Modelling strategies to improve estimates of prognostic factors analyses with patient reported outcomes: a simulation study

Modelling strategies to improve estimates of prognostic factors analyses with patient reported outcomes: a simulation study. Aims: The number of studies addressing the prognostic value of patient-reported outcomes (PROs) in oncology has been increasing over the last two decades. However, PROs are typically assessed using multi-dimensional questionnaires, and, without a priori hypotheses on which scales to consider in regression analysis, their simultaneous inclusion may impair the stability of the final prognostic model and parameters estimates, particularly when scales are highly correlated. We aimed to compare the performance of standard stepwise and penalized regression strategies in estimating parameters of interest, when multicollinearity exists amongst PRO scales. Methods: We carried out a simulation study to compare the performance in estimating regression coefficients (by calculating standardized bias and root mean squared error, RMSE) of stepwise and ridge Cox regression (Cox-R). Stepwise was based both on Akaike Information Criterion (Cox-AIC) and entry/exit significance level α=0.05 (Cox-P). Twenty-seven different scenarios were investigated, according to the combination of different degrees of multicollinearity (0.2, 0.4 and 0.8), event rates (30%, 50% and 70%) and sample sizes (100, 300 and 500 patients). Four clinical/socio-demographical variables and five PROs correlated scales were simulated and associated to overall survival (OS) times, considering a follow-up period of 24 months. Right censoring of OS times was allowed. The five PRO scales were simulated using the polytomous Rasch partial credit model, and comprised Global health status/QoL, Physical functioning, Fatigue, Pain and Appetite loss from the EORTC QLQ-C30 questionnaire. For each scenario, all methods described above were applied to each of 1000 independently generated datasets. Results: CoxR showed better performance in all scenarios, particularly in those with medium-high multicollinearity and small sample size. Conversely, stepwise methods performed particularly poorly, generally not selecting any of the highly correlated scales (Cox-P) or including only some of them (Cox-AIC). In addition, their coefficients were overestimated with wide 95% Confidence Intervals (CIs). Cox-R provided narrower CIs, lower bias, ranging from 0.00 to 0.10 vs 0.00 to 3.64 of stepwise methods, and lower RMSEs, ranging from 0.02 to 0.11 vs 0.03 to 0.19 of stepwise methods. Conclusions: Our results suggest ridge Cox regression as the best approach when performing prognostic factor analyses with multiple and collinear PROs scales.