Comparison of different parametric proportional hazards models for interval-censored data: a simulation study.

Interval censoring occurs frequently in clinical trials, but is often simplified to a right censoring problem because statistical methods in this area are under developed. It is recognized that analyzing interval censored data as right-censored data can lead to biased results. Although statistical methods have been developed to estimate survival function and to test hypothesis, estimating hazard ratio (HR) in a proportional hazards (PH) model for interval censored data remains as a challenge. Semi-parametric PH model was developed but difficult to implement, and thus rarely used in practice. Parametric PH method can be easily implemented but received little attention in practice because the impact of mis-specifying baseline hazard function on HR estimate was not well understood. We examined the performance of parametric PH models, using 3 baseline hazard functions: exponential, Weibull, and a 10-piece exponential function, under different underlying data distributions and censoring schema, through an extensive simulation study. Data were generated from 6 different models representing a range of possible scenarios in clinical trials. The simulation study revealed that mis-specifying baseline hazard function had little impact on the HR estimates. Robust estimate of HR with little bias and small mean square errors (MSE) were obtained using a PH model with a Weibull or 10-piece exponential function approximating baseline hazard function. Bigger bias and MSE were observed when using an exponential function to approximate a complex baseline hazard function. Examples are included. Based on these findings, we advocate the use of parametric PH models for the analysis of interval censored data.