We would like to clarify a few points and report an erratum to our paper entitled “Parametric mixture models to evaluate and summarize hazard ratios in the presence of competing risks with time-dependent hazards and delayed entry” .
First, there is a minor typographical error on page 655 third line from the bottom. In the equation for the cumulative incidence function that integrates the net survival function, the hazard should be indexed by j such that the correct equation should be as follows:
Second, as a point of clarification in the sentence subsequent to equation (6), we mention that S0j(t) is the net survival function for the arbitrary baseline hazard function. However, in our prior notation we stated that the net survival function was S(t). Therefore, to be consistent with our prior notation the net survival function should not be indexed by j, and equation (6) should be the following:
Additionally, in equation (7) there was a minor typographical error in that an asterisk was inadvertently left out of the first denominator and should be as follows:
Furthermore, the likelihood function in the appendix for left truncation and interval censoring is incorrect as the contributions should be conditioned on the net survival rather than being indexed by event type. Therefore, the likelihood for left truncation is the following:
and for left truncation and interval censoring is as follows:
where again S(t) is the net survival function which may be written as a mixture of the two distributions' corresponding survival functions as indicated in the paper (S(t) = πS1(t) + (1 − π)S2(t)). The correction to the likelihood shifted the curves in Figure 2, but overall patterns and inferences were similar and do not impact the main results in Tables 1 and 2 or Figure 1 as those results were not subject to left truncation.
Finally, it has come to our attention that stata 11 (and more recent versions) can account for left truncation in the Fine and Gray subdistribution proportional hazards model. In closing, we would like to thank Professor Alvaro Muñoz for his careful reading of our paper.