Subgroup analysis of treatment effects for misclassified biomarkers with time‐to‐event data

Analysing subgroups defined by biomarkers is of increasing importance in clinical research. In many situations the biomarker is subject to misclassification error, meaning that the subgroups are identified with imperfect sensitivity and specificity. In these cases, it is improper to assume the Cox proportional hazards model for the subgroup‐specific treatment effects for time‐to‐event data with respect to the true subgroups, since the survival distributions with respect to the diagnosed subgroups will not adhere to the proportional hazards assumption. This precludes the possibility of using simple adjustment procedures. Two approaches to modelling are considered; the corrected score approach and a method based on formally modelling the data as a mixture of Cox models using an expectation–maximization algorithm for estimation. The methods are comparable for moderate‐to‐large sample sizes, but the expectation–maximization algorithm performs better when there are 100 patients per group. An estimate of the overall population treatment effect is obtained through the interpretation of the hazard ratio as a concordance odds. The methods are illustrated on data from a renal cell cancer trial.