Proportional hazards regression for cancer screening data

The complication in analysing tumour data is that the tumours detected in a screening programme tend to be slowly progressive, which is the so-called left-truncated sampling that is inherent in screening studies. Under the assumption that all subjects have the same tumour growth function, Ghosh [Proportional hazards regression for cancer studies, Biometrics 64 (2008), pp. 141-148] developed estimation procedures for proportional hazards model. In this note, by modelling growth function as a function of covariates and parameterizing the distribution function of left truncation time, we demonstrate that Ghosh's approach can be extended to the case when each subject has a specific growth function. A simulation study is conducted to demonstrate the potential usefulness of the proposed estimators for the regression parameters in the proportional hazards model.