Approximating the baseline Hazard function by Taylor series for interval-censored time-to-event data

In many oncology clinical trials, time-to-event data are generated from scanning for cancer within a specific interval, resulting in interval censoring along with complete-time and right-left-censored time-to-event data. A common practice in analyzing data from this type of trial is to impute the interval-censored event time using the midpoint or right endpoint (i.e., the first observed time) of the interval so that well-known statistical methods developed for right-censored time-to-event data, such as Cox regression, may be used for the requisite analyses. This may introduce bias and lead to erroneous conclusions. In this paper, a Taylor series is proposed to approximate the log baseline hazard function in Cox proportional hazards regression to mitigate the bias arising from analyzing the imputed time-to-event data. With this formulation, the likelihood ratio test can be used to select an appropriate order for this Taylor series approximation and maximum likelihood techniques used to estimate model parameters and provide statistical inference, for example, on treatment effect. The application of this novel method is demonstrated by a simulation study and application to data from a breast cancer clinical trial.