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

A multistate competing risks framework for preconception prediction of pregnancy outcomes

Background

Preconception pregnancy risk profiles—characterizing the likelihood that a pregnancy attempt results in a full-term birth, preterm birth, clinical pregnancy loss, or failure to conceive—can provide critical information during the early stages of a pregnancy attempt, when obstetricians are best positioned to intervene to improve the chances of successful conception and full-term live birth. Yet the task of constructing and validating risk assessment tools for this earlier intervention window is complicated by several statistical features: the final outcome of the pregnancy attempt is multinomial in nature, and it summarizes the results of two intermediate stages, conception and gestation, whose outcomes are subject to competing risks, measured on different time scales, and governed by different biological processes. In light of this complexity, existing pregnancy risk assessment tools largely focus on predicting a single adverse pregnancy outcome, and make these predictions at some later, post-conception time point.

Methods

We reframe the individual pregnancy attempt as a multistate model comprised of two nested multinomial prediction tasks: one corresponding to conception and the other to the subsequent outcome of that pregnancy. We discuss the estimation of this model in the presence of multiple stages of outcome missingness and then introduce an inverse-probability-weighted Hypervolume Under the Manifold statistic to validate the resulting multivariate risk scores. Finally, we use data from the Effects of Aspirin in Gestation and Reproduction (EAGeR) trial to illustrate how this multistate competing risks framework might be utilized in practice to construct and validate a preconception pregnancy risk assessment tool.

Results

In the EAGeR study population, the resulting risk profiles are able to meaningfully discriminate between the four pregnancy attempt outcomes of interest and represent a significant improvement over classification by random chance.

Conclusions

As illustrated in our analysis of the EAGeR data, our proposed prediction framework expands the pregnancy risk assessment task in two key ways—by considering a broader array of pregnancy outcomes and by providing the predictions at an earlier, preconception intervention window—providing obstetricians and their patients with more information and opportunities to successfully guide pregnancy attempts.

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.