# Sensitivity analysis for reporting bias on the time-dependent summary receiver operating characteristics curve in meta-analysis of prognosis studies with time-to-event outcomes

## TL;DR

This paper introduces a new method to adjust for reporting bias in meta-analyses of biomarker prognostic studies with time-to-event outcomes.

## Contribution

A novel sensitivity analysis method is proposed to quantify and adjust reporting bias in time-dependent SROC curves.

## Key findings

- The proposed method reduces reporting bias when the selection probability is correctly specified.
- The method was successfully applied to a real-world meta-analysis of Ki67 in breast cancer.
- Simulation studies validated the effectiveness of the sensitivity analysis approach.

## Abstract

In prognosis studies with time-to-event outcomes, the survivals of groups with high/low biomarker expression are often estimated by the Kaplan–Meier method, and the difference between groups is measured by the hazard ratios (HRs). Since the high/low expressions are usually determined by study-specific cutoff values, synthesizing only HRs for summarizing the prognostic capacity of a biomarker brings heterogeneity in the meta-analysis. The time-dependent summary receiver operating characteristics (SROC) curve was proposed as a cutoff-free summary of the prognostic capacity, extended from the SROC curve in meta-analysis of diagnostic studies. However, estimates of the time-dependent SROC curve may be threatened by reporting bias in that studies with significant outcomes, such as HRs, are more likely to be published and selected in meta-analyses. Under this conjecture, this paper proposes a sensitivity analysis method for quantifying and adjusting reporting bias on the time-dependent SROC curve. We model the publication process determined by the significance of the HRs and introduce a sensitivity analysis method based on the conditional likelihood constrained by some expected proportions of published studies. Simulation studies showed that the proposed method could reduce reporting bias given the correctly-specified marginal selection probability. The proposed method is illustrated on the real-world meta-analysis of Ki67 for breast cancer.