Effects of adjusting for variable follow-up on the results of meta-analyses of time-to-event outcomes

Article type
Authors
Vale C, Tierney J, Stewart L
Abstract
Background: For meta-analyses of time-to-event outcomes such as survival or time to recurrence, the most appropriate outcome statistic is the hazard ratio. This takes account of both the number of events and the time to these events and so also allows for censoring. However, the hazard ratio can only be calculated directly if individual patient data has been collected. Alternatively, it can be estimated provided that sufficient statistical information is presented in the trial reports. The former approach is quite rare and the latter often practically difficult. More commonly, meta-analyses of time-to-event outcomes rely on estimating odds ratios (ORs) at fixed points in time. If these trials have been published at different stages in follow-up, censoring patterns will vary from trial to trial, and may affect the comparability and possibly the reliability of the different results. Methods are available to adjust (reduce) the numbers of patients at risk to allow for variable follow-up, but these are rarely applied. We have looked at the effect of using a simple method to adjust for variable follow-up on the survival results of meta-analyses in cancer.

Methods: Three meta-analyses of published survival data were carried out in lung cancer, bladder cancer and soft tissue sarcoma. Data at 1, 2, 3, 4 and 5 years were extracted from the trial reports. For the unadjusted meta-analyses, the numbers of patients that had died and the numbers at risk were used to calculate the ORs and associated statistics. For the adjusted meta-analyses, the number of patients at risk were first adjusted (reduced) based on the extent of follow-up, using a model that assumes constant and non-informative censoring. Based on these adjusted figures, adjusted ORs and associated statistics were derived.

Results: In the three meta-analyses, adjusting for limited follow-up had the direct effect of decreasing the weighting of individual trials in the pooled ORs. This effect becomes more pronounced where the follow-up becomes more disparate i.e. for 3, 4 and 5-year survival. Comparing the results of adjusted with unadjusted, the pooled ORs changed in nearly 80% of cases and the confidence intervals were almost always narrower. Again these differences tended to be greater at the 3, 4 and 5-year time points. Furthermore, in one case, adjusting altered the p-value associated with the pooled OR from being non-significant to coventionally significant, and in others the changes to the p-value may have affected interpretation of the results. The assessment of heterogeneity was also affected by adjusting for variable follow-up. The results of these completed and further ongoing comparisons will be presented.

Conclusions: The standard (unadjusted) method for carrying out a meta-analysis of published time-to-event data, assumes that follow-up is complete at the time point of analysis e.g. at 3 years all patients have been followed to 3 years, yet trial reports may state otherwise. Adjusting the numbers at risk and the numbers of events, ensures that trials are weighted according to the information they contribute, such that a large trial with poor follow-up is not given undue weight. It also means that ORs, confidence intervals and p-values reflect the uncertainty of curves extrapolated to distant time points