Individual patient data meta-analysis (IPD-MA) in the presence of competing risks
- I Hozo, B. Djulbegovic
- Cochrane Colloquium,
Introduction and objective The presence of a competing risk (CR) E2 in a time-to-event analysis of event E1 may render the use of conventional Kaplan-Meier estimates of cumulative event rates invalid if the times to occurrence of E1 and E2 are correlated (informative censoring). For instance, in cancer patients one may wish to assess the risk of occurrence of late treatment toxicities. Deaths due to cancer (or any causes other than the toxicity of interest) appear as a CR; the subsequent occurrence of toxicities, had the patient survived, can no longer be observed. The risk of cancer death may plausibly be correlated with the risk of toxicity. Methods are available for the calculation of valid cumulative incidence (CI) rates as a function of time in the presence of competing risks [1-3] for a single group of cases. CI methods are widely employed for CR in cancer patients such as graft-versus-host disease, recurrence and death , or local and distant recurrence . We propose two alternative methods for the calculation of competing risks cumulative incidence (CRCI) curves for each of the two treatment arms in a meta-analysis for which the individual patient survival times and event data are available. We applied these methods to a meta-analysis of second malignancy (SM) rates following treatment for Hodgkin’s lymphoma (HL); competing risks are deaths from causes other than SM. Materials and methods Our first approach is based upon Peto’s method for computation of odds ratios and time-to-event curves pooled over several trials [4,5]. Firstly, Peto’s method is used to compute pooled event-free survival (EFS) odds ratios and cumulative rates for each treatment arm at regular timepoints based on the occurrence of the first event of either type (E1, E2). Secondly, Peto’s method is applied to calculate pooled odds ratios for the event of interest (E1) at the same timepoints. Thirdly, the pooled EFS cumulative rates and the pooled E1 odds ratios are combined  to obtain cause-specific incidences, which are cumulated over time to give CRCI rates for event E1 in the presence of competing risk E2. In our second approach, CRCI rates and their variances are calculated separately for each arm of each trial. Within-trial differences in CRCI rates between the arms are pooled over trials using the inverse variance weighting method. Finally, pooled differences are used to compute pooled CRCI rates in each arm. The meta-analysis used for illustration was based upon individual patient data from 37 randomised trials comparing radiotherapy alone (RT), chemotherapy alone (CT) and combined chemo-radiotherapy (CRT) for untreated HL . For each treatment comparison, CRCI curves for SM, with non-SM death as competing risk, were computed and compared qualitatively with the conventional Peto time-to-SM curves. A further analysis of SM risk focussed on the effect of first-line therapy only, and censored at HL recurrence. Accordingly, HL recurrence was here regarded as a CR in addition to non-SM death. Results Illustrative results from our first approach (Peto-based) for the comparison RT versus CRT comparing conventional Peto cumulative SM rates with Peto-computed CRCI rates are depicted in Fig. 1, separately for patients with early and advanced stage disease. CRCI rates were markedly lower than the equivalent conventional Peto rates. In advanced stage patients, the disparity is larger due to the higher rate of non-SM death. However, the results with and without consideration of CR agree qualitatively with respect to the ratio of event rates between treatment arms. In the further analysis with censoring at HL recurrence, conventional cumulative SM rates were similar in both treatment arms, whereas CRCI rates were lower in the RT arm than in the CRT arm. This is a consequence of the higher HL recurrence rate after RT alone. Results of the second approach applied to the same data will be presented at the meeting.