervention significantly affected the expenditure for managing CAD. CABG intervention was taken as a baseline, and the β coefficients (p-value) for CAG, MT and PTCA were found to be -2.1064305(<0.01), -2.7330792 (<0.01) and -0.3644606 (<0.01). The patient's age (β = -0.0014330) and gender (β =0.0248592) had negative and positive effects, respectively, but were not statistically significant. The constants obtained in the model were associated with a significant level of significance. (Table 5) We performed quantile regression to estimate the effect size of explanatory variables on different percentiles of expenditure, and the results show that as the distribution quantile of the dependent variable (cost) increased, the beta coefficient also surged from 27,041 to 4,63,000. The magnitude of the estimated coefficient was due to the skewness of the dependent variable. (Table 6). In all percentiles (50%, 75%, 90% and 95%) of the cost distribution, the male patients positively affected the expenditure. Age showed a negative association with expenditure in all quantiles of data distribution. Results of the estimation of coefficients showed that the distance to the hospital had a positive effect on expenditure in all quantiles except on the highest (95 th quantile). SES score varied expenditure across different quantiles (positive on 50 th quantile and negative on 75 th , 90 th , 95 th quantile). When patients undergoing CABG was taken as baseline, all the interventions had a negative effect on the expenditure for managing CAD across all the quantiles. A comparison of the multiple linear regression, gamma regression and quantile and regression was conducted. Multiple regression model was found have the lowest RMSE (21489.32) and MAE (13816.55) as compared to other two models. However, when comparing quantile regression and gamma regression, quantile regression was found to have lesser RMSE (151437.7) and MAE (112213.1) than gamma regression. (Table 7). For the models that predicted median cost, a median regression line was superimposed on the plot [36]. These plots are depicted in Figure 2 & 3. The models that predicted mean costs tended to fit the data well. Linear regression and gamma regression model predicted median costs well. Discussion This study estimated the direct and indirect costs of managing CAD in an Indian tertiary care center and determine the relationship between these costs and independent variables using multiple linear regression, gamma regression, and quantile regression methods and compared the results of these models. This study found that a significant part (50%) of the costs incurred by the patients for managing CADs through medical therapy pertained to the costs of medications which is similar to another study, which concluded that the cost of drugs accounts for the principal proportion (39%) of economic burden on patients [36]. Karan et al (2010) in a discussion paper published by the World Bank state that the expenses per OPD visit to a private hospital for any heart disease were INR 485 (US$ 6) [37]. The results from the study by Chauhan et al (2012) conducted in North India, estimated the costs incurred by patients who got treated in outpatient department sessions as INR 48578 (US$ 584) for two years, which is comparable to our study where annual cost was estimated to be US$ 246 per patient [36]. Huffman et al (2011) calculated the mean out-of-pocket expenditure for heart diseases for over 15 months as Int$2,917 (US$ 35) in India [38]. Gheorghe et al (2018) conducted a systematic review of the economic burden of CVD and HTN in low- and middle-income countries.[39] This study concluded that for CHD and stroke cost estimates were generally higher, with several estimates over $5000 per episode, which is nearly half of the estimate for CAD patients who were hospitalised and underwent PTCA in our study (US$ 2545). The cost estimates for ACS have been reported in Iran, which is a lower-middle-income country like India. In Iran, Sheikhgholami et al. (2021) calculated the economic costs associated with ACS. [40] They estimated the costs for medical therapy, PCI and CABG as USD1906 [US$(2023) 2115], US$4710 [US$(2023) 5225] and US$6545 [USD(2023) 7261), as compared to our study, we also found that the expenditure was lowest for medical therapy and highest for CABG. However, the cost for CABG was fairly high in our study. A review by Gregori et al. (2011) found that no specific model can address all the problems of the analysis of healthcare expenditure and concluded that the decisive model is identified based on the type and design of the study [41]. However, many studies have used different regression models to arrive at the most appropriate model. [42-43] The present study performed multiple linear regression analysis to identify the best model that can explain all the data, and the model that best fits the data was identified. The most suitable model was employed to investigate the relationship between factors associated with costs and expenditures. Regression, which performs well even in the presence of outliers, enables us to observe the relationship between the expenditure for managing CAD and the independent variables. The results from quantile regression were found to be more informative than linear and gamma regression, even in the presence of outliers. This was proved from the results of the effects of explanatory variables on different quantiles of cost data distribution and also from the fact that the RMSE and MAE were lesser for quantile regression than gamma regression. AIC criteria was used to identify the best model which ensures the goodness of fit of the regression models. The results of the quantile regression reveal that distance to the hospital and socioeconomic status have a positive effect on healthcare expenditure, which is understandable because the distance to the hospital tends to increase expenditure, as more resources are required to cover greater distances. Additionally, patients from higher socioeconomic backgrounds tend to spend more on healthcare. SES score had positive effect on the expenditure. Types of intervention and age have negative effect on the expenditure in quantile regression. Age has found to be negatively affecting the expenditure, as the age increases the expenditure decreases. This could be due to the fact that nowadays, people in younger age group have started having CAD and prefer to undergo invasive intervention like PTCA to have better clinical outcome. [44] Karan et al (2014) conducted propensity score matching to estimate the effects of co-variates on CVD expenditure and concluded that OOPE on outpatient visits, transportation and drugs were significantly higher in CVD households than controls. [13] Distance to the hospital was found to be predictor of healthcare expenditure in our study also and drugs contributed the major portion of healthcare expenditure in CAD patients receiving only medical therapy. Yadav et al (2021) studied the relationship between demographic and clinical characteristics of patients with non-communicable diseases and the catastrophic expenditure using multivariable logistic regression analysis. They found that the households seeking care in private hospitals had higher percentage CHE due to hospitalisation than public hospitals. CHE also increased with longer duration of stay. [14] Patel et al (2020) used random effects logistic model to estimate the association of explanatory variables on CVD expenditure in India. They reported that urban areas and affluent individuals were significantly associated with higher expenditure. [15] Patients with high socio-economic status (SES) score were found to have higher expenditure on healthcare. A study by Walker et al (2016), which examined healthcare utilisation and costs of patients with CAD using gamma regression, observed that being male and suffering from co-morbidities positively affect the CAD expenditure in the UK. [20] In Japan, Mukurami et al (2013) performed gamma regression and revealed that the annual medical expenditure was positively associated with CVD risk factors irrespective of a age and gender. [21] This differs from our study as we have not evaluated the effect of risk factors on the healthcare budget. The logistic (binomial and multinomial) regression by Nkemdirin et al (2023) conducted on USA cost data of CAD patients reported that demographics and clinical characteristics (co-morbidities, number of times of hospitalisation and length of stay) were significant predictors of healthcare utilisation. [22] As in our study, demographic characteristics such as socioeconomic status (SES) score and distance to the hospital positively affected healthcare expenditure. Quantile regression was performed by Lu et al. (2023) to identify key determinants of healthcare costs in patients with CVD in China. They found that the patients with high healthcare costs were male and older. [19] We also found that being male positively affects the healthcare expenditure and, conversely, age was found to have negative effects on the CAD healthcare expenditure. We compared the predictive abilities of these models using the RMSE and MAE and found that quantile regression has a lesser RMSE and MAE when compared to gamma regression. So, quantile regression was a better model than gamma regression in our study. Similarly, Mohammadpour et al (2020) found that quantile regression was better for gastric cancer. [45] Austin et al (2003) compared different regression models for analysing CABG costs and concluded that the median regression model (of which quantile regression is a type) predicted the costs well. [46] In addition to the mentioned studies, gamma regression and quantile regression have been performed on healthcare expenditures for diseases other than CVDs, such as cancer [47], arthritis [48], multimorbidity [49], and surgical site infections [50]. To our knowledge, this is the first study of its kind to estimate the total cost of treatment for CAD and analyse the relationship between independent variables and healthcare expenditure for CAD in India using regression models. The limitations of this study include the cost data on which the analysis is based, which is limited to only one private hospital. Cost data from multiple private and government hospitals across the country could provide more generalizable results for a large country such as India. The operational, administrative, and human resource costs could not be calculated due to the hospital's unavailability of data. Additionally, the prevalence method was used to collect the cost details, which could only provide us with the annual costs. As total costs of managing CAD also include the subsequent costs for adherence to medicines and laboratory tests for follow-up years, this study was conducted only to estimate the expenditure for managing CAD to help the health policy planners or decision-makers take better decisions for health policy and resource allocation. Conclusion The findings of this study indicate that a cost analysis for CAD could be instrumental in planning and distributing healthcare resources in a resource-constrained country like India. The direct costs contributed significantly to the total costs as compared to the indirect costs. Among direct costs, intervention costs dominated other costs in patients who underwent invasive intervention. For patients who received only medical therapy, the highest costs were associated with the cost of medications. Statistically analysing the disease cost can be a potential economic asset for decision-makers to evaluate the economic burden of CAD in India. Abbreviations CAD Coronary artery disease MT Medical therapy CAG Coronary angiography PTCA Percutaneous transluminal coronary angioplasty CABG Coronary artery bypass graft Declarations Clinical trial registration: Not applicable Funding: No funding was sought for this research. Author contributions: SA and ST conceptualised the topic. SD, VS and SA collected the data. DJ and SA did the data analysis. SA developed the first draft with support from DJ. All authors reviewed and edited the draft. All authors agreed before the submission of the final manuscript. Conflicts of interest: The authors declare no conflict of interest. Data availability statement : Dataset is available at doi: 10.6084/m9.figshare.28173890 Ethical Approval : The study protocol has been approved by the Institutional Ethics Committee of Delhi Pharmaceutical Sciences and Research University (DPSRU-BREC/2022/A/041) and the National Heart Institute (3/9/002/EC/2023). Patients were given an informed consent form, and consent was obtained before data collection. Consent to participate: Written informed consent was obtained from all participants before data collection (Supplementary File 1) Consent to publish: Not applicable Acknowledgements: The authors thank Dr Vivek Verma, Department of Statistics, Assam University, Silchar, Assam-788011, India, for supporting the data analysis. References Mensah G, Fuster V, Murray CJL, et al. Global Burden of Cardiovascular Diseases and Risks, 1990–2022. J Am Coll Cardiol. 2023;82(25):2350–473. Kumar AS, Sinha N. Cardiovascular disease in India: A 360 degree overview. Med J Armed Forces India. 2020;76(1):1–3. Jo C. Cost-of-illness studies: concepts, scopes, and methods. Clin Mol Hepatol. 2014;20(4):327–37. https//doi/10.3350/cmh.2014.20.4.327 . Allarakha S, Yadav J, Yadav AK. Financial Burden and financing strategies for treating the cardiovascular diseases in India. 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[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] Coronary artery disease (CAD) is a condition when the heart does not get sufficient blood and oxygen due to obstruction in the coronary arteries. [\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e] In 2022, globally, CAD affected 300 people, with a prevalence and mortality rate of 3610.2 and 108.8 per 1,00,000 population, respectively. [\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e] In 2016, CAD was the most prevalent type of cardiovascular disease, with a prevalence of 11% in India, contributing to a high economic burden. [\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/p\u003e\u003cp\u003eRecent evidence has suggested that CVDs are implicated in poverty due to cataclysmic health spending and mounting out-of-pocket expenditure (OOPE). (4\u0026ndash;6) CVDs are responsible for the increased financial burden on the household budget and, ultimately, the national economy. Cost of Illness (COI) study provides evidence of the economic burden of disease on a country\u0026rsquo;s economy and offers insights to decision-makers to utilise the limited resources efficiently. COI is defined as the value of the resources that are expended or forgone due to a health problem, and includes health sector costs (direct costs), the value of decreased or lost productivity by the patient (indirect costs), and the cost of pain and suffering (intangible costs). [\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/p\u003e\u003cp\u003eIn India, COI studies have been conducted for CVDs [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e], but not specifically for CAD. Previous studies have estimated the overall healthcare costs and OOPE for CVDs [\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]. However, the use of regression models has been limited. Propensity Score matching [\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e] and logistic regression [\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e] methods have been widely used to estimate the effect of predictors on healthcare expenditures. Studies conducted in settings other than India have used different regression models to ascertain the relationship between expenditure on CVDs and covariates. Studies published from Finland, the United Kingdom and New Zealand used machine learning prediction models to conduct the regression analysis. [\u003cspan additionalcitationids=\"CR17\" citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]. Lu et al (2023) used quantile regression to estimate the effect of independent variables on the expenditure of CVD for China. [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e] Other generalised linear models were used in different countries, such as gamma regression in England and Japan [\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e, \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e] and logistic regression in the USA [\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/p\u003e\u003cp\u003eIn health economics, estimating the population mean costs is widely accepted as a statistic of interest to policymakers. [\u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e23\u003c/span\u003e] The non-negative nature of healthcare costs data most often exhibits substantial positive skewness, with heavy tails and is often multimodal. Estimating the mean cost and establishing a relationship between the costs and the predictor variables are the main challenges in developing regression models in healthcare. [\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e] As mentioned above, in healthcare systems, various statistical models are commonly used in predicting expenditure based on explanatory variables. Generalised Linear Models (GLMs) are regression models used to identify relationships between a dependent variable and predictor variables, including linear, logistic, Poisson, and exponential relationships. GLMs enable us to perform regression for non-normal distributions of the dependent variable. [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e] The application of these models shows that they are robust to the placement of covariates and random effects. [\u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e] Gamma regression is a type of GLM that is commonly used for analysing health expenditure for patients incurring costs greater than zero. Gamma regression models are flexible and do not require data transformation or removal of outliers to accommodate many outcome distribution shapes. [\u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e27\u003c/span\u003e, \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e] Similar to gamma regression, quantile regression also works well in the presence of outliers and non-normal data. Quantile regression predicts the effect of a change in the defined quantile of the dependent variable with a change in the unit of the independent variable. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e] This approach has been found to be superior to linear regression and provides an inclusive presentation of factors that affect health expenditure. [\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e]\u003c/p\u003e\u003cp\u003eThe current study aimed to apply more commonly used linear, gamma and quantile regression models in medical literature for analysing cost data in a cohort of patients receiving treatment for CAD to assess the consistency of findings regarding the significance of the clinical variables. It was hypothesised that the different models would result in different conclusions about the impact of demographic and clinical factors on the cost of treatment. The different models would have different abilities to correctly predict patient costs for CAD treatment in tertiary care healthcare facilities in India, and similar geographical settings.\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003eThis study was based on a cross-sectional survey conducted at a cardiac-specific tertiary care hospital in New Delhi from May-October 2023.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eSample Size Calculation\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eThe sample size was calculated based on the estimated average costs, regardless of age and comorbidity. A previous study [10] shows that the standard deviation of average costs is approximately $ 2,400, and the average cost is $979. Expecting a precision of 20% on either side and estimating the average cost with a 95% confidence level, the sample size calculated was 555 subjects. Therefore, a total of 560 samples were taken for the study.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eN=\u003cu\u003e(Z\u003csub\u003e1-\u0026alpha;/2)\u003c/sub\u003e\u003csup\u003e2 *\u0026nbsp;\u003c/sup\u003e(SD)\u003csup\u003e2\u003c/sup\u003e\u003c/u\u003e\u003c/p\u003e\n\u003cp\u003eE\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003eN=(\u003cu\u003e1.96)\u003csup\u003e2\u003c/sup\u003e* (2400)\u003csup\u003e2\u003c/sup\u003e\u003c/u\u003e\u003c/p\u003e\n\u003cp\u003e(200)\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e\n\u003cp\u003e553\u0026cong;555\u003c/p\u003e\n\u003cp\u003eZ=Z score at 95% confidence interval, value=1.96\u003c/p\u003e\n\u003cp\u003eSD= Standard deviation from Gupta et al. (2020)\u003c/p\u003e\n\u003cp\u003eE=Margin of error (calculated as E=mean x precision, E=979*0.2=195.8\u0026cong;200)\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eEligibility criteria\u0026nbsp;\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003ePatients were directly recruited during their visits for regular check-ups in the hospital\u0026apos;s cardiac OPD. Written informed consent was obtained prior to starting any interview with the patient. The template of informed consent, as per guidelines by ICMR, has been included in the supplementary material (Supplementary 1). Patients above 18 years of age, both genders, visiting the hospital, and suffering from coronary artery diseases were included in the data collection. Patients having diseases other than coronary artery diseases like rheumatic heart disease, heart failure, congenital heart diseases, etc., patients not continuing the treatment at the hospital, and patients who were unwilling to participate in the study were excluded.\u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eData Collection\u0026nbsp;\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eTwo experts (ST \u0026amp; AK) designed the case record form (CRF) and two cardiologists (SD and VS) validated it (Supplementary 1). Firstly, the CRF was used to collect data from 20 patients in May 2023 and the collected data was checked for its adherence with the objectives. Changes suggested at this step were incorporated in the final CRF. The final CRF was used to collect information on socio-demographic characteristics, medical history, and treatment costs. Patients were selected using convenience sample and the information collected from May-October 2023. \u0026nbsp;\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eCost calculation\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eParticipants were inquired if they received either medical therapy (MT) or any invasive procedure for CAD in the previous 12 months. The patients were divided into four groups, namely, only MT, MT+CAG (Coronary angiography), MT+ PTCA (Percutaneous Transluminal Coronary Angioplasty) and MT+CABG (Coronary Artery Bypass Graft). \u0026nbsp;Participants were asked if they had received either an outpatient (OP) or inpatient (IP) hospitalisation treatment (invasive procedure) for CAD in the previous 12 months. If affirmative for only MT, participants were asked to report the number of visits and medical expenditures for each category: medications, consultation fees, and laboratory or radiological tests. If the participant was hospitalised for any procedure, then the information about the procedure, length of hospital stay, and hospital costs was obtained from the hospital medical records. Data on direct non-medical expenditures, including expenses on travel to and from the clinic/hospital, whereas indirect costs included the time duration the patient spent at the hospital, and the number of days the patient was hospitalised. The cost of illness was calculated by considering both direct and indirect costs. Direct medical costs included the costs of medications, laboratory tests, consultations, procedures, and hospitalisation costs. Direct non-medical costs included travel costs, and indirect costs were productivity losses by the patient. The final cost data were converted into USD 2023 using the conversion rate of 1 US$ = 83.1164 INR [30].\u003c/p\u003e\n\u003cp\u003eThe costs of medicines for CAD patients were identified from the CIMS (Current Index of Medical Specialities) website for branded drugs and the Jan Aushadhi website for \u0026nbsp;generic drugs. For the patients who underwent any invasive intervention at the hospital, the total costs for their treatment, length of stay, laboratory costs, and consultation costs were obtained from their medical records and corroborated with payment receipts. The distance between the patient\u0026apos;s point of origin and the hospital was calculated using the address present in the medical records. The average travel cost was used to calculate INR 30 (US$ 0.4) for 1.5 km and INR 11 (US$ 0.1) per kilometer[1]. The cost was calculated for the patient\u0026apos;s arrival and departure from the hospital. The number of visits done in one year multiplied by the travel cost per visit. Regarding the CAD patients on medical therapy, those who need to visit the OPD for regular check-ups were asked how many hours they spend at the hospital during each visit. If the number of hours was \u0026lt;4, it was considered a half-day loss of productivity; if the patients reported spending \u0026gt; 4 hours on every visit, it was considered a full-day loss of productivity. The number of days lost due to hospital visits or hospital stays was multiplied by INR 176 (minimum wage per day) in India (US$ 2). The minimum wage was 176 Indian rupees, as reported by the Ministry of Labour in the wage floor index. [31]\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u003cem\u003eIndependent variables\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSocio-economic status was calculated using the Kuppuswamy scale [33], presented in the Supplementary material (Supplementary 3). This scale is based on a cumulative score-based on education, occupation, and income variables. Based on this scale, patients were classified into five socio-economic status categories: Upper (I), Upper Middle (II), Lower Middle (III), Lower (IV), and Very Lower (V). However, socioeconomic status (SES) was taken as a continuous variable for the analysis, using the Kuppuswamy score as the SES score. Other variables included age, gender, distance to hospital, and type of intervention undergone by the CAD patients\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eStatistical Analysis\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eThe descriptive statistics were used to calculate the measure of central tendency and measures of dispersion (Mean, median, Standard deviation and interquartile range) using MS Excel. \u0026nbsp;Appropriate statistical tests were used to measure the significance level between the mean values. \u0026nbsp;The costs were presented as mean, standard deviation, median and interquartile range (IQR) values. The socioeconomic class was calculated based on the Kuppuswamy scale [32].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eFirst, simple linear regression was used to identify the factors associated with annual cost. The dependent variable was the total expenditure. The explanatory variables, which could explain the dependent variable, were identified as age, gender, distance to the hospital, socioeconomic status score, and type of intervention the CAD patients underwent. Then, a multiple regression analysis was performed to determine the factors affecting the total expenditure, and adjusted coefficients with a 95% confidence interval (CI) were calculated. The best-fit model was identified using multiple regression.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eNext, gamma regression models were conducted to estimate the healthcare expenditure associated with explanatory variables and the model with the lowest AIC (Akaike information criterion) score was considered. In most conditions, the gamma regression model effectively estimates population means of healthcare costs. [34] The generalised linear model with log link and gamma distribution was found be appropriate, and age, gender, distance to hospital, SES score and type of intervention were the independent variables. Age, distance to hospital and SES score were taken as continuous variables and gender and type of intervention were taken as categorical variable.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eQuantile regression for expenditure was performed at intervals of 50\u003csup\u003eth\u003c/sup\u003e, 75\u003csup\u003eth\u003c/sup\u003e, 90\u003csup\u003eth\u0026nbsp;\u003c/sup\u003eand 95\u003csup\u003eth\u003c/sup\u003e percentile, and the coefficients (95% CI) were checked for positive or negative impact of expenditure [30].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe ability to predict costs was assessed using root mean squared (RMSE) and mean absolute errors (MAE) were calculated for all the regression models used to identify a better model. The errors for quantile regression were calculated for 50th percentile (by default quantile regression is a median regression) [34].\u003c/p\u003e\n\u003cp\u003eR software v4.4.2 (R Foundation for Statistical Computing, Vienna, Austria) was used to analyse the data, and a p-value of \u0026lt;0.05 was considered statistically significant. All costs were converted into US$ per 2023 values (1 INR= 83.1164 US$) based on December 29, 2023)[2].\u003c/p\u003e\n\u003ch2\u003e\u003cem\u003eEthical Approval\u0026nbsp;\u003c/em\u003e\u003c/h2\u003e\n\u003cp\u003eThe study protocol has been approved by the Institutional Ethics Committee of Delhi Pharmaceutical Sciences and Research University (DPSRU-BREC/2022/A/041) and the National Heart Institute (3/9/002/EC/2023). Patients were administered with informed consent form and consent was obtained prior to data collection. \u0026nbsp;\u0026nbsp;\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eThe mean age (SD) of the 555 respondents was 62 (± 10.50) years, with two-thirds of the respondents being males (Table 1). About 85% of the participants were married and 61% were retired. More than half (67%) of the participants belonged to upper middle class, followed by lower middle (17.3%) and upper (14.1%) classes. Of the participants, 32.5% underwent only medical therapy, and the remaining 67.5% either PCI or CABG in addition to MT in the last year. \u0026nbsp;(Table 1) The distribution of cost data was positively skewed, with a small minority of patients having very high costs (Figure 1).\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe median (IQR) annual illness cost for patients who only took medical therapy was [US$ 220(US$166-US$290)] (Table 2). For patients who underwent coronary angiography and received medical therapy, the median (IQR) cost of illness was estimated to be US$ 445 (US$380-US$500) per year. For patients who underwent percutaneous intervention or CABG in conjunction with medical therapy in the previous year, the median cost of illness was calculated to be US$ 2,420 (US$ 2,334-US$ 2,741) and US$ 3,323 (US$ 3,246-US$ 3,782), respectively. For patients on MT, almost half (48.5%) of the cost of illness was attributed to medications. In the case of invasive interventions, the cost of interventions dominated the cost of illness. \u0026nbsp;The median (IQR) annual direct costs for only medical therapy were US$ 214(US$156-US$279). For patients on medical therapy and an invasive intervention, the median direct costs were US$ 430(US$370-US$487) for CAG, US$ 2409(US$2323-US$2729) for PTCA and US$ 3297(US$3219-US$3756) for CABG. The highest indirect costs (US$ 25(US$22-US$29)] were observed for CAD patients undergoing CABG, and the lowest for only MT [US$ 7(US$5-US$11)]. (Table 2) Most of the costs were statistically insignificant (p\u0026gt;0.05). The mean cost of treating CAD without procedures and with CAG in lower middle socio-economic status was statistically significant compared to the upper middle group with p values of 0.02 and 0.04, respectively. Similarly, the mean cost of CAG was reported to be statistically significant when compared between males and females (p=0.01). (Table 3) \u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe \u003cem\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e value for the linear regression was 95.53% indicating the variation in the outcome variable expenditure explained by the predictors. The adjusted \u003cem\u003eR\u003csup\u003e2\u003c/sup\u003e\u003c/em\u003e is almost equal to the multiple R-square, thus highlighting that the model has good cross-validity. The effect of the type of intervention was found to be statistically significant. The coefficient for age was -58.41, gender 4359.18, distance 136.48, and SES score -23.85, with the intercept at 300776.13. Gender and distance to the hospital had a statistically significant impact on the expenditure for managing CAD, with p values of 0.0389 and 0.0169, respectively. (Table 4)\u003c/p\u003e\n\u003cp\u003eGamma regression with the logarithmic function was identified as the appropriate model because it had the lowest AIC. \u0026nbsp;Gamma regression found that only the type of intervention significantly affected the expenditure for managing CAD. CABG intervention was taken as a baseline, and the β coefficients (p-value) for CAG, MT and PTCA were found to be -2.1064305(\u0026lt;0.01), -2.7330792 (\u0026lt;0.01) and -0.3644606 (\u0026lt;0.01). The patient's age (β = -0.0014330) and gender (β =0.0248592) had negative and positive effects, respectively, but were not statistically significant. The constants obtained in the model were associated with a significant level of significance. (Table 5)\u003c/p\u003e\n\u003cp\u003eWe performed quantile regression to estimate the effect size of explanatory variables on different percentiles of expenditure, and the results show that as the distribution quantile of the dependent variable (cost) increased, the beta coefficient also surged from 27,041 to 4,63,000. The magnitude of the estimated coefficient was due to the skewness of the dependent variable. (Table 6). In all percentiles (50%, 75%, 90% and 95%) of the cost distribution, the male patients positively affected the expenditure. Age showed a negative association with expenditure in all quantiles of data distribution. Results of the estimation of coefficients showed that the distance to the hospital had a positive effect on expenditure in all quantiles except on the highest (95\u003csup\u003eth\u003c/sup\u003e quantile). SES score varied expenditure across different quantiles (positive on 50\u003csup\u003eth\u003c/sup\u003e quantile and negative on 75\u003csup\u003eth\u003c/sup\u003e, 90\u003csup\u003eth\u003c/sup\u003e, 95\u003csup\u003eth\u003c/sup\u003e quantile). When patients undergoing CABG was taken as baseline, all the interventions had a negative effect on the expenditure for managing CAD across all the quantiles.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA comparison of the multiple linear regression, gamma regression and quantile and regression was conducted. Multiple regression model was found have the lowest RMSE (21489.32) and MAE (13816.55) as compared to other two models. However, when comparing quantile regression and gamma regression, quantile regression was found to have lesser RMSE (151437.7) and MAE (112213.1) than gamma regression. (Table 7). For the models that predicted median cost, a median regression line was superimposed on the plot [36]. These plots are depicted in Figure 2 \u0026amp; 3. The models that predicted mean costs tended to fit the data well. Linear regression and gamma regression model predicted median costs well.\u0026nbsp;\u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study estimated the direct and indirect costs of managing CAD in an Indian tertiary care center and determine the relationship between these costs and independent variables using multiple linear regression, gamma regression, and quantile regression methods and compared the results of these models.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThis study found that a significant part (50%) of the costs incurred by the patients for managing CADs through medical therapy pertained to the costs of medications which is similar to another study, which concluded that the cost of drugs accounts for the principal proportion (39%) of economic burden on patients [36]. Karan et al (2010) in a discussion paper published by the World Bank state that the expenses per OPD visit to a private hospital for any heart disease were INR 485 (US$ 6) [37]. The results from the study by Chauhan et al (2012) conducted in North India, estimated the costs incurred by patients who got treated in outpatient department sessions as INR 48578 (US$ 584) for two years, which is comparable to our study where annual cost was estimated to be US$ 246 per patient [36]. Huffman et al (2011) calculated the mean out-of-pocket expenditure for heart diseases for over 15 months as Int$2,917 (US$ 35) in India [38].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eGheorghe et al (2018) conducted a systematic review of the economic burden of CVD and HTN in low- and middle-income countries.[39] This study concluded that for CHD and stroke cost estimates were generally higher, with several estimates over $5000 per episode, which is nearly half of the estimate for CAD patients who were hospitalised and underwent PTCA in our study (US$ 2545). The cost estimates for ACS have been reported in Iran, which is a lower-middle-income country like India. In Iran, Sheikhgholami et al. (2021) calculated the economic costs associated with ACS. [40] They estimated the costs for medical therapy, PCI and CABG as USD1906 [US$(2023) 2115], US$4710 [US$(2023) 5225] and US$6545 [USD(2023) 7261), as compared to our study, we also found that the expenditure was lowest for medical therapy and highest for CABG. However, the cost for CABG was fairly high in our study.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA review by Gregori et al. (2011) found that no specific model can address all the problems of the analysis of healthcare expenditure and concluded that the decisive model is identified based on the type and design of the study [41]. However, many studies have used different regression models to arrive at the most appropriate model. [42-43] The present study performed multiple linear regression analysis to identify the best model that can explain all the data, and the model that best fits the data was identified. The most suitable model was employed to investigate the relationship between factors associated with costs and expenditures. Regression, which performs well even in the presence of outliers, enables us to observe the relationship between the expenditure for managing CAD and the independent variables. The results from quantile regression were found to be more informative than linear and gamma regression, even in the presence of outliers. This was proved from the results of the effects of explanatory variables on different quantiles of cost data distribution and also from the fact that the RMSE and MAE were lesser for quantile regression than gamma regression. AIC criteria was used to identify the best model which ensures the goodness of fit of the regression models.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eThe results of the quantile regression reveal that distance to the hospital and socioeconomic status have a positive effect on healthcare expenditure, which is understandable because the distance to the hospital tends to increase expenditure, as more resources are required to cover greater distances. Additionally, patients from higher socioeconomic backgrounds tend to spend more on healthcare. SES score had positive effect on the expenditure. Types of intervention and age have negative effect on the expenditure in quantile regression. Age has found to be negatively affecting the expenditure, as the age increases the expenditure decreases. This could be due to the fact that nowadays, people in younger age group have started having CAD and prefer to undergo invasive intervention like PTCA to have better clinical outcome. [44]\u003c/p\u003e\n\u003cp\u003eKaran et al (2014) conducted propensity score matching to estimate the effects of co-variates on CVD expenditure and concluded that OOPE on outpatient visits, transportation and drugs were significantly higher in CVD households than controls. [13] Distance to the hospital was found to be predictor of healthcare expenditure in our study also and drugs contributed the major portion of healthcare expenditure in CAD patients receiving only medical therapy. Yadav et al (2021) studied the relationship between demographic and clinical characteristics of patients with non-communicable diseases and the catastrophic expenditure using multivariable logistic regression analysis. They found that the households seeking care in private hospitals had higher percentage CHE due to hospitalisation than public hospitals. CHE also increased with longer duration of stay. [14] Patel et al (2020) used random effects logistic model to estimate the association of explanatory variables on CVD expenditure in India. They reported that urban areas and affluent individuals were significantly associated with higher expenditure. [15] Patients with high socio-economic status (SES) score were found to have higher expenditure on healthcare.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eA study by Walker et al (2016), which examined healthcare utilisation and costs of patients with CAD using gamma regression, observed that being male and suffering from co-morbidities positively affect the CAD expenditure in the UK. [20] In Japan, Mukurami et al (2013) performed gamma regression and revealed that the annual medical expenditure was positively associated with CVD risk factors irrespective of \u0026nbsp;a age and gender. [21] This differs from our study as we have not evaluated the effect of risk factors on the healthcare budget. The logistic (binomial and multinomial) regression by Nkemdirin et al (2023) conducted on USA cost data of CAD patients reported that demographics and clinical characteristics (co-morbidities, number of times of hospitalisation and length of stay) were significant predictors of healthcare utilisation. [22] As in our study, demographic characteristics such as socioeconomic status (SES) score and distance to the hospital positively affected healthcare expenditure. Quantile regression was performed by Lu et al. (2023) to identify key determinants of healthcare costs in patients with CVD in China. They found that the patients with high healthcare costs were male and older. [19] We also found that being male positively affects the healthcare expenditure and, conversely, age was found to have negative effects on the CAD healthcare expenditure.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eWe compared the predictive abilities of these models using the RMSE and MAE and found that quantile regression has a lesser RMSE and MAE when compared to gamma regression. So, quantile regression was a better model than gamma regression in our study. Similarly, Mohammadpour et al (2020) found that quantile regression was better for gastric cancer. [45] Austin et al (2003) compared different regression models for analysing CABG costs and concluded that the median regression model (of which quantile regression is a type) predicted the costs well. [46] In addition to the mentioned studies, gamma regression and quantile regression have been performed on healthcare expenditures for diseases other than CVDs, such as cancer [47], arthritis [48], multimorbidity [49], and surgical site infections [50].\u0026nbsp;\u003c/p\u003e\n\u003cp\u003eTo our knowledge, this is the first study of its kind to estimate the total cost of treatment for CAD and analyse the relationship between independent variables and healthcare expenditure for CAD in India using regression models. The limitations of this study include the cost data on which the analysis is based, which is limited to only one private hospital. Cost data from multiple private and government hospitals across the country could provide more generalizable results for a large country such as India. The operational, administrative, and human resource costs could not be calculated due to the hospital's unavailability of data. Additionally, the prevalence method was used to collect the cost details, which could only provide us with the annual costs. As total costs of managing CAD also include the subsequent costs for adherence to medicines and laboratory tests for follow-up years, this study was conducted only to estimate the expenditure for managing CAD to help the health policy planners or decision-makers take better decisions for health policy and resource allocation.\u0026nbsp;\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe findings of this study indicate that a cost analysis for CAD could be instrumental in planning and distributing healthcare resources in a resource-constrained country like India. The direct costs contributed significantly to the total costs as compared to the indirect costs. Among direct costs, intervention costs dominated other costs in patients who underwent invasive intervention. For patients who received only medical therapy, the highest costs were associated with the cost of medications. Statistically analysing the disease cost can be a potential economic asset for decision-makers to evaluate the economic burden of CAD in India.\u0026nbsp;\u003c/p\u003e"},{"header":"Abbreviations","content":"\u003cdiv class=\"DefinitionList\"\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cb\u003eCAD\u003c/b\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003e\u003cb\u003eCoronary artery disease\u003c/b\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cb\u003eMT\u003c/b\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003e\u003cb\u003eMedical therapy\u003c/b\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cb\u003eCAG\u003c/b\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003e\u003cb\u003eCoronary angiography\u003c/b\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cb\u003ePTCA\u003c/b\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003e\u003cb\u003ePercutaneous transluminal coronary angioplasty\u003c/b\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003cdiv class=\"DefinitionListEntry\"\u003e\u003cdiv class=\"Term\"\u003e\u003cb\u003eCABG\u003c/b\u003e\u003c/div\u003e\u003cdiv class=\"Description\"\u003e\u003cp\u003e\u003cb\u003eCoronary artery bypass graft\u003c/b\u003e\u003c/p\u003e\u003c/div\u003e\u003c/div\u003e\u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eClinical trial registration:\u0026nbsp;\u003c/strong\u003eNot applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding:\u0026nbsp;\u003c/strong\u003eNo funding was sought for this research.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions:\u0026nbsp;\u003c/strong\u003eSA and ST conceptualised the topic. SD, VS and SA collected the data. DJ and SA did the data analysis. SA developed the first draft with support from DJ. All authors reviewed and edited the draft. All authors agreed before the submission of the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConflicts of interest:\u0026nbsp;\u003c/strong\u003eThe authors declare no conflict of interest.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability statement\u003c/strong\u003e: Dataset is available at doi:\u0026nbsp;10.6084/m9.figshare.28173890\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthical Approval\u003c/strong\u003e\u003cem\u003e\u003cstrong\u003e:\u003c/strong\u003e\u0026nbsp;\u003c/em\u003eThe study protocol has been approved by the Institutional Ethics Committee of Delhi Pharmaceutical Sciences and Research University (DPSRU-BREC/2022/A/041) and the National Heart Institute (3/9/002/EC/2023). Patients were given an informed consent form, and consent was obtained before data collection.\u0026nbsp;\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to participate:\u003c/strong\u003e Written informed consent was obtained from all participants before data collection (Supplementary File 1)\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConsent to publish:\u003c/strong\u003e Not applicable\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgements:\u0026nbsp;\u003c/strong\u003eThe authors thank Dr Vivek Verma, Department of Statistics, Assam University, Silchar, Assam-788011, India, for supporting the data analysis.\u0026nbsp;\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eMensah G, Fuster V, Murray CJL, et al. Global Burden of Cardiovascular Diseases and Risks, 1990\u0026ndash;2022. J Am Coll Cardiol. 2023;82(25):2350\u0026ndash;473.\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003eKumar AS, Sinha N. 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Ann Surg. 2017;265(2):331\u0026ndash;9. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1097/SLA.0000000000001590\u003c/span\u003e\u003cspan address=\"10.1097/SLA.0000000000001590\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"},{"header":"Tables","content":"\u003cp\u003eTables are available in the Supplementary Files section.\u003c/p\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":false,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"discover-public-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Public Health](https://link.springer.com/journal/12982)","snPcode":"12982","submissionUrl":"https://submission.springernature.com/new-submission/12982/3","title":"Discover Public Health","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true},"keywords":"Cost analysis, coronary artery diseases, health expenditure, regression","lastPublishedDoi":"10.21203/rs.3.rs-7890011/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7890011/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003ch2\u003eIntroduction\u003c/h2\u003e\u003cp\u003e: There is no uniformly agreed regression model for analysing cost data. The objective of the current study was to compare the performance of linear regression, gamma regression, and quantile regression and predict a better model using costs among patients with coronary artery disease (CAD).\u003c/p\u003e\u003ch2\u003eMethods\u003c/h2\u003e\u003cp\u003eA cross-sectional survey was conducted on CAD patients at a tertiary care hospital in New Delhi between May and October 2023. Descriptive statistics for direct and indirect costs were estimated, and their association with demographic and clinical variables was explored using linear, gamma and quantile regression along with prediction errors.\u003c/p\u003e\u003ch2\u003eResults\u003c/h2\u003e\u003cp\u003e560 CAD patients were interviewed (mean age 62\u0026thinsp;\u0026plusmn;\u0026thinsp;10.50years). 182 patients were found to be on medical therapy only, and 378 patients underwent any procedure along with medical treatment. The highest and lowest costs were observed for patients who underwent coronary artery bypass graft (US\u003cspan\u003e$\u003c/span\u003e3323/per patient) and received only medical therapy (US\u003cspan\u003e$\u003c/span\u003e220/per patient). According to linear regression, gender, distance to the hospital and type of intervention significantly affected the expenditure. In gamma regression, only the type of intervention was statistically significant. In quantile regression, being male, living away from the hospital and having a high SES score positively affected the expenditure. Quantile regression was found to have fewer prediction errors.\u003c/p\u003e\u003ch2\u003eConclusion\u003c/h2\u003e\u003cp\u003eEstablishing an appropriate statistical model is fundamental for predicting the costs, which could be affected by several factors, and the final choice of the regression model should be made after careful assessment of predictive ability and tailored to specific data.\u003c/p\u003e","manuscriptTitle":"Factors associated with treatment costs in patients with coronary artery disease in India: Comparison of linear regression, gamma regression and quantile regression methods","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-11-21 01:06:32","doi":"10.21203/rs.3.rs-7890011/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-01-02T15:47:41+00:00","index":"","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-12-24T04:15:10+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-18T16:49:35+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-15T16:30:06+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"119468900574555721056330209918570881121","date":"2025-11-15T16:23:32+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"144821173939748861398968022369557838493","date":"2025-11-13T03:40:53+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"339197932274036299279255951884886076614","date":"2025-11-12T16:52:06+00:00","index":"hide","fulltext":""},{"type":"editorInvitedReview","content":"","date":"2025-11-11T21:29:23+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"240682285551747263439341858977132148959","date":"2025-11-11T21:02:56+00:00","index":"hide","fulltext":""},{"type":"reviewerAgreed","content":"332870148926388781933998084423050020371","date":"2025-11-11T05:45:16+00:00","index":"hide","fulltext":""},{"type":"reviewersInvited","content":"","date":"2025-11-10T15:03:43+00:00","index":"","fulltext":""},{"type":"editorInvited","content":"","date":"2025-10-23T14:42:01+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2025-10-21T13:25:54+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2025-10-21T13:24:07+00:00","index":"","fulltext":""},{"type":"submitted","content":"Discover Public Health","date":"2025-10-17T23:35:15+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"discover-public-health","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"","sideBox":"Learn more about [Discover Public Health](https://link.springer.com/journal/12982)","snPcode":"12982","submissionUrl":"https://submission.springernature.com/new-submission/12982/3","title":"Discover Public Health","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"stoa","reportingPortfolio":"Discover Series","inReviewEnabled":true,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"21d38253-42d2-49d5-b0ad-9eb9cb302149","owner":[],"postedDate":"November 21st, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-03-20T18:09:01+00:00","versionOfRecord":[],"versionCreatedAt":"2025-11-21 01:06:32","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7890011","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7890011","identity":"rs-7890011","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}