Using dynamic path analysis to estimate a mediation effect through a survival variable

Time-to-event composite outcomes are common in clinical trials. Reporting guidelines recommend that the treatment effect estimate for each component event be reported. In the setting with two components, when one precedes the other, there may be interest in estimating the indirect effect of treatment on the final event through the intermediate one. This thesis proposes a pragmatic solution to this problem. The motivating example is a dataset pooled from three clinical trials investigating a treatment effect on time to cancer progression or death in patients with advanced non-small cell lung cancer. There is interest in exploring whether treatment had an indirect effect on death through its effect on progression. This problem could be addressed by implementing dynamic path analysis, which combines linear regression and additive hazards models to estimate the indirect effect of an exposure on a time-to-event outcome. However, it is only appropriate for settings with continuous intermediate variables. The thesis therefore suggests an extension dealing with settings where both intermediate and final events are time-to-event variables. This extension is described and tested using simulation studies. The results suggest that this method gives rise to results very close to those predicted, when the rate of the intermediate event is not very fast relative to the final event rate. When the intermediate event occurs much more quickly than the final event, depletion of individuals from the risk set by experiencing the final event causes divergence between the estimated and expected indirect treatment effects. The extension of dynamic path analysis is implemented for the clinical trials dataset, showing a protective indirect effect of treatment on death through cancer progression. The thesis concludes that the extension of dynamic path analysis to settings with a time-to-event intermediate outcome is feasible, although some results should be interpreted with care.