Study design and statistical methods to account for unexplained heterogeneity in medical studies with a time to event outcome
Final Report Abstract
In many medical studies the time to some event is of primary interest, for example the time to disease progression or the time to re-hospitalisation. Frequently, regression modelling techniques are used to explore treatment effects or differences between patients with respect to event times. Unfortunately, often some of the patient characteristics that considerably affect the outcome are not yet known or not yet properly investigated. Such unexplained heterogeneity between subjects within the same study will not only reduce the precision of study results but can also cause bias of regression coefficient estimates. Whereas the consequences of unexplained heterogeneity are well understood for single event time data, they have only been investigated for few multiple event data settings before. In the present project, analytical tools for quantifying biases in effect estimates and thus for comparing different modeling strategies have been derived for some important situations. Motivated by cardiovascular clinical trials, we particularly focussed on recurrent event data with competing, terminal events. Here, treatment effects both on mortality (assessed as cardiovascular death) and morbidity (assessed as recurrent non-fatal hospitalisations) are to be evaluated. Random (frailty) terms that act both on the recurrent and terminal event rate can describe unobserved patient heterogeneity, will induce an association between both rates, and violate the proportional hazards assumption of prominent marginal models. In the present project, we derived the asymptotic characteristics of parameter estimates (log-hazard-ratio estimates or more generally maximum partial likelihood estimates) when erroneously relying on such a marginal model. We particularly considered the frequently applied LWYY regression model and a recently proposed proportional means model, where inverse probability weights are used to estimate expected event frequencies. Our published findings clearly show, how terminal events affect marginal hazard ratio estimates for recurrent events and in which situations we get systematically over- or underestimated effects. Our results also well explain differences between treatment effect estimates when derived from different modeling strategies, as reported for large heart failure trials. We consider this as strongly needed for a proper interpretation of trial results. Furthermore, we could use our findings to investigate, how adverse treatment effects on mortality may be masked within a composite endpoint. Further work in progress covers the research question how landmark methods can help to deal with unexplained and potentially time-varying heterogeneity in time-to-event data. This might contribute to the analysis of cohort data with subject-specific treatment durations. Whithin the project we also fitted joint frailty models to real and simulated data and surprisingly found out that neither an established R package nor a published SAS®-macro for fitting joint frailty models provide reliable results. By deriving a proper decomposition of the conditional likelihood into event-specific contributions and using probability-integral-transformations and likelihoodreformulation methods we identified a robust implementation using SAS®. Our published results also include user-friendly macros with the recommended implementation as a supplement. In summary, our research will help to identify proper modeling strategies for multiple event data, provide a better understanding of published treatment effect estimates from clinical trials and support users in the computational implementation of methods.
Publications
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(2017). A DAG-based comparison of interventional effect underestimation between composite endpoint and multi-state analysis in cardiovascular trials. BMC Medical Research Methodology 17, 92
Jahn-Eimermacher, A., Ingel, K., Preussler, S., Bayes-Genis, A., and Binder, H.
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(2018). Timeto-first-event versus recurrent-event analysis: points to consider for selecting a meaningful analysis strategy in clinical trials with composite endpoints. Clinical Research in Cardiology 107, 437–443
Rauch, G., Kieser, M., Binder, H., Bayes-Genis, A., and Jahn-Eimermacher, A.
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(2019). Marginal hazard ratio estimates in joint frailty models for heart failure trials. Biometrical Journal 61, 1385-1401
Toenges, G., and Jahn-Eimermacher, A.
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(2020). Computational issues in fitting joint frailty models for recurrent events with an associated terminal event. Computer Methods and Programs in Biomedicine 188, 105259
Toenges, G., and Jahn-Eimermacher, A.
