  In the analysis of prognosis studies with time-to-event outcomes,
dichotomization of patients is often made. As the evaluations of prognostic
capacity, the survivals of groups with high/low expression of the biomarker are
often estimated by the Kaplan-Meier method, and the difference between groups
is summarized via the hazard ratio (HR). The high/low expressions are usually
determined by study-specific cutoff values, which brings heterogeneity over
multiple prognosis studies and difficulty to synthesizing the results in a
simple way. In meta-analysis of diagnostic studies with binary outcomes, the
summary receiver operating characteristics (SROC) analysis provides a useful
cutoff-free summary over studies. Recently, this methodology has been extended
to the time-dependent SROC analysis for time-to-event outcomes in meta-analysis
of prognosis studies. In this paper, we propose a sensitivity analysis method
for evaluating the impact of publication bias on the time-dependent SROC
analysis. Our proposal extends the recently introduced sensitivity analysis
method for meta-analysis of diagnostic studies based on the bivariate normal
model on sensitivity and specificity pairs. To model the selective publication
process specific to prognosis studies, we introduce a trivariate model on the
time-dependent sensitivity and specificity and the log-transformed HR. Based on
the proved asymptotic property of the trivariate model, we introduce a
likelihood based sensitivity analysis method based on the conditional
likelihood constrained by the expected proportion of published studies. We
illustrate the proposed sensitivity analysis method through the meta-analysis
of Ki67 for breast cancer. Simulation studies are conducted to evaluate the
performance of the proposed method.
