Multivariate meta-analysis of prognostic factor studies with multiple cut-points and/or methods of measurement

Abstract

A prognostic factor is any measure that is associated with the risk of future health outcomes in those with existing disease. Often, the prognostic ability of a factor is evaluated in multiple studies. However, meta-analysis is difficult because primary studies often use different methods of measurement and/or different cut-points to dichotomise continuous factors into 'high' and 'low' groups; selective reporting is also common. We illustrate how multivariate random effects meta-analysis models can accommodate multiple prognostic effect estimates from the same study, relating to multiple cut-points and/or methods of measurement. The models account for within-study and between-study correlations, which utilises more information and reduces the impact of unreported cut-points and/or measurement methods in some studies. The applicability of the approach is improved with individual participant data and by assuming a functional relationship between prognostic effect and cut-point to reduce the number of unknown parameters. The models provide important inferential results for each cut-point and method of measurement, including the summary prognostic effect, the between-study variance and a 95% prediction interval for the prognostic effect in new populations. Two applications are presented. The first reveals that, in a multivariate meta-analysis using published results, the Apgar score is prognostic of neonatal mortality but effect sizes are smaller at most cut-points than previously thought. In the second, a multivariate meta-analysis of two methods of measurement provides weak evidence that microvessel density is prognostic of mortality in lung cancer, even when individual participant data are available so that a continuous prognostic trend is examined (rather than cut-points).

Keywords: cut-points; heterogeneity; multivariate meta-analysis; odds ratios and hazard ratios; prognostic factors.

Figure 1

Forest plot of the study estimates and meta‐analysis results for the prognostic effect of Ki‐67 for overall survival in patients with breast cancer.

Figure 2

Comparison of the individual study estimates and the summary meta‐analysis results obtained from model (5), assuming either a linear trend or an inverse quadratic trend, for the prognostic effect of the Apgar score at each cut‐point, in relation to neonatal mortality. Confidence intervals around each point are not shown for cosmetic reasons, but are provided for the summary estimates in Table 3. Odds ratios are defined as the odds of death for those with an Apgar score $\le$ cut‐point value, divided by the odds of death for those with an Apgar score > cut‐point value.