  Analysing subgroups defined by biomarkers is of increasing importance in
clinical research. In some situations the biomarker is subject to
misclassification error, meaning the true subgroups are identified with
imperfect sensitivity and specificity. For time-to-event data, it is improper
to assume the Cox proportional hazards model for the effects 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. Instead,
we present a method based on formally modelling the data as a mixture of Cox
models using an EM algorithm for estimation. An estimate of the overall
population treatment effect is obtained through the interpretation of the
hazard ratio as a concordance odds. Profile likelihood is used to construct
individual and simultaneous confidence intervals of treatment effects. The
resulting confidence intervals are shown to have close to nominal coverage for
moderately large sample sizes in simulations and the method is illustrated on
data from a renal-cell cancer trial.
