Accounting for past patient composition in evaluations of quality reporting

Objective To investigate whether accounting for past patient composition in evaluations of the association between public quality reports and patient selectivity changes findings and conclusions. Data Sources Secondary data analysis of public reports of Assisted Reproductive Technology Clinic success rates between 2011 and 2018. Study Design Two sets of fixed effects models, (1) a standard fixed‐effects model (FE) and (2) a dynamic panel model using structural equation modeling estimated with maximum‐likelihood (ML‐SEM) with one‐ and two‐year lagged patient characteristics, are compared. The outcome variables are patient composition features associated with success rates, including two age categories and eight diagnoses of infertility. Two‐year lagged success rates for any live birth and a singleton live birth are central predictor variables. Data Collection/Extraction Methods Clinics with complete records for the 2011–2018 period were included (N = 303). Principal Findings For live birth success rates, the two models show increases in the two‐year lagged success rate is associated with a reduction in (1) the transformed percentage of patients with endometriosis (FE: β = −0.006, SE = 0.002, p < 0.01; ML‐SEM: β = −0.005, SE = 0.002, p < 0.01) and (2) the percentage of patients with tubal diagnoses (FE: β = −0.090, SE = 0.017, p < 0.001; ML‐SEM: β = −0.064, SE = 0.027, p < 0.05). For singleton birth success rates, the models show positive associations between the two‐year lagged success rate and the percent of patients over 35 years old (FE: β = 0.219, SE = 0.033, p < 0.001; ML‐SEM: β = 0.095, SE = 0.047, p < 0.05). Overall, the FE models show numerous significant associations with the two‐year lagged success rate not observed in the ML‐SEM models. Thus, the preferred and theoretically appropriate model (ML‐SEM) and the more commonly used model (FE) yield different results.

Researchers and policymakers should use models that account for past patient composition when evaluating the associations between quality reports and patient selectivity.

ART, dynamic panel modeling, patient selection, quality reporting What is known on this topic Public quality reporting is a common regulatory and incentivization tool in the United States. Key concerns about public quality reporting include the possibility of changes in patient composition due to increased consumer choice and/or provider behavior. Evidence of this kind of patient selection via the provider or patient mechanisms is mixed and often does not address how past patient composition may influence these associations. What this study adds The comparison of two fixed‐effects approaches, one that accounts for past patient composition and one that does not, demonstrates the importance of addressing past patient composition when investigating the association between past quality reports and current patient composition. The paper employs a dynamic panel model using structural equation modeling estimated with the maximum likelihood that can be used to account for associations between lagged quality report metrics and patient composition changes while also accounting for previous patient composition. 1. INTRODUCTION Quality reporting is an increasingly common mechanism used for regulation and incentivization in the US health care system. Often, these reports are made publicly available with the aim of helping consumers make informed choices about their health care. Whether such metrics influence consumer behavior is somewhat unclear, 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 but some research has found public reporting is associated with quality improvement work by health care providers and a reduction in health care costs. 10 , 11 , 12 , 13 , 14 , 15 Nevertheless, concerns about the effects of public reporting have been the focus of numerous scholars. 3 , 16 , 17 , 18 , 19 , 20 , 21 , 22 Of particular concern is the possibility that quality reporting may result in a differential treatment of patients, which has been termed “gaming” or “cherry‐picking.” 17 , 18 , 23 , 24 , 25 , 26 Evidence of this type of differential patient selection is varied with some finding evidence of such behavior 16 , 23 , 27 , 28 , 29 and others finding minimal effects. 30 , 31 One issue with typical analytic approaches used for research on this topic, such as difference‐in‐difference methodologies and general use of fixed‐effects (FE), is the possibility that both past quality reports and current patient composition are influenced by past patient composition. While quality reports may be risk‐adjusted, the sufficiency of such adjustments are debated, 19 , 24 , 32 , 33 , 34 , 35 and more importantly, these approaches do not specifically address the correlation between past patient composition and current patient composition. Thus, in these types of approaches, the relationship between past quality reports and patient composition may simply be a correlation related to the characteristics of the patients served previously and not an effect of quality reporting. Despite this potential issue, these approaches are commonly used. 1.1. Lagged‐dependent variable approaches A straightforward way to address this analytical issue is by including lagged dependent variables (in this case, patient composition variables) into statistical modeling. However, incorporating lagged dependent variables characteristics into fixed‐effects models is problematic because of endogeneity between the error term and lagged‐dependent variables. 36 , 37 , 38 Specifically, fixed‐effects models with a lagged independent variable is estimated with the general Equation (1): | (1) | In the present scenario, the dependent variable is current patient composition and the key predictor variable is a lagged quality indicator , is the unobserved time‐invariant clinic effect, and is the time‐variant error term. Introducing a lagged patient composition variable (y it−1), as we suggest above, violates the strict exogeneity assumption of fixed‐effects models when carrying out the necessary transformation to address . While it is clear that the coefficient of y it−1 will be biased due to this violation, others have shown that if T is small, the other coefficients, including on , will also be biased downward or toward zero as the covariance estimator becomes itself inconsistent. 38 , 39 Given this known limitation, alternatives have been developed. A common approach is the Arellano‐Bond method, which uses lagged instrumental variables and the Generalized Method of Moments estimator. 37 The Arellano‐Bond approach allows for lagged dependent variables and maintains the benefits of a fixed‐effects approach. However, a recently developed approach—a dynamic cross‐lagged panel model using structural equation models estimated with maximum‐likelihood (ML‐SEM)—also meets the needs of such an analysis and has advantages over the Arellano‐Bond approach. The ML‐SEM model was proposed in a series of works by Allison, Williams, and Moral‐Benito. 36 , 40 , 41 , 42 As Moral‐Benito and colleagues 41 show, this approach makes the same identification assumptions as the Arellano‐Bond approach, making the two approaches asymptotically equivalent. However, the ML‐SEM model is estimated within a structural equation model framework and uses a maximum likelihood estimator rather than a Generalized Methods of Moments estimator. Thus, the ML‐SEM approach can also accommodate lagged‐dependent variables while also preserving the ability to remove within‐cluster effects and heterogeneity and reduce omitted variable bias. 36 , 40 , 41 Importantly, prior research has argued and shown the ML‐SEM approach is more efficient, simpler, easier to specify, has fewer assumptions, has missing‐data procedures, allows for the inclusion of time‐invariant covariates, and has fewer potential biases due to sample sizes or number of instruments than the Arellano‐Bond approach. 40 , 41 Thus, in our analyses, we employ this approach. In short, this paper is concerned with the possibility that past values of patient characteristics may be an important omitted variable that may change the nature of the relationship between quality metrics and current patient composition. We investigate whether addressing prior patient composition substantively impacts the results of research testing the association between past quality reports and current patient composition. We demonstrate the effects of including this variable by comparing the results from the commonly employed FE model and the ML‐SEM model. 1.2. Quality reporting setting: Assisted reproductive technology clinics In our analyses, we use data from assisted reproductive technology (ART) clinics. ART clinics are required by the Fertility Clinic Success Rate and Certification Act of 1992 43 to report their live birth and singleton birth success rates, which are publicly reported by the Centers for Disease Control and Prevention (CDC). ART clinics are not just a convenient setting for our analysis; ART clinics also occupy a unique position for both their potential for provider gaming and the role of patient choice in relation to quality reporting. As a result, the findings have the potential to be useful beyond demonstrating the theoretical import of modeling past patient composition in quality reporting evaluations. When considering the potential for provider gaming, ART clinics differ from other health care venues in several ways. First, ART success rates are not formally incentivized nor framed as ideal indicators of the quality of a clinic, as the CDC reports highlight 44 ; that is, although quality reporting is required, low success rates are not subject to penalty and are acknowledged by the reporting institution as an incomplete or lacking metric. Curiously, however, there are few other metrics of quality included consistently in these reports. Second, ART success rates are highly associated with patient composition, including age, type of diagnosis, and other patient features. 45 , 46 While this association is true to some extent in other health care settings, multidimensional quality metrics are generally in place, as well as risk‐adjustment in public reporting or evaluation. There is no similar approach in ART clinic reporting. The strong association between patient composition and success rates may, therefore, encourage client “cherry‐picking,” if a clinic is seeking to improve their reported success rates. Third, the out‐of‐pocket costs of using ART are high 47 , 48 and insurance coverage is variable. 49 Specifically, the median cost of in‐vitro fertilization, a common ART, was estimated around $38,000 in a 2011 study, with a successful treatment estimated at $61,377 (due to multiple cycles of treatment often being needed). 47 Among those with insurance, the median out‐of‐pocket cost for in‐vitro fertilization was $19,234 in a study from 2014. 48 With high costs, even with insurance, many ART clinics are privately owned and for‐profit, 50 unlike other health systems. Given the high cost of ARTs and the fee‐for‐service, for‐profit market they are in, such clinics may be driven to recruit patients irrespective of the likelihood of success. Alternatively, due to competitive forces from public reporting or other sources, there may be pressures to pick patients who are more likely to have successful cycles of ART. There are reasons both for and against, taken together, provider gaming of success rates, which make it unclear whether or to what extent success rate reporting will influence provider selection of patients. ART clinics may also be situated differently from other health clinics in terms of the role of consumer choice. Prior work from Bundorf and colleagues 51 of older ART clinic success rate data using a difference‐in‐difference approach found a moderate association between higher birth success rates in a clinic and the market‐share of cycles for a given clinic after the introduction of quality reporting. The authors suggest that consumer choice is, therefore, associated with this type of reporting. 51 However, prior patient composition and patient selection by clinics were not investigated. While prior work suggests a role for success rate reporting on consumer choice, many areas in the United States have none or only one ART clinic available. 52 In effect, little competition exists in many regions, which may make consumers less sensitive to ART quality metrics. Unfortunately, there is little evidence about what factors consumers prioritize in selecting an ART clinic. Thus, we use the consistently reported live birth and singleton live birth rates as quality metrics. In this paper, we simultaneously investigate (1) whether accounting for past patient composition in evaluations of how quality reporting impacts patient selectivity (whether via consumer choice, provider gaming, or other mechanisms) changes substantive conclusions or findings, and (2) the substantive question of whether there is evidence of an association between quality reports and patient composition changes in ART clinics. We conclude with a discussion of the implications of these findings for researchers and policymakers. 2. MATERIALS AND METHODS 2.1. Data Data for this study come from the publicly available ART Clinic Success Rates published by the CDC. Data for the years 2011–2018 are available from the CDC's website (https://www.cdc.gov/art/reports/archive.html and https://www.cdc.gov/art/artdata/). Generally, these reports are made available to the public with a two‐year lag of data, such that the 2017 data were reported only in 2019. Thus, for our analyses, we assume that a two‐year lag is associated with the publication of these quality reports. Although data are available as early as 1995, changes in the reporting on key covariates and measures prohibit a longer‐scale analysis. However, the reports from 2011 to 2018 are largely consistent, making analysis possible. For the purposes of this paper, we include only clinics with complete data for the period under study as issues of attrition are outside the scope of the present analyses. 2.2. Measures The outcome variables of interest for this paper are focused on patient composition. These variables were derived from the available reported data and include the percentage of ART transfers to women under 35 and the percentage of ART transfers to women over 43. In addition, the percentage of ART transfers to patients with the following diagnoses were used as dependent variables: tubal factor, ovulatory factor, uterine factor, diminished ovarian reserve (DOR), unknown, other, endometriosis, and male factor. The following variables were inverse‐hyperbolic sine, or IHS, transformed due to right‐skew and issues with model convergence that arise with non‐normally distributed data: percentage of transfers to women over 43, percentage of patients with ovulatory factor diagnoses, endometriosis diagnoses, and male factor diagnoses. This transformation was used to preserve meaningful zeros in the data. Newer measures of diagnoses introduced in the CDC's 2017 report are not included because there is insufficient lagged data to conduct these analyses. Similarly, race and education are not included in public reports or are not collected in these data. The focal predictor variables include two types of success rates: (1) the percentage of transfers that end in a live birth and (2) the percentage of transfers that end in a singleton live birth (i.e., birth of one infant rather than multiple infants). We use live birth and singleton live birth rates as the primary indicators of quality in part because they are the focus of the reporting requirements. 43 Although many seeking infertility treatments are focused on a live birth of any kind, singleton live births are less costly to both the patient and hospital systems and are less risky than multiple births. 53 , 54 Separate models for any live birth and singleton live births were run, and a one‐ and two‐year lag of these success rates is the central predictor variable for the present study. Notably, the non‐lagged success rates are not included in the models as these temporally occur after patient composition. We identify these lagged success rates as predetermined, or not‐strictly exogenous, variables in the ML‐SEM models. These two types of success rates are not provided directly in the CDC's reports. Instead, the CDC's reports provide success rates by age for nondonor transfers and for all ages aggregated for donor transfers. To calculate overall success rates, we identified the number of transfers for each group individually using the success rates and the number of transfers reported and then summed the number of successful transfers and divided by the total number of transfers for all groups (donor and nondonor). We also created age‐specific nondonor success rates, which more closely resemble the data provided to consumers. However, comparisons of Bayesian information criterion (BIC) suggested the overall success rate generally fit the data better. The results from the age‐specific models (available upon request), however, do not differ meaningfully from those presented below. Controls for time‐variant clinic factors assumed to be exogenous included the number of transfers in the year of the outcome variable (IHS transformed to aid model convergence) and the percentage of ART transfers to nondonor patients. In the ML‐SEM model, we are also able to estimate a time‐invariant exogenous effect for the region of the clinic (Northeast, Midwest, South, and West) based upon the state where the clinic is located. In a traditional fixed‐effects model, this time‐invariant characteristic would be excluded. However, as Williams and colleagues 40 explain, introducing an additional assumption that there is no covariance between the fixed effects and the time‐variant strictly exogenous variable(s) permits such estimations, and this assumption is central to model identification. Importantly, we also introduce 1‐ and 2‐year lagged dependent variables to the ML‐SEM models to control for the patient composition in the prior years. 2.3. Analytic method Two approaches were used to analyze whether the success rates 2 years prior were associated with later patient composition. First, and most simply, we estimate a clinic fixed‐effects model. We opt for a fixed effects rather than a random‐effects approach to address bias from omitted time‐invariant variables, consistent with our Hausman test 55 results. For the reasons discussed in the introduction, lagged‐dependent variables are excluded from this fixed‐effects model, despite their potential importance. Still, this approach is attractive in its simplicity to fit, as well as the fact that it does address time‐invariant features related to the clinic. Moreover, this approach is highlighted as it is found commonly in the literature. Importantly, this fixed‐effects model can be estimated using structural equation modeling using maximum likelihood estimation. Indeed, such an estimation using structural equation modeling and maximum likelihood estimation will produce identical results to a standard fixed‐effects model when constraints on constants and error variance across time are implemented. 56 The second approach we use includes clinic fixed effects along with lagged‐dependent variables. We estimate the dynamic cross‐lagged panel model using structural equation models estimated with maximum‐likelihood (ML‐SEM) detailed in several works by Allison, Williams, and Moral‐Benito. 36 , 40 , 41 , 42 Figure 1 provides the path model for our analyses, and Equations (2) and (3) below from Williams, Allison, and Moral‐Benito's 40 restatement of Moral‐Benito's 42 equations provide the model estimated. | (2) | and | (3) | In Equation (2), y it is the value of y, the various patient composition variables, for a clinic i at time t, is the predetermined lagged dependent variable (though in our study we included both and , x it is a vector of sequentially exogenous/predetermined time‐varying variables, including lagged success rates, w i is a vector of time invariant (not included in Equation (1) as it is netted out from in the traditional fixed‐effects transformations), strictly exogenous variables, including location, α i is the unobservable time‐invariant fixed effect, is the unobserved common factors across units in the panel, and is the time‐varying error term. The ML‐SEM models used Satorra‐Bentler robust standard errors in order to address non‐normality of the data. 57 Structural equation model fit indices, including the RMSEA, CFI, TLI, and the SRMR, were used to evaluate the ML‐SEM model fit (available upon request). The analyses were conducted in Stata 17 using standard packages and the user‐written command xtdpdml. 40 3. RESULTS 3.1. Descriptive statistics In total, 303 clinics were included in the sample and eight time periods for a total of 2424 observations. The clinics were located throughout the United States with 20.1% in the Northeast, 18.9% in the Midwest, 33.0% in the South, and 28.1% in the West. Table 1 provides the means and standard deviations for each of the time‐variant variables. TABLE 1. | Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | Overall | |---|---|---|---|---|---|---|---|---|---| | Outcome variables | ||||||||| | % Under 35 | 48.14 (12.77) | 48.51 (12.53) | 49.03 (12.45) | 48.96 (12.30) | 49.00 (13.04) | 48.44 (11.51) | 52.18 (12.36) | 53.99 (15.59) | 49.78 (13.00) | | % Over 43 (untransformed) | 4.43 (4.38) | 4.62 (4.77) | 4.58 (4.93) | 4.37 (4.75) | 4.17 (4.40) | 4.46 (4.56) | 3.12 (4.55) | 1.81 (3.70) | 3.95 (4.61) | | % Over 43 (Transformed) a | 1.78 (0.99) | 1.86 (0.91) | 1.80 (0.98) | 1.75 (0.99) | 1.73 (0.96) | 1.81 (0.94) | 1.35 (1.02) | 0.74 (1.08) | 1.60 (1.05) | | % With tubal factor | 16.42 (9.77) | 15.89 (8.71) | 15.17 (8.74) | 15.02 (8.29) | 15.14 (8.85) | 14.34 (8.17) | 13.62 (7.88) | 13.03 (7.35) | 14.83 (8.55) | | % with ovulatory | 15.54 (9.54) | 14.91 (8.82) | 15.51 (9.50) | 15.79 (9.42) | 15.97 (9.17) | 16.75 (10.44) | 16.48 (11.55) | 15.81 (10.60) | 15.84 (9.92) | | % With ovulatory (transformed) a | 3.23 (0.70) | 3.21 (0.67) | 3.24 (0.70) | 3.26 (0.70) | 3.26 (0.73) | 3.27 (0.84) | 3.21 (0.91) | 3.20 (0.82) | 3.24 (0.76) | | % With uterine | 5.83 (6.07) | 5.82 (5.70) | 5.36 (5.46) | 5.69 (6.10) | 5.98 (6.42) | 6.17 (6.69) | 5.87 (6.47) | 5.87 (6.71) | 5.82 (6.21) | | % with DOR | 29.87 (15.75) | 31.15 (15.57) | 31.60 (15.45) | 30.99 (15.28) | 29.85 (14.60) | 30.19 (14.08) | 28.96 (14.73) | 28.58 (13.98) | 30.15 (14.95) | | % Unknown | 10.08 (8.91) | 9.95 (8.83) | 11.64 (12.58) | 10.87 (10.14) | 11.18 (10.38) | 10.70 (9.18) | 10.32 (9.46) | 10.21 (8.81) | 10.62 (9.86) | | % Other | 12.91 (11.30) | 13.07 (12.55) | 13.61 (12.48) | 14.27 (13.22) | 15.32 (14.70) | 19.76 (16.27) | 19.05 (16.78) | 19.74 (19.36) | 15.97 (15.05) | | % Endometriosis (untransformed) | 11.31 (9.46) | 10.99 (9.20) | 10.38 (8.43) | 10.35 (8.65) | 9.59 (8.07) | 9.10 (7.53) | 8.42 (7.15) | 8.00 (6.53) | 9.77 (8.24) | | % Endometriosis (transformed) a | 2.80 (0.87) | 2.79 (0.82) | 2.73 (0.84) | 2.73 (0.84) | 2.64 (0.87) | 2.60 (0.85) | 2.51 (0.87) | 2.50 (0.78) | 2.66 (0.85) | | % Male factor (untransformed) | 37.57 (15.52) | 36.57 (15.57) | 35.17 (14.71) | 35.62 (15.23) | 35.19 (14.97) | 34.18 (14.81) | 30.76 (13.88) | 30.56 (13.76) | 34.45 (14.99) | | % Male factor (transformed) a | 4.22 (0.52) | 4.18 (0.54) | 4.14 (0.57) | 4.15 (0.54) | 4.14 (0.54) | 4.11 (0.54) | 3.99 (0.61) | 4.01 (0.49) | 4.12 (0.55) | | Time‐variant exogenous variables | ||||||||| | Number of transfers | 328.34 (473.74) | 340.40 (495.55) | 341.19 (496.69) | 351.57 (494.62) | 358.23 (514.56) | 384.67 (564.96) | 333.78 (497.07) | 328.71 (506.67) | 345.86 (505.68) | | Number of transfers (transformed) a | 5.94 (1.05) | 5.99 (1.03) | 6.00 (1.02) | 6.04 (1.02) | 6.04 (1.04) | 6.09 (1.07) | 5.94 (1.09) | 5.85 (1.20) | 5.99 (1.07) | | % of transfers to non‐donors | 87.33 (10.16) | 86.92 (10.72) | 86.72 (11.21) | 86.40 (11.40) | 86.47 (11.79) | 85.96 (11.42) | 83.05 (13.11) | 82.08 (17.76) | 85.62 (12.52) | | Success rates | ||||||||| | % Transfers with live birth | 35.38 (10.48) | 36.71 (10.36) | 37.90 (10.56) | 38.86 (10.94) | 38.70 (11.72) | 41.80 (10.54) | 42.29 (10.34) | 39.44 (13.35) | 38.89 (11.28) | | % Transfers with singleton live birth | 24.93 (7.61) | 26.18 (7.69) | 27.51 (8.11) | 29.16 (8.58) | 30.14 (9.69) | 34.01 (9.68) | 37.17 (10.28) | 34.56 (13.77) | 30.46 (10.44) | Note: Standard deviation in parentheses. Abbreviation: DOR, diminished ovarian reserve diagnosis. Inverse hyperbolic sine transformed. 3.2. FE approach In the results from the standard FE model (Table 2), we observe that the 2‐year lagged success rate (t − 2) for all live births is positively associated with the percent of transfers to women under 35 years old at time t. By contrast, we observe that the two‐year lagged success rate for live births is negatively associated with the following outcomes: (1) the IHS‐transformed percent of transfers to women over 43 years old, (2) percent with tubal factor diagnosis, (3) percent with diminished ovarian reserve diagnosis, (4) percent with IHS‐transformed endometriosis diagnosis, and (5) the IHS‐transformed percent of male factor diagnosis. TABLE 2. | % Under 35 | % Over 43 a | % Tubal factor | % Ovulatory a | % Uterine | % DOR | % Unknown | % Other | % Endometriosis a | % Male factor a | | |---|---|---|---|---|---|---|---|---|---|---| | Panel A: Live birth success rates | |||||||||| | Time‐variant exogenous variables | |||||||||| | Number of transfers a | −0.740 (0.821) | 0.729*** (0.079) | −0.736 (0.466) | 0.166** (0.051) | 0.893* (0.354) | 4.224*** (0.774) | −2.707*** (0.682) | −0.872 (1.178) | 0.100 (0.051) | 0.083* (0.035) | | % of transfers to non‐donors | 0.077* (0.032) | 0.014*** (0.003) | 0.003 (0.018) | 0.012*** (0.002) | −0.012 (0.014) | −0.232*** (0.030) | 0.118*** (0.026) | −0.059 (0.045) | 0.006** (0.002) | 0.006*** (0.001) | | Lagged success rate | |||||||||| | Live birth success rate | |||||||||| | 1 year lagged | 0.104*** (0.030) | −0.015*** (0.003) | −0.009 (0.017) | 0.002 (0.002) | −0.001 (0.013) | −0.052 (0.029) | −0.027 (0.025) | 0.012 (0.044) | 0.001 (0.002) | −0.001 (0.001) | | 2 year lagged | 0.183*** (0.030) | −0.012*** (0.003) | −0.090*** (0.017) | 0.001 (0.002) | 0.010 (0.013) | −0.073* (0.029) | 0.006 (0.025) | 0.067 (0.044) | −0.006** (0.002) | −0.005*** (0.001) | | Constant | 37.063*** (5.422) | −2.910*** (0.521) | 22.372*** (3.076) | 1.156*** (0.339) | 1.093 (2.340) | 29.334*** (5.109) | 17.852*** (4.506) | 24.140** (7.781) | 1.680*** (0.337) | 3.353*** (0.230) | | sigma_u | 10.459 | 0.892 | 6.987 | 0.636 | 5.620 | 12.855 | 9.278 | 11.978 | 0.720 | 0.463 | | sigma_e | 7.700 | 0.740 | 4.368 | 0.481 | 3.324 | 7.256 | 6.399 | 11.051 | 0.479 | 0.327 | | rho | 0.649 | 0.592 | 0.719 | 0.636 | 0.741 | 0.758 | 0.678 | 0.540 | 0.693 | 0.667 | | Panel B: Singleton birth success rates | |||||||||| | Time‐variant exogenous variables | |||||||||| | Number of transfers a | −0.107 (0.808) | 0.654*** (0.076) | −1.043* (0.464) | 0.174*** (0.051) | 0.888* (0.355) | 3.899*** (0.771) | −2.810*** (0.683) | −0.250 (1.171) | 0.081 (0.051) | 0.067 (0.035) | | % of transfers to non‐donors | 0.102** (0.031) | 0.010*** (0.003) | −0.007 (0.018) | 0.012*** (0.002) | −0.013 (0.014) | −0.246*** (0.030) | 0.111*** (0.026) | −0.022 (0.045) | 0.006** (0.002) | 0.005*** (0.001) | | Lagged success rate | |||||||||| | Singleton live birth success rate | |||||||||| | 1 year lagged | 0.166*** (0.030) | −0.027*** (0.003) | −0.055** (0.017) | 0.004 (0.002) | −0.007 (0.013) | −0.097*** (0.029) | −0.054* (0.025) | 0.153*** (0.044) | −0.002 (0.002) | −0.003* (0.001) | | 2 year lagged | 0.219*** (0.033) | −0.015*** (0.003) | −0.088*** (0.019) | −0.002 (0.002) | 0.009 (0.014) | −0.082** (0.031) | 0.009 (0.028) | 0.110* (0.048) | −0.006** (0.002) | −0.005*** (0.001) | | Constant | 30.863*** (5.286) | −1.968*** (0.500) | 25.432*** (3.034) | 1.150*** (0.336) | 1.568 (2.323) | 32.947*** (5.045) | 19.617*** (4.467) | 12.481 (7.663) | 1.863*** (0.334) | 3.508*** (0.227) | | sigma_u | 10.793 | 0.844 | 6.930 | 0.638 | 5.615 | 12.778 | 9.362 | 11.876 | 0.715 | 0.459 | | sigma_e | 7.562 | 0.715 | 4.341 | 0.481 | 3.324 | 7.218 | 6.391 | 10.963 | 0.478 | 0.325 | | rho | 0.671 | 0.582 | 0.718 | 0.638 | 0.740 | 0.758 | 0.682 | 0.540 | 0.691 | 0.665 | Note: Standard errors in parentheses; *p < 0.05; **p < 0.01; ***p < 0.001. Abbreviation: DOR, diminished ovarian reserve diagnosis. Inverse hyperbolic sine‐transformed. Similar results were found when using the singleton‐live birth rates such that two‐year lagged success rate was significantly and positively associated with (1) percent of transfers to women under 35 years old and (2) percent with an “other” diagnosis of infertility. Additionally, the two‐year lagged success rate was significantly and negatively associated with: (1) the IHS‐transformed percent of transfers to women over 43 years old, (2) percent with tubal factor diagnosis, (3) percent with diminished ovarian reserve diagnosis, (4) the IHS‐transformed percent with endometriosis, and (5) the IHS‐transformed percent of male factor diagnosis. 3.3. ML‐SEM approach In the ML‐SEM approach, once the lagged dependent variables are introduced, a number of the significant associations from the FE model are no longer evident (Table 3). We observe the two‐year lagged success rate for all live births is negatively associated with the percent with tubal factor diagnoses and percent with IHS‐transformed endometriosis net of the lagged dependent variables and other covariates. Specifically, for every one percentage point decrease in the two‐year lagged live birth success rate, the percent of patients with tubal factor and IHS‐transformed endometriosis diagnoses increase by 0.064 (SE = 0.027, p < 0.05) and 0.005 (SE = 0.002, p < 0.01), respectively. TABLE 3. | % Under 35 | % Over 431 | % Tubal | % Ovulatory a | % Uterine | % DOR | % Unknown | % Other | % Endometriosis a | % Male factor a | | |---|---|---|---|---|---|---|---|---|---|---| | Panel A: Live birth success rates | |||||||||| | Dependent variable lag | |||||||||| | 1 year lag | 0.401*** (0.052) | 0.257*** (0.037) | 0.534*** (0.048) | 0.447*** (0.045) | 0.571*** (0.036) | 0.500*** (0.049) | 0.342*** (0.103) | 0.646*** (0.060) | 0.296*** (0.044) | 0.336*** (0.043) | | 2 year lag | 0.083* (0.037) | 0.027 (0.038) | 0.183*** (0.035) | 0.116** (0.044) | 0.162*** (0.039) | 0.088** (0.034) | 0.115* (0.049) | 0.085 (0.049) | 0.086 (0.045) | 0.016 (0.020) | | Time‐variant exogenous variables | |||||||||| | Number of transfers a | 1.641 (1.307) | 0.332*** (0.084) | −1.062 (0.734) | 0.106 (0.074) | 0.942** (0.336) | 1.661 (0.905) | −2.084* (0.889) | −0.050 (1.252) | 0.070 (0.071) | −0.061 (0.055) | | % of transfers to non‐donors | 0.109* (0.053) | 0.003 (0.003) | −0.057 (0.031) | 0.004 (0.003) | −0.017 (0.002) | −0.256*** (0.065) | 0.064 (0.037) | −0.010 (0.060) | 0.002 (0.004) | 0.003* (0.001) | | Time‐invariant exogenous variables | |||||||||| | Region (Ref = West) | |||||||||| | Northeast | −1.952 (1.139) | 0.163 (0.106) | 0.896 (0.540) | 0.040 (0.072) | 0.166 (0.422) | 0.612 (1.195) | 3.207** (1.240) | −2.407* (1.025) | −0.076 (0.074) | −0.083 (0.052) | | Midwest | 5.149*** (1.320) | −0.447*** (0.101) | 1.032* (0.417) | 0.251*** (0.068) | 0.454 (0.368) | −1.828 (1.114) | −0.291 (0.892) | −1.568 (1.038) | 0.301*** (0.091) | 0.058 (0.049) | | South | 4.195*** (1.095) | −0.299*** (0.082) | 1.597** (0.488) | 0.201** (0.062) | 0.777* (0.349) | −1.398 (1.041) | −1.172 (0.768) | −0.746 (0.898) | 0.320*** (0.085) | 0.068 (0.044) | | Predetermined variables | |||||||||| | All live birth success rate | |||||||||| | 1 year lagged | −0.051 (0.036) | −0.000 (0.003) | 0.023 (0.026) | −0.004 (0.004) | −0.001 (0.022) | 0.044 (0.035) | 0.003 (0.025) | −0.009 (0.080) | −0.001 (0.003) | 0.001 (0.002) | | 2 year lagged | 0.061 (0.040) | 0.003 (0.003) | −0.064* (0.027) | 0.001 (0.002) | −0.010 (0.016) | −0.011 (0.042) | 0.015 (0.023) | −0.009 (0.061) | −0.005** (0.002) | −0.004 (0.002) | | Panel B: Singleton birth success rates | |||||||||| | Dependent variable lag | |||||||||| | 1 year lag | 0.386*** (0.051) | 0.263*** (0.039) | 0.530*** (0.048) | 0.437*** (0.042) | 0.569*** (0.036) | 0.500*** (0.050) | 0.335*** (0.097) | 0.644*** (0.059) | 0.291*** (0.045) | 0.328*** (0.043) | | 2 year lag | 0.081* (0.035) | 0.030 (0.038) | 0.182*** (0.033) | 0.112** (0.043) | 0.161*** (0.039) | 0.089** (0.034) | 0.111* (0.047) | 0.086 (0.049) | 0.083 (0.045) | 0.011 (0.020) | | Time variant exogenous variables | |||||||||| | Number of transfers a | 1.735 (1.304) | 0.333*** (0.084) | −1.176 (0.739) | 0.113 (0.077) | 0.934** (0.339) | 1.642 (0.913) | −2.098* (0.886) | −0.016 (1.260) | 0.064 (0.071) | −0.064 (0.054) | | % of transfers to non‐donors | 0.112* (0.054) | 0.003 (0.003) | −0.053 (0.031) | 0.004 (0.003) | −0.017 (0.021) | −0.258*** (0.065) | 0.063 (0.037) | −0.012 (0.060) | 0.002 (0.004) | 0.003* (0.001) | | Time‐invariant exogenous variables | |||||||||| | Region (Ref = West) | |||||||||| | Northeast | −1.622 (1.133) | 0.166 (0.105) | 1.041 (0.545) | 0.065 (0.070) | 0.160 (0.406) | 0.347 (1.135) | 3.247** (1.224) | −2.590** (0.928) | −0.057 (0.073) | −0.079 (0.052) | | Midwest | 5.616*** (1.285) | −0.433*** (0.101) | 1.036* (0.420) | 0.271*** (0.068) | 0.429 (0.369) | −1.948 (1.094) | −0.292 (0.919) | −1.707 (1.046) | 0.308*** (0.091) | 0.058 (0.048) | | South | 4.610*** (1.098) | −0.288*** (0.084) | 1.634*** (0.481) | 0.221*** (0.061) | 0.763* (0.344) | −1.545 (1.021) | −1.204 (0.779) | −0.878 (0.902) | 0.330*** (0.087) | 0.068 (0.044) | | Predetermined variables | |||||||||| | Singleton live birth success rate | |||||||||| | 1 year lagged | 0.008 (0.038) | 0.000 (0.004) | 0.006 (0.029) | 0.002 (0.004) | −0.010 (0.024) | 0.011 (0.040) | −0.002 (0.029) | −0.036 (0.076) | −0.000 (0.003) | 0.000 (0.002) | | 2 year lagged | 0.095* (0.047) | 0.005 (0.004) | −0.034 (0.030) | −0.001 (0.003) | −0.007 (0.019) | −0.028 (0.047) | 0.019 (0.024) | −0.029 (0.065) | −0.004 (0.003) | −0.003 (0.002) | Note: Standard errors in parentheses; *p < 0.05; **p < 0.01; ***p < 0.001. Abbreviation: DOR, diminished ovarian reserve diagnosis. Inverse hyperbolic sine‐transformed. The 2‐year lagged success rate for singleton live births is positively associated with the percentage of transfers to women under 35 years old; that is, for every one percentage point increase in the two‐year lagged success rate for singleton live births, the percentage of transfers to women under 35 increases by 0.095 (SE = 0.047, p < 0.05). No other associations were observed for the singleton live birth two‐year lagged success rate. 3.4. Sensitivity analyses Two sets of sensitivity analyses are included to contextualize the results. First, we provide the results from the ML‐SEM model that includes an additional year lag for the dependent variable (t − 3). This specification accounts for the possibility that success rates at time t − 2 are related to the patient composition at t − 3. When incorporating in an additional year lag for the dependent variable in the ML‐SEM model, the focal association between lagged success rates and changes in patient composition remains unchanged (Tables S1 and S2). Second, we show the ML‐SEM model without any lagged dependent variables for comparison. Importantly, the ML‐SEM model presented in this sensitivity analysis maintains the assumptions of the main ML‐SEM model, which differentiate it from a standard FE model. Specifically, we are able to include the time‐invariant geography variable, we treat the lagged success rates as predetermined, we employ the Satorra‐Bentler robust standard errors, and we allow both the constants and error to vary across years. This specification, therefore, is substantively different from the commonly employed FE models found in the literature, even without the lagged‐dependent variables. The use of the ML‐SEM without any lagged dependent variables yields different findings from the FE model, which was expected due to the differing assumptions of the model (Table S3). Regarding our focal association, the findings were similar between the two specifications of the ML‐SEM models. For example, consistent with the model in Table 2, we observe significant negative associations between the two‐year live birth lagged success rate and the percent of patients with tubal factor and the IHS‐transformed percent of patients with endometriosis. We also observe a positive association between the two‐year lagged singleton success rate and the percentage under 35, observed in the final model. Yet the ML‐SEM model without lagged dependent variables also shows a significant negative association between the 2‐year lagged live birth success rate and the IHS‐transformed percent with male factor diagnoses not observed in the final model. 4. LIMITATIONS This paper has several limitations. First, clinics that did not remain open for the entire study period were excluded. The impact of attrition on these results is not clear and is difficult to quantify due to the limited research on ART clinic closures. For example, patient composition, success rates, and patient volume could vary between the clinics that were closed or consolidated versus those that remained open. Moreover, it is possible that closed clinics differ from the included clinics in the association between success rates and changing patient demographics. However, the clinics that did not remain open are of marginal interest for our question related to ART‐clinic behaviors as they likely represent unsuccessful clinics. Rather, we focus on successful clinics that continue to provide ART because these clinics are likely more representative of ongoing practices and the patterning of interest for our substantive question related to ART clinics. Second, the results do not account for selection on the basis of race or socioeconomic status, despite known associations between ART success rates and these features. 58 , 59 Unfortunately, these data are either not publicly reported or not collected in the current CDC reports. Future research could pursue this question more directly by pairing geographic data from the ART clinic locations with sociodemographic information from the Census or other sources to more directly address this question. Finally, neither model presented identifies or distinguishes between possible mechanisms underlying these associations. This limitation is also true, to some extent, for difference‐in‐difference models, and with the Arellano‐Bond estimator may require qualitative studies within health care settings or other forms of data to evaluate. 5. DISCUSSION AND CONCLUSION Public reporting of quality metrics is widespread in the United States. While the efficacy of these initiatives is still under examination, these reports have the potential to positively impact quality and costs of care in the United States. 6 , 7 , 15 , 24 , 25 Key questions in this literature focus on evaluating negative unintended effects such as provider gaming and intended effects such as shifting consumer utilization toward higher quality care centers. Much of this research focuses on changes in patient composition using a difference‐in‐difference approach or other fixed effects approaches. Unfortunately, these approaches do not address the possibility that past patient composition may drive observed associations. Thus, these common approaches may suffer from omitted variable bias. Due to the assumptions of these models, lagged dependent variables cannot be accommodated, despite their potential importance in understanding the nature of the relationship between previously reported quality metrics and current patient composition. In this paper, we used two approaches to investigate whether omitting measures of past patient composition shapes results of models investigating current patient characteristics and past quality reports. The first model, a standard FE model, cannot be estimated to account for these past patient composition variables without introducing bias into the model. The second model, the ML‐SEM model, however, can include these indicators. As such, we suggest that the ML‐SEM model, or others that account for lagged patient composition, are a more theoretically appropriate model to employ when exploring the association between quality reporting and current patient composition. In our findings, both models find a negative association between the two‐year lagged live birth success rate, the percentage with endometriosis diagnosis, and the percentage with tubal factor diagnoses. However, the ML‐SEM model does not find evidence for the other focal associations between lagged success rates and current patient/diagnosis compositions observed in the FE model. Similarly, the ML‐SEM and FE model align in showing the two‐year lagged singleton birth rate is positively associated with percent of transfers to women under 35 years old, while the ML‐SEM model finds no support for the numerous other associations observed in the FE model. Thus, the ML‐SEM model results suggest that the patterns observed in the FE may be driven by the omission of lagged dependent variables. These findings have important theoretical, substantive, and policy implications. First, theoretically, the findings demonstrate the potential pitfalls of investigating patient composition without accounting for prior trends. Specifically, we show that the standard FE model finds associations between past quality reports and later patient composition. In contrast, explicitly accounting for past patient composition in the dynamic panel model with lagged dependent variables finds fewer associations. These findings suggest future research should be cautious in drawing conclusions about associations between quality reports and patient characteristics in models that do not expressly address prior patient characteristics. Second, substantively, this paper suggests that when using the correct model, there are still some associations between the previous year's success rates and patient characteristics in subsequent years in ART clinics. This finding could suggest there is evidence of provider gaming or consumer behavior shifts associated with past success rate publications for the characteristics assessed in this paper. However, the model itself does not provide greater insight into the extent to which either mechanism may be central. As a result, we must look to the available literature related to success rates and diagnoses. Specifically, some evidence shows a successful live birth is associated with tubal diagnoses, and both endometriosis and tubal factor diagnoses are associated with clinical pregnancy following ART. 46 At the same time, the evidence on these two diagnoses is mixed, and other diagnoses in our study that have been associated with improved success rates showed no associations with past quality reports. 60 , 61 Similarly, the association between increases in younger patients, who are more likely to have a successful ART cycle, 62 and higher previous success rates is inconsistent with the provider gaming hypothesis. Thus, when reviewing the findings of the ML‐SEM model in light of the literature, the results do not support the idea of systematic provider gaming. Instead, the results may provide some evidence of consumer choice consistent with the conclusions from prior research. 51 This finding provides new evidence to the growing literature assessing and evaluating the impacts of quality reporting on patient selection. At the same time, future research is needed to empirically disentangle these two types of mechanisms. Third, for applied social scientists and policymakers evaluating quality reporting research, the findings of this paper provide important information about the effects of modeling techniques on evaluations and conclusions. In short, traditional approaches may lead to incorrect or misleading conclusions. Notably, the use of the ML‐SEM approach is straightforward, transparent, and requires no additional or new information to be collected; that is, patient composition data are already collected for evaluation purposes meaning lagged data should also be available. In sum, using these models provides a more accurate estimate of the impacts of these policy interventions without incurring the costs that are associated with increased data collection. Further, the limited evidence of systematic and patterned associations between past quality metrics and future patient composition may emerge from the unique features of ART clinics aforementioned, which may be protective against provider gaming. Thus, the differences between the findings for ART clinics presented here and other significant findings in other health care venues yield insights into how to address unintended consequences of public reporting. For example, the incentive structure of ART clinics may contribute to these findings. Specifically, ART cycles are often expensive, insurance coverage minimal, and many ART clinics are for‐profit. 47 , 48 , 49 , 50 It would be unwise, however, to recommend reduction of insurance coverage, increases in fee‐for‐service care, or high out‐of‐pocket costs for other venues of care. That being said, shifts in the incentive structure that are more consistent with “bending the cost curve,” such as global or capitated payments, may help to reduce provider gaming and may improve quality as well. 63 , 64 That is, such approaches could create incentives to serve more patients, as is the case for ART clinics, but without the cost‐related issues of fee‐for‐service reimbursements. Notably, such reimbursement structures are not without their own issues. 65 , 66 Additionally, ART success rates are reported with caution, and there are no formal consequences for poor success rates. In this way, these quality reports could be seen as having lower stakes than those in other settings. Thus, it may be helpful to more fully contextualize quality reports in other settings to help prevent health systems or providers from becoming risk‐adverse or hostile to the reporting. Ultimately, quality reports could benefit health systems, consumers, and providers. However, researchers must evaluate the utility, impact, and unintended consequences of these systems using the most up‐to‐date and accurate methods. CONFLICT OF INTERESTS The authors declare no conflicts of interest. Supporting information ACKNOWLEDGMENTS The authors acknowledge material and technological support of their work from Western Michigan University and Duke University. The authors also acknowledge the data for these analyses come from the Centers for Disease Control and Prevention. The opinions, results, and conclusions of these analyses do not reflect the opinions or views of Western Michigan University, Duke University, or the Centers for Disease Control and Prevention. Tierney KI, Fishman S. Accounting for past patient composition in evaluations of quality reporting. Health Serv Res. 2022;57(3):668-680. doi: 10.1111/1475-6773.13942

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