Quantifying Change Over Time: Interpreting Time-varying Effects In Duration Analyses

Duration analyses in political science often model nonproportional hazards through interactions with analysis time. To facilitate their interpretation, methodologists have proposed methods to visualize time-varying coefficients or hazard ratios. While these techniques are a useful, initial postestimation step, I argue that they are insufficient to identify the overall impact of a time-varying effect and may lead to faulty inference when a coefficient changes its sign. I show how even significant changes of a coefficient’s sign do not imply that the overall effect is reversed over time. In order to enable a correct interpretation of time-varying effects in this context, researchers should visualize their results with survivor functions. I outline how survivor functions are calculated for models with time-varying effects and demonstrate the need for such a nuanced interpretation using the prominent finding of a time-varying effect of mediation on interstate conflict. The reanalysis of the data using the proposed visualization methods indicates that the conclusions of earlier mediation research are misleading. The example highlights how survivor functions are an essential tool to clarify the ambiguity inherent in time-varying coefficients in event history models.

Conditional Transformation Models for Survivor Function Estimation

In survival analysis, the estimation of patient-specific survivor functions that are conditional on a set of patient characteristics is of special interest. In general, knowledge of the conditional survival probabilities of a patient at all relevant time points allows better assessment of the patient’s risk than summary statistics, such as median survival time. Nevertheless, standard methods for analysing survival data seldom estimate the survivor function directly. Therefore, we propose the application of conditional transformation models (CTMs) for the estimation of the conditional distribution function of survival times given a set of patient characteristics. We used the inverse probability of censoring weighting approach to account for right-censored observations. Our proposed modelling approach allows the prediction of patient-specific survivor functions. In addition, CTMs constitute a flexible model class that is able to deal with proportional as well as non-proportional hazards. The well-known Cox model is included in the class of CTMs as a special case. We investigated the performance of CTMs in survival data analysis in a simulation that included proportional and non-proportional hazard settings and different scenarios of explanatory variables. Furthermore, we re-analysed the survival times of patients suffering from chronic myelogenous leukaemia and studied the impact of the proportional hazards assumption on previously published results.