How uncertainties could affect the establishment of tumour control probability profiles in radiopharmaceutical therapy?

How uncertainties could affect the establishment of tumour control probability profiles in radiopharmaceutical therapy? | 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 How uncertainties could affect the establishment of tumour control probability profiles in radiopharmaceutical therapy? Arnaud Dieudonné This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5972271/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Purpose This study examines the impact of uncertainties in absorbed dose and response evaluations on establishing tumour control probability (TCP) profiles in radiopharmaceutical therapy (RPT). Methods Using three simulated TCP models with varying slopes (γ50), the impact of uncertainties of up to 30% in absorbed dose and response classification errors were studied. Logistic regressions on 100 simulated datasets assessed the accuracy of TCP parameters. Results The results show that dose uncertainties significantly affect TCP models but can be mitigated by increasing the sample size. Errors in response classification have a smaller impact. Parameters like x50 (dose for 50% tumour control) were more accurately predicted than γ50 (radiosensitivity). Accuracy improves notably when sample sizes exceed 300 and dose uncertainties remain below 15%. Conclusion The findings highlight the importance of estimating uncertainties and increasing sample size to improve TCP model reliability in clinical studies. Figures Figure 1 Figure 2 Introduction The implementation of dosimetry in radiopharmaceutical therapy (RPT) requires not only to establish dose-effect relationships, but also to provide tools to adapt the treatment delivery according to the clinical outcome. Hence, one of the challenges of dosimetry is to establish tumour control probability (TCP) models from clinical data. Such studies have been developed for the selective internal radionuclide therapy (SIRT) of liver neoplasms with yttrium 90 microspheres ( 90 Y-microspheres). Indeed, various TCP modelling are available for the treatment of hepatocellular carcinoma with resin 90 Y-microspheres ( 1 – 3 ) and glass 90 Y-microspheres ( 4 – 6 ). The tumour control probability (TCP) for a given absorbed dose D can be expressed as a linear quadratic (LQ) function of a set of radiobiological parameters ( 7 ) with \(\:\varvec{T}\varvec{C}\varvec{P}\left(\varvec{D}\right)={\varvec{e}}^{-{\varvec{N}}_{0}{\varvec{e}}^{-\varvec{\alpha\:}\varvec{D}-\varvec{G}\varvec{\beta\:}{\varvec{D}}^{2}}}\) Equation 1 with \(\:{N}_{o}\) being the number of clonogenic cells, \(\:\alpha\:\) and \(\:\beta\:\) are respectively the linear and quadratic cell killing constants. \(\:G\) is the generalized Lea–Catcheside time factor which can be expressed as \(\:G=\:\frac{2}{{D}^{2}}{\int\:}_{0}^{+\infty\:}\dot{D}\left(t\right)\text{d}\text{t}{\int\:}_{0}^{t}{e}^{-\mu\:(t-w)}\dot{D}\left(w\right)dw\) Equation 2 With \(\:\dot{D}\left(t\right)\) being the absorbed dose rate and \(\:\mu\:\) the is the DNA repair constant. A much simpler formulation in external beam radiation therapy (EBRT) and RPT \(\:\left\{\begin{array}{c}EBRT:G=1/n\\\:RPT:\:G=\lambda\:/(\lambda\:+\mu\:)\end{array}\right.\) Equation 3 \(\:n\) being the number of fractions in EBRT, \(\:\lambda\:\) is the effective half-life of the radio-compound in a given tissue. The LQ model rely on a radiobiological underlying concept that assumes that the cell killing constants are independent of the level of observation (cellular or tissue) and independent of the type of particles. Much simpler functions are available for TCP modelling such as the log-logistic function \(\:TCP\left(D\right)=\frac{1}{1+\text{e}\text{x}\text{p}\left[4{\gamma\:}_{50}\left(1-D/{D}_{50}\right)\right]}\) Equation 4 \(\:{D}_{50}\) being the absorbed dose for which \(\:TCP\left({D}_{50}\right)=0.5\) and \(\:{\gamma\:}_{50}\) is the percent change of TCP per percent change of absorbed dose around \(\:{D}_{50}\) , i.e. the slope of the linear part of the TCP curve. The fact that absorbed dose estimates in RPT are associated with large uncertainties is well documented. Indeed, while uncertainties in EBRT are below 5%, the uncertainties in RPT can go up to 40% ( 8 – 10 ) depending mainly on the size of the target. Another source of error in establishing TCP models is the uncertainty related to the response evaluation. The most common method for response evaluation is the response evaluation criteria in solid tumours (RECIST). The RECIST v1.1 defines four response criteria according the measurement of lesions diameters ( 11 ). The complete response (CR) stand as the disappearance of all target and non-target lesions and the normalisation of tumour marker level and lymph nodes size. The partial response (PR) is at least 30% decrease in the sum of target lesions diameters or the persistence of one or more non-target lesions or abnormal tumour marker level. The progressive disease (PD) is at least 20% increase in the target lesions diameters from the nadir or the progression of non-target lesions or the appearance of new lesions. The stable disease (SD) is the state in between PR and PD. In clinical studies, CR, PR and SD criteria are also classified as disease control (DC), and CR and PR as objective response (OR). In a review by Fournier et al. ( 12 ) we found that the reproducibility of the diameter measurements vary from 10–30% which could result in up to 30% of patients misclassified. In order to study the influence of uncertainties in the establishment of TCP models, we propose to model the two sources of uncertainties into simulated TCP models and to study their influence on the establishment of these models. Materials and Methods Three TCP models were defined from the logit function in Eq. 1 as a function of D/D 50 , so that TCP(x 50 ) = 0.5, with x 50 = 1, for all models, but γ 50 values were respectively of 0.5, 0.75, and 1.0. For practical reason, the variable D/D 50 is noted x in the following equation: \(\:TCP\left(x\right)=\frac{1}{1+\text{e}\text{x}\text{p}\left[4{\gamma\:}_{50}\left(1-x/{x}_{50}\right)\right]}\) Equation 5 Starting from these models, 100 replicates of dose-response data. The variable x was first uniformly sampled in the range [0;2] and the response variable \(\:r\) was simulated as a binomial distribution following the probability law of Eq. 5. This dataset was labelled as the non-biased data. Then, r values were randomly modified to simulate an error rate in response classification of 10, 20 and 30%. An uncertainty was added to x values following a normal distribution with relative standard deviation of 5, 10, 15, 20 and 30% to simulate the uncertainty associated with the absorbed dose calculation. Then for each simulated biased dataset a logistic regression was performed. The adjusted logit function parameters γ 50 and x 50 were then compared to those of the actual TCP model. Additionally, the predicted characteristic value x 80 giving TCP(x 80 ) = 0.8 was compared to the actual one. The percentage root mean squared error (%RMSE) over all the evaluations were calculated following Eq. 6 for γ 50 , x 50 and x 80 . \(\:\%RMSE=\frac{\sqrt{\sum\:_{i=1}^{n}{\frac{1}{n}\left({predicted}_{i}-actual\right)}^{2}}}{actual}\times\:100\) Equation 6 The values of %RMSE(γ 50 ), %RMSE(x 50 ) and %RMSE(x 80 ) were then plotted against the number of samples simulated stratified by the absorbed dose uncertainty and response error rate. Spearman correlations were calculated between %RMSE and dose uncertainty, response error rate and number of samples. Below 0.3, we considered there was no correlation, between 0.3 and 0.5, the correlation was weak, between 0.5 and 0.7, moderate and over 0.7, strong. All the study was done using R version 4.2.2 ( 13 ). Results All three models had the same x 50 value of 1.0, while x 80 values were 1.80 for γ 50 = 0.5, 1.54 for γ 50 = 0.75 and 1.40 for γ 50 = 1.0. Figure 1 shows examples of unbiased and biased data made for various values of γ50, dose uncertainty, response error rate, and number of samples. These examples illustrate how uncertainties affect the data and the logit fit in comparison to the original TCP model. Figure 2 shows that the more samples are used, the better the accuracy is on the estimation of TCP parameters, regardless of the uncertainty and error rate that biased the data. Lower values of γ 50 were associated with higher error levels for x 50 and x 80 . %RMSE(x 50 ) was lower than 10% when the number of samples was over 250 for γ 50 = 0.5, 175 for γ 50 = 0.75, and 150 for γ 50 = 1.0. In predicting γ 50 , the median (IQR) %RMSE was 21% (17%), while for D 50 it was 7.4% (5.8%) and for D 80 9.4% (7.8%) as shown in Fig. 2 . The %RMSE(γ 50 ) was 23% (14%) for γ 50 = 0.5, 21% (18%) for γ 50 = 0.75, and 20% (19%) for γ 50 = 1.0. %RMSE(x 50 ) was 9.2% (6.8%) for γ 50 = 0.5, 7.0% (4.8%) for γ 50 = 0.75, and 6.4% (4.0%) for γ 50 = 1.0. %RMSE(x 80 ) was 13% (12%) for γ 50 = 0.5, 8.9% (7.3%) for γ 50 = 0.75, and 7.5% (6.2%) for γ 50 = 1.0. %RMSE(x 80 ) remained below 10% for more than 300 samples when dose uncertainties were below 15% with γ 50 = 0.5. It remained below 10% over 250 samples with dose uncertainties below 20% and γ 50 = 0.75 and for more than 100 samples with dose uncertainties below 20% with γ 50 = 1.0. %RMSE(γ 50 ) was consistently over 10%, except for the highest number of samples (500) and the lowest dose uncertainties. %RMSE(γ 50 ) was of approximately 30% for a dose uncertainty of 30%. Discussion This study aimed to evaluate the impact of uncertainties on the development of tumour control probability (TCP) models in targeted radionuclide therapy. Two primary sources of uncertainty were analysed: those related to the absorbed dose and those stemming from response evaluation. Additionally, the influence of sample size on TCP estimation accuracy was investigated. To achieve this, 100 replicates of dose-response datasets were generated randomly, based on the probability function of three TCP profiles characterized by γ 50 and x 50 . Various levels of uncertainties were introduced into these simulations. Here, x 50 , which represents a relative dose (x = D/D 50 , x 50 = 1), serves as a surrogate for D 50 , the dose associated with a 50% probability of tumour control. γ 50 indicates the slope around x 50 , functioning as a measure of radiosensitivity akin to the α/β ratio in the Lea-Catcheside linear-quadratic model; higher γ 50 values denote greater radiosensitivity. The results demonstrated that x 50 and x 80 were estimated with higher accuracy compared to γ 50 , with median %RMSE values of 7.4% and 9.4% for x 50 and x 80 , respectively, versus 21% for γ 50 . Interestingly, the increased error from greater dose uncertainty was mitigated by larger sample sizes. For example, a %RMSE of 4.63% for x 50 was achieved with 200 samples and no dose or response errors. The same error was observed with 500 samples, a 20% dose uncertainty, and a 30% response error rate. Overall, %RMSE values were more influenced by dose uncertainty and sample size than by response error rates. Conclusion The estimation of uncertainties is a crucial step in establishing dose-response profiles through TCP modelling in targeted radionuclide therapy. This study shows how the fitted TCP profiles are impacted by absorbed dose and response uncertainties. It also shows how increasing the number of samples (i.e. patients) can improve accuracy. Those results could help to design dose-effect relationship studies in radiopharmaceutical therapy clinical trials. Declarations Contributions All authors contributed to the study conception and design. All authors read and approved the final manuscript. Ethics declarations Competing interests The authors declare no conflicts of interest regarding financial or non-financial relationships that could influence the objectivity of this research. Funding Not applicable. Data availability Data from this article are available from the corresponding author on reasonable request. References Strigari L, Sciuto R, Rea S, et al. Efficacy and toxicity related to treatment of hepatocellular carcinoma with 90Y-SIR spheres: radiobiologic considerations. J Nucl Med. 2010;51:13771385. Hermann A-L, Dieudonné A, Ronot M et al. Relationship of Tumor Radiation–absorbed Dose to Survival and Response in Hepatocellular Carcinoma Treated with Transarterial Radioembolization with 90 Y in the SARAH Study. Radiology. 2020:191606. Veenstra EB, Ruiter SJS, de Haas RJ, Bokkers RPH, de Jong KP, Noordzij W. Post-treatment three-dimensional voxel-based dosimetry after Yttrium-90 resin microsphere radioembolization in HCC. EJNMMI Res. 2022;12:9. Kappadath SC, Mikell J, Balagopal A, Baladandayuthapani V, Kaseb A, Mahvash A. Hepatocellular Carcinoma Tumor Dose Response After 90Y-radioembolization With Glass Microspheres Using 90Y-SPECT/CT-Based Voxel Dosimetry. Int J Radiat Oncol Biol Phys. 2018;102:451461. Dewaraja YK, Devasia T, Kaza RK et al. Prediction of tumor control in 90Y radioembolization by logit models with PET/CT based dose metrics. Journal of nuclear medicine: official publication, Society of Nuclear Medicine . 2019:jnumed.119.226472. Romanò C, Mazzaglia S, Maccauro M, et al. Radioembolization of Hepatocellular Carcinoma with 90Y Glass Microspheres: No Advantage of Voxel Dosimetry with Respect to Mean Dose in Dose–Response Analysis with Two Radiological Methods. Cancers (Basel). 2022;14:959. Brenner DJ, Point. The linear-quadratic model is an appropriate methodology for determining iso-effective doses at large doses per fraction. Semin Radiat Oncol. 2008;18:234–9. Finocchiaro D, Gear JI, Fioroni F, et al. Uncertainty analysis of tumour absorbed dose calculations in molecular radiotherapy. EJNMMI Phys. 2020;7:63. Kayal G, Barbosa N, Marín C, et al. Precision in dosimetric analysis and generation of a benchmark dosimetry dataset - An IAEA study. J Nucl Med. 2022;63:2812–2812. Kayal G, Barbosa N, Marín CC et al. October. Quality Assurance Considerations in Radiopharmaceutical Therapy Dosimetry Using PLANETDose: An International Atomic Energy Agency Study. Journal of Nuclear Medicine . 2023. Eisenhauer EA, Therasse P, Bogaerts J, et al. New response evaluation criteria in solid tumours: Revised RECIST guideline (version 1.1). Eur J Cancer. 2009;45:228–47. Fournier L, De Geus-Oei L-F, Regge D, et al. Twenty Years On: RECIST as a Biomarker of Response in Solid Tumours an EORTC Imaging Group – ESOI Joint Paper. Front Oncol. 2022;11:800547. R Core Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2022. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5972271","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":418216268,"identity":"c05ec48e-8f28-4edd-b330-971c76f07eff","order_by":0,"name":"Arnaud Dieudonné","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5UlEQVRIiWNgGAWjYNACNgbGNiAlAWLzk65FsoFYLQ0wLQYHCCjmn3324GeeMgbZPvYewxsfd9yRM752+ADDj4ptOLVInMtLluY5x2DcxnPG2HLmmWfGZrfTEhh7ztzGbc0ZHgNp3jaGxDaJHDMg43Ditts5BsyMbbi1yJ/hMf4N1iL/BqylfvPs/A94tRic4TGD2gJmHE4wkM5hwKvFEKjFcs45CaBf0ootZ7YdNpxxO83gID6/yAEdduNNmY3s/PbDG298bDsszz87+eGDHxV4vA8BEqjcA4TUj4JRMApGwSjADwCrBVIN4dndVQAAAABJRU5ErkJggg==","orcid":"https://orcid.org/0000-0003-2825-2085","institution":"Centre Henri Becquerel","correspondingAuthor":true,"prefix":"","firstName":"Arnaud","middleName":"","lastName":"Dieudonné","suffix":""}],"badges":[],"createdAt":"2025-02-06 09:56:27","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5972271/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5972271/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":77048721,"identity":"928cd1b6-e5fe-4b8f-864a-7e18c13c623b","added_by":"auto","created_at":"2025-02-24 15:22:16","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":569897,"visible":true,"origin":"","legend":"\u003cp\u003ePlots of original TCP models (red curve) and generated sampled data (red circles), in blue: biased data (blue circles) and fitted TCP model (blue curve) for varying γ50 values, dose uncertainty, response error rate and number of samples.\u003c/p\u003e","description":"","filename":"Picture1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5972271/v1/5573132fb3b2911b32ef6c97.jpg"},{"id":77048722,"identity":"a0c79a88-fe2e-47bc-a68e-5ba1f0331e0b","added_by":"auto","created_at":"2025-02-24 15:22:16","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":411850,"visible":true,"origin":"","legend":"\u003cp\u003eSemi-log plots of %RMSE(g\u003csub\u003e50\u003c/sub\u003e) on top, %RMSE(x\u003csub\u003e50\u003c/sub\u003e) in the middle and %RMSE(x\u003csub\u003e80\u003c/sub\u003e) on bottom according to the number of samples stratified by the absorbed dose uncertainty (by colors) and the response error rate (by linetype and dot shape).\u003c/p\u003e","description":"","filename":"Picture2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-5972271/v1/1ca7cd75e64211b4ceba5917.jpg"},{"id":79425188,"identity":"e81184c6-81a5-46c7-8923-9e10e07ae6d8","added_by":"auto","created_at":"2025-03-28 09:26:29","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1366887,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5972271/v1/91578b97-80ec-449d-a0da-cfc60deee1c1.pdf"}],"financialInterests":"","formattedTitle":"How uncertainties could affect the establishment of tumour control probability profiles in radiopharmaceutical therapy?","fulltext":[{"header":"Introduction","content":"\u003cp\u003eThe implementation of dosimetry in radiopharmaceutical therapy (RPT) requires not only to establish dose-effect relationships, but also to provide tools to adapt the treatment delivery according to the clinical outcome. Hence, one of the challenges of dosimetry is to establish tumour control probability (TCP) models from clinical data. Such studies have been developed for the selective internal radionuclide therapy (SIRT) of liver neoplasms with yttrium 90 microspheres (\u003csup\u003e90\u003c/sup\u003eY-microspheres). Indeed, various TCP modelling are available for the treatment of hepatocellular carcinoma with resin \u003csup\u003e90\u003c/sup\u003eY-microspheres (\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e) and glass \u003csup\u003e90\u003c/sup\u003eY-microspheres (\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e).\u003c/p\u003e\n\u003cp\u003eThe tumour control probability (TCP) for a given absorbed dose D can be expressed as a linear quadratic (LQ) function of a set of radiobiological parameters (\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e) with\u003c/p\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\varvec{T}\\varvec{C}\\varvec{P}\\left(\\varvec{D}\\right)={\\varvec{e}}^{-{\\varvec{N}}_{0}{\\varvec{e}}^{-\\varvec{\\alpha\\:}\\varvec{D}-\\varvec{G}\\varvec{\\beta\\:}{\\varvec{D}}^{2}}}\\)\u0026nbsp; \u0026nbsp; \u0026nbsp;Equation 1\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003ewith \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{N}_{o}\\)\u003c/span\u003e\u003c/span\u003e being the number of clonogenic cells, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\alpha\\:\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\beta\\:\\)\u003c/span\u003e\u003c/span\u003e are respectively the linear and quadratic cell killing constants.\u0026nbsp;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:G\\)\u003c/span\u003e\u003c/span\u003e is the generalized Lea\u0026ndash;Catcheside time factor which can be expressed as\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tabb\" border=\"1\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:G=\\:\\frac{2}{{D}^{2}}{\\int\\:}_{0}^{+\\infty\\:}\\dot{D}\\left(t\\right)\\text{d}\\text{t}{\\int\\:}_{0}^{t}{e}^{-\\mu\\:(t-w)}\\dot{D}\\left(w\\right)dw\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEquation 2\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eWith \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\dot{D}\\left(t\\right)\\)\u003c/span\u003e\u003c/span\u003e being the absorbed dose rate and\u0026nbsp;\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e\u003c/span\u003e the is the DNA repair constant. A much simpler formulation in external beam radiation therapy (EBRT) and RPT\u003c/p\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tabc\" border=\"1\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\left\\{\\begin{array}{c}EBRT:G=1/n\\\\\\:RPT:\\:G=\\lambda\\:/(\\lambda\\:+\\mu\\:)\\end{array}\\right.\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEquation 3\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e being the number of fractions in EBRT, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\lambda\\:\\)\u003c/span\u003e\u003c/span\u003e is the effective half-life of the radio-compound in a given tissue. The LQ model rely on a radiobiological underlying concept that assumes that the cell killing constants are independent of the level of observation (cellular or tissue) and independent of the type of particles.\u003c/p\u003e\n\u003cp\u003eMuch simpler functions are available for TCP modelling such as the log-logistic function\u003c/p\u003e\n\u003ctable id=\"Tabd\" border=\"1\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:TCP\\left(D\\right)=\\frac{1}{1+\\text{e}\\text{x}\\text{p}\\left[4{\\gamma\\:}_{50}\\left(1-D/{D}_{50}\\right)\\right]}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eEquation 4\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u0026nbsp;\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{50}\\)\u003c/span\u003e\u0026nbsp;\u003c/span\u003e being the absorbed dose for which \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:TCP\\left({D}_{50}\\right)=0.5\\)\u003c/span\u003e\u003c/span\u003e and \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{\\gamma\\:}_{50}\\)\u003c/span\u003e\u003c/span\u003e is the percent change of TCP per percent change of absorbed dose around \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:{D}_{50}\\)\u003c/span\u003e\u003c/span\u003e, i.e. the slope of the linear part of the TCP curve.\u003c/p\u003e\n\u003cp\u003eThe fact that absorbed dose estimates in RPT are associated with large uncertainties is well documented. Indeed, while uncertainties in EBRT are below 5%, the uncertainties in RPT can go up to 40% (\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u0026ndash;\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e) depending mainly on the size of the target.\u003c/p\u003e\n\u003cp\u003eAnother source of error in establishing TCP models is the uncertainty related to the response evaluation. The most common method for response evaluation is the response evaluation criteria in solid tumours (RECIST). The RECIST v1.1 defines four response criteria according the measurement of lesions diameters (\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e). The complete response (CR) stand as the disappearance of all target and non-target lesions and the normalisation of tumour marker level and lymph nodes size. The partial response (PR) is at least 30% decrease in the sum of target lesions diameters or the persistence of one or more non-target lesions or abnormal tumour marker level. The progressive disease (PD) is at least 20% increase in the target lesions diameters from the nadir or the progression of non-target lesions or the appearance of new lesions. The stable disease (SD) is the state in between PR and PD. In clinical studies, CR, PR and SD criteria are also classified as disease control (DC), and CR and PR as objective response (OR). In a review by Fournier et al. (\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e) we found that the reproducibility of the diameter measurements vary from 10\u0026ndash;30% which could result in up to 30% of patients misclassified.\u003c/p\u003e\n\u003cp\u003eIn order to study the influence of uncertainties in the establishment of TCP models, we propose to model the two sources of uncertainties into simulated TCP models and to study their influence on the establishment of these models.\u003c/p\u003e"},{"header":"Materials and Methods","content":"\u003cp\u003eThree TCP models were defined from the logit function in Eq.\u0026nbsp;1 as a function of D/D\u003csub\u003e50\u003c/sub\u003e, so that TCP(x\u003csub\u003e50\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;0.5, with x\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1, for all models, but γ\u003csub\u003e50\u003c/sub\u003e values were respectively of 0.5, 0.75, and 1.0. For practical reason, the variable D/D\u003csub\u003e50\u003c/sub\u003e is noted x in the following equation:\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:TCP\\left(x\\right)=\\frac{1}{1+\\text{e}\\text{x}\\text{p}\\left[4{\\gamma\\:}_{50}\\left(1-x/{x}_{50}\\right)\\right]}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEquation 5\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eStarting from these models, 100 replicates of dose-response data. The variable x was first uniformly sampled in the range [0;2] and the response variable \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:r\\)\u003c/span\u003e\u003c/span\u003e was simulated as a binomial distribution following the probability law of Eq.\u0026nbsp;5. This dataset was labelled as the non-biased data. Then, \u003cem\u003er\u003c/em\u003e values were randomly modified to simulate an error rate in response classification of 10, 20 and 30%. An uncertainty was added to x values following a normal distribution with relative standard deviation of 5, 10, 15, 20 and 30% to simulate the uncertainty associated with the absorbed dose calculation. Then for each simulated biased dataset a logistic regression was performed. The adjusted logit function parameters γ\u003csub\u003e50\u003c/sub\u003e and x\u003csub\u003e50\u003c/sub\u003e were then compared to those of the actual TCP model. Additionally, the predicted characteristic value x\u003csub\u003e80\u003c/sub\u003e giving TCP(x\u003csub\u003e80\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;0.8 was compared to the actual one. The percentage root mean squared error (%RMSE) over all the evaluations were calculated following Eq.\u0026nbsp;6 for γ\u003csub\u003e50\u003c/sub\u003e, x\u003csub\u003e50\u003c/sub\u003e and x\u003csub\u003e80\u003c/sub\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\:\\%RMSE=\\frac{\\sqrt{\\sum\\:_{i=1}^{n}{\\frac{1}{n}\\left({predicted}_{i}-actual\\right)}^{2}}}{actual}\\times\\:100\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEquation 6\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe values of %RMSE(γ\u003csub\u003e50\u003c/sub\u003e), %RMSE(x\u003csub\u003e50\u003c/sub\u003e) and %RMSE(x\u003csub\u003e80\u003c/sub\u003e) were then plotted against the number of samples simulated stratified by the absorbed dose uncertainty and response error rate. Spearman correlations were calculated between %RMSE and dose uncertainty, response error rate and number of samples. Below 0.3, we considered there was no correlation, between 0.3 and 0.5, the correlation was weak, between 0.5 and 0.7, moderate and over 0.7, strong.\u003c/p\u003e \u003cp\u003eAll the study was done using R version 4.2.2 (\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e).\u003c/p\u003e"},{"header":"Results","content":"\u003cp\u003eAll three models had the same x\u003csub\u003e50\u003c/sub\u003e value of 1.0, while x\u003csub\u003e80\u003c/sub\u003e values were 1.80 for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.5, 1.54 for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.75 and 1.40 for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows examples of unbiased and biased data made for various values of γ50, dose uncertainty, response error rate, and number of samples. These examples illustrate how uncertainties affect the data and the logit fit in comparison to the original TCP model.\u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e shows that the more samples are used, the better the accuracy is on the estimation of TCP parameters, regardless of the uncertainty and error rate that biased the data. Lower values of γ\u003csub\u003e50\u003c/sub\u003e were associated with higher error levels for x\u003csub\u003e50\u003c/sub\u003e and x\u003csub\u003e80\u003c/sub\u003e. %RMSE(x\u003csub\u003e50\u003c/sub\u003e) was lower than 10% when the number of samples was over 250 for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.5, 175 for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.75, and 150 for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0.\u003c/p\u003e \u003cp\u003eIn predicting γ\u003csub\u003e50\u003c/sub\u003e, the median (IQR) %RMSE was 21% (17%), while for D\u003csub\u003e50\u003c/sub\u003e it was 7.4% (5.8%) and for D\u003csub\u003e80\u003c/sub\u003e 9.4% (7.8%) as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The %RMSE(γ\u003csub\u003e50\u003c/sub\u003e) was 23% (14%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.5, 21% (18%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.75, and 20% (19%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0. %RMSE(x\u003csub\u003e50\u003c/sub\u003e) was 9.2% (6.8%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.5, 7.0% (4.8%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.75, and 6.4% (4.0%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0. %RMSE(x\u003csub\u003e80\u003c/sub\u003e) was 13% (12%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.5, 8.9% (7.3%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.75, and 7.5% (6.2%) for γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0.\u003c/p\u003e \u003cp\u003e%RMSE(x\u003csub\u003e80\u003c/sub\u003e) remained below 10% for more than 300 samples when dose uncertainties were below 15% with γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.5. It remained below 10% over 250 samples with dose uncertainties below 20% and γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;0.75 and for more than 100 samples with dose uncertainties below 20% with γ\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1.0. %RMSE(γ\u003csub\u003e50\u003c/sub\u003e) was consistently over 10%, except for the highest number of samples (500) and the lowest dose uncertainties. %RMSE(γ\u003csub\u003e50\u003c/sub\u003e) was of approximately 30% for a dose uncertainty of 30%.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e"},{"header":"Discussion","content":"\u003cp\u003eThis study aimed to evaluate the impact of uncertainties on the development of tumour control probability (TCP) models in targeted radionuclide therapy. Two primary sources of uncertainty were analysed: those related to the absorbed dose and those stemming from response evaluation. Additionally, the influence of sample size on TCP estimation accuracy was investigated.\u003c/p\u003e \u003cp\u003eTo achieve this, 100 replicates of dose-response datasets were generated randomly, based on the probability function of three TCP profiles characterized by γ\u003csub\u003e50\u003c/sub\u003e and x\u003csub\u003e50\u003c/sub\u003e. Various levels of uncertainties were introduced into these simulations. Here, x\u003csub\u003e50\u003c/sub\u003e, which represents a relative dose (x\u0026thinsp;=\u0026thinsp;D/D\u003csub\u003e50\u003c/sub\u003e, x\u003csub\u003e50\u003c/sub\u003e\u0026thinsp;=\u0026thinsp;1), serves as a surrogate for D\u003csub\u003e50\u003c/sub\u003e, the dose associated with a 50% probability of tumour control. γ\u003csub\u003e50\u003c/sub\u003e indicates the slope around x\u003csub\u003e50\u003c/sub\u003e, functioning as a measure of radiosensitivity akin to the α/β ratio in the Lea-Catcheside linear-quadratic model; higher γ\u003csub\u003e50\u003c/sub\u003e values denote greater radiosensitivity.\u003c/p\u003e \u003cp\u003eThe results demonstrated that x\u003csub\u003e50\u003c/sub\u003e and x\u003csub\u003e80\u003c/sub\u003e were estimated with higher accuracy compared to γ\u003csub\u003e50\u003c/sub\u003e, with median %RMSE values of 7.4% and 9.4% for x\u003csub\u003e50\u003c/sub\u003e and x\u003csub\u003e80\u003c/sub\u003e, respectively, versus 21% for γ\u003csub\u003e50\u003c/sub\u003e. Interestingly, the increased error from greater dose uncertainty was mitigated by larger sample sizes. For example, a %RMSE of 4.63% for x\u003csub\u003e50\u003c/sub\u003e was achieved with 200 samples and no dose or response errors. The same error was observed with 500 samples, a 20% dose uncertainty, and a 30% response error rate.\u003c/p\u003e \u003cp\u003eOverall, %RMSE values were more influenced by dose uncertainty and sample size than by response error rates.\u003c/p\u003e"},{"header":"Conclusion","content":"\u003cp\u003eThe estimation of uncertainties is a crucial step in establishing dose-response profiles through TCP modelling in targeted radionuclide therapy. This study shows how the fitted TCP profiles are impacted by absorbed dose and response uncertainties. It also shows how increasing the number of samples (i.e. patients) can improve accuracy. Those results could help to design dose-effect relationship studies in radiopharmaceutical therapy clinical trials.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eContributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAll authors contributed to the study conception and design. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eEthics declarations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare no conflicts of interest regarding financial or non-financial relationships that could influence the objectivity of this research.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eNot applicable.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData from this article are available from the corresponding author on reasonable request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eStrigari L, Sciuto R, Rea S, et al. Efficacy and toxicity related to treatment of hepatocellular carcinoma with 90Y-SIR spheres: radiobiologic considerations. J Nucl Med. 2010;51:13771385.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHermann A-L, Dieudonn\u0026eacute; A, Ronot M et al. Relationship of Tumor Radiation\u0026ndash;absorbed Dose to Survival and Response in Hepatocellular Carcinoma Treated with Transarterial Radioembolization with 90 Y in the SARAH Study. Radiology. 2020:191606.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVeenstra EB, Ruiter SJS, de Haas RJ, Bokkers RPH, de Jong KP, Noordzij W. Post-treatment three-dimensional voxel-based dosimetry after Yttrium-90 resin microsphere radioembolization in HCC. EJNMMI Res. 2022;12:9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKappadath SC, Mikell J, Balagopal A, Baladandayuthapani V, Kaseb A, Mahvash A. Hepatocellular Carcinoma Tumor Dose Response After 90Y-radioembolization With Glass Microspheres Using 90Y-SPECT/CT-Based Voxel Dosimetry. Int J Radiat Oncol Biol Phys. 2018;102:451461.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDewaraja YK, Devasia T, Kaza RK et al. Prediction of tumor control in 90Y radioembolization by logit models with PET/CT based dose metrics. \u003cem\u003eJournal of nuclear medicine: official publication, Society of Nuclear Medicine\u003c/em\u003e. 2019:jnumed.119.226472.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRoman\u0026ograve; C, Mazzaglia S, Maccauro M, et al. Radioembolization of Hepatocellular Carcinoma with 90Y Glass Microspheres: No Advantage of Voxel Dosimetry with Respect to Mean Dose in Dose\u0026ndash;Response Analysis with Two Radiological Methods. Cancers (Basel). 2022;14:959.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBrenner DJ, Point. The linear-quadratic model is an appropriate methodology for determining iso-effective doses at large doses per fraction. Semin Radiat Oncol. 2008;18:234\u0026ndash;9.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFinocchiaro D, Gear JI, Fioroni F, et al. Uncertainty analysis of tumour absorbed dose calculations in molecular radiotherapy. EJNMMI Phys. 2020;7:63.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKayal G, Barbosa N, Mar\u0026iacute;n C, et al. Precision in dosimetric analysis and generation of a benchmark dosimetry dataset - An IAEA study. J Nucl Med. 2022;63:2812\u0026ndash;2812.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKayal G, Barbosa N, Mar\u0026iacute;n CC et al. October. Quality Assurance Considerations in Radiopharmaceutical Therapy Dosimetry Using PLANETDose: An International Atomic Energy Agency Study. \u003cem\u003eJournal of Nuclear Medicine\u003c/em\u003e. 2023.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eEisenhauer EA, Therasse P, Bogaerts J, et al. New response evaluation criteria in solid tumours: Revised RECIST guideline (version 1.1). Eur J Cancer. 2009;45:228\u0026ndash;47.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eFournier L, De Geus-Oei L-F, Regge D, et al. Twenty Years On: RECIST as a Biomarker of Response in Solid Tumours an EORTC Imaging Group \u0026ndash; ESOI Joint Paper. Front Oncol. 2022;11:800547.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eR Core Team. R: A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing; 2022.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"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":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"","lastPublishedDoi":"10.21203/rs.3.rs-5972271/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5972271/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003e\u003cstrong\u003ePurpose\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis study examines the impact of uncertainties in absorbed dose and response evaluations on establishing tumour control probability (TCP) profiles in radiopharmaceutical therapy (RPT).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eMethods\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eUsing three simulated TCP models with varying slopes (γ50), the impact of uncertainties of up to 30% in absorbed dose and response classification errors were studied. Logistic regressions on 100 simulated datasets assessed the accuracy of TCP parameters.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eResults\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe results show that dose uncertainties significantly affect TCP models but can be mitigated by increasing the sample size. Errors in response classification have a smaller impact. Parameters like x50 (dose for 50% tumour control) were more accurately predicted than γ50 (radiosensitivity). Accuracy improves notably when sample sizes exceed 300 and dose uncertainties remain below 15%.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eConclusion\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe findings highlight the importance of estimating uncertainties and increasing sample size to improve TCP model reliability in clinical studies.\u003c/p\u003e","manuscriptTitle":"How uncertainties could affect the establishment of tumour control probability profiles in radiopharmaceutical therapy?","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-02-24 15:22:11","doi":"10.21203/rs.3.rs-5972271/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"8640951a-9d0a-4e9b-9683-74e1e14f2639","owner":[],"postedDate":"February 24th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-03-28T09:18:21+00:00","versionOfRecord":[],"versionCreatedAt":"2025-02-24 15:22:11","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5972271","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5972271","identity":"rs-5972271","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}