Comparison of statistical methods for the analysis of patient-reported outcomes (PROs), particularly the Short-Form 36 (SF-36), in randomised controlled trials (RCTs) using standardised effect size (SES):an empirical analysis

Background: The Short-Form 36 (SF-36), a widely used patient-reported outcome (PRO), is a questionnaire completed by patients measuring health outcomes in clinical trials. The PRO scores can be discrete, bounded, and skewed. Various statistical methods have been suggested to analyse PRO data, but their results may not be presented on the same scale as the original score, making it difficult to interpret and compare different approaches. This study aims to unify and compare the estimates from different statistical methods for analysing PROs, particularly the SF-36, in randomised controlled trials (RCTs), using standardised effect size (SES) summary measure. Methods: SF-36 outcomes were analysed using ten statistical methods: multiple linear regression (MLR), median regression (Median), Tobit regression (Tobit), censored absolute least deviation regression (CLAD), beta-binomial regression (BB), binomial-logit-normal regression (BLN), ordered logit model (OL), ordered probit model (OP), fractional logistic regression (Frac), and beta regression (BR). Each SF-36 domain score at a specific follow-up in three clinical trials was analysed. The estimated treatment coefficients and SESs were generated, compared, and interpreted. Model fit was evaluated using the Akaike information criterion. Results: Estimated treatment coefficients from the untransformed scale-based methods (Tobit, Median, & CLAD) deviated from MLR, whereas the SESs from Tobit produced almost identical values. Transformed scale-based methods (OL, OP, BB, BLN, Frac, and BR) shared a similar pattern, except that OL generated higher absolute coefficients and BLN produced higher SESs than other methods. The SESs from Tobit, BB, OP, and Frac had better agreement against MLR than other included methods. Conclusions: The SES is a simple method to unify and compare estimates produced from various statistical methods on different scales. As these methods did not produce identical SES values, it is crucial to comprehensively understand and carefully select appropriate statistical methods, especially for analysing PROs like SF-36, to avoid drawing wrong estimates and conclusions using clinical trial data. Future research will focus on simulation analysis to compare the estimation accuracy and robustness of these methods.