Robust Inference for Time-Varying Treatment Effects Under Irregular Longitudinal Sampling

Abstract

Among the key statistical problems in applied survival analysis is the proper estimation of time-to-event outcomes in cases where longitudinal measurements are irregular. The traditional Cox proportional hazards models are often assumed to have covariate effects that remain constant, and the observations are spaced at a regular time interval, which is not typically true in longitudinal data. To address bias due to nonregular time intervals and time-varying covariate effects, this paper suggests a more efficient time-varying coefficient joint model that serves to correct bias. The method is a composite Cox-type hazard model and penalized spline smoothing of temporal effects and a joint longitudinal sub-model to provide within-subject variability. To examine the performance in relation to the standard Cox model and shared random effects models, simulation experiments with different levels of irregularity and censoring were performed. The results indicate that the suggested approach can significantly decrease the estimation bias, enhance the accuracy of estimating hazard ratios, and offer a more accurate representation of the changing treatment impacts. Diagnostic tests ensure a stable model fit, constant variance, and decreased residual bias with time. The applicability of the model is also illustrated by empirical data of actuarial and biomedical situations, when covariate and survival processes can be observed. Overall, the results emphasize that ignoring the time-dependent and irregular nature of longitudinal data can lead to biased hazard estimates and misguided conclusions. The proposed model provides a statistically robust and computationally practical tool for analyzing such data. The paper concludes with recommendations for broader adoption of time-varying joint models and future research integrating regularization and machine learning approaches for high-dimensional and large-scale time-dependent data.