Model misspecification effect in univariable regression models for right-censored survival data

We examine the effect of model misspecification for two classes of semi-parametric survival models frequently used for the analysis of right-censored survival data, additive and multiplicative models for the conditional hazard rate. The additive class will be represented by Aalen’s linear model [1], while the multiplicative class will be represented by the Cox proportional hazards (PH) model [2] and Gray’s time-varying coefficients (TVC) model [3]. Both Aalen’s and Gray’s model incorporate TVC, which will receive a particular attention. It is often the case that right-censored survival data are analyzed without prior verification of the assumptions of an assumed model. We perform a simulation study to cross-analyze survival data that follow either additive or multiplicative model for the conditional hazard rate involving a single continuous covariate. The effect of misspecifying the true model is assessed by estimating the power of Aalen’s, Cox’s and Gray’s analysis model, respectively, to detect an existing effect and by comparing the mean square error (MSE) and bias of the conditional estimator of survival obtained for each of the three models used in analyzing the data. Formulas for the bias and MSE of the conditional survival distribution rely on the ability of the fitted model to estimate survival. Specifically, the survival function estimator for Gray’s PC-TVC model [4] is used for the evaluation of the bias, MSE and the true survival function, when Gray’s model is assumed. Under the multiplicative Cox PH model, for a patient with covariates z ∈ R, the conditional hazard rate λ(t|z) is modeled as: λ(t|z) = λ0(t) exp {β z} , (1)