A comparison of the beta-geometric model with landmarking for dynamic prediction of time to pregnancy

We conducted a simulation study to compare two methods that have been recently used in clinical literature for the dynamic prediction of time to pregnancy. The first is landmarking, a semi-parametric method where predictions are updated as time progresses using the patient subset still at risk at that time point. The second is the beta-geometric model that updates predictions over time from a parametric model estimated on all data and is specific to applications with a discrete time to event outcome. The beta-geometric model introduces unobserved heterogeneity by modelling the chance of an event per discrete time unit according to a beta distribution. Due to selection of patients with lower chances as time progresses, the predicted probability of an event decreases over time. Both methods were recently used to develop models predicting the chance to conceive naturally. The advantages, disadvantages and accuracy of these two methods are unknown. We simulated time-to-pregnancy data according to different scenarios. We then compared the two methods by the following out-of-sample metrics: bias and root mean squared error in the average prediction, root mean squared error in individual predictions, Brier score and c statistic. We consider different scenarios including data-generating mechanisms for which the models are misspecified. We applied the two methods on a clinical dataset comprising 4999 couples. Finally, we discuss the pros and cons of the two methods based on our results and present recommendations for use of either of the methods in different settings and (effective) sample sizes.