Comparison of statistical methods for the analysis of recurrent adverse events in the presence of non-proportional hazards and unobserved heterogeneity: a simulation study

Noel Patson,Marinus J C Eijkemans,Mavuto Mukaka,Don Mathanga,Tobias Chirwa,Miriam K Laufer,Lawrence Kazembe

doi:10.1186/s12874-021-01475-8

Abstract

BackgroundIn preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected. Challenges in modelling the risk of the AEs include accounting for time-to-AE and within-patient-correlation, beyond the conventional methods. The correlation comes from two sources; (a) individual patient unobserved heterogeneity (i.e. frailty) and (b) the dependence between AEs characterised by time-dependent treatment effects. Potential AE-dependence can be modelled via time-dependent treatment effects, event-specific baseline and event-specific random effect, while heterogeneity can be modelled via subject-specific random effect. Methods that can improve the estimation of both the unobserved heterogeneity and treatment effects can be useful in understanding the evolution of risk of AEs, especially in preventive trials where time-dependent treatment effect is expected.MethodsUsing both a simulation study and the Chloroquine for Malaria in Pregnancy (NCT01443130) trial data to demonstrate the application of the models, we investigated whether the lognormal shared frailty models with restricted cubic splines and non-proportional hazards (LSF-NPH) assumption can improve estimates for both frailty variance and treatment effect compared to the conventional inverse Gaussian shared frailty model with proportional hazard (ISF-PH), in the presence of time-dependent treatment effects and unobserved patient heterogeneity. We assessed the bias, precision gain and coverage probability of 95% confidence interval of the frailty variance estimates for the models under varying known unobserved heterogeneity, sample sizes and time-dependent effects.ResultsThe ISF-PH model provided a better coverage probability of 95% confidence interval, less bias and less precise frailty variance estimates compared to the LSF-NPH models. The LSF-NPH models yielded unbiased hazard ratio estimates at the expense of imprecision and high mean square error compared to the ISF-PH model.ConclusionThe choice of the shared frailty model for the recurrent AEs analysis should be driven by the study objective. Using the LSF-NPH models is appropriate if unbiased hazard ratio estimation is of primary interest in the presence of time-dependent treatment effects. However, ISF-PH model is appropriate if unbiased frailty variance estimation is of primary interest.Trial registrationClinicalTrials.gov; NCT01443130

Highlights

In preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected
We present the findings of our simulation study and apply the models to the analysis of recurrent AEs observed in Chloroquine for Malaria in pregnancy trial (NCT01443130)
Frailty variance estimates coverage probability, bias and mean square error (MSE) across the shared frailty models Based on 1000 simulations for each scenario, we observed a 100% convergence rate of all the models that were fitted

Summary

Introduction

In preventive drug trials such as intermittent preventive treatment for malaria prevention during pregnancy (IPTp), where there is repeated treatment administration, recurrence of adverse events (AEs) is expected. In the framework of benefit-risk assessment, two models (the Andersen Gill model and Prentice, Williams and Peterson model) have been demonstrated to be useful in providing both direct and indirect effects of treatment on AE recurrence [6] These models yield unbiased estimates if the AEs are uncorrelated and do not efficiently capture (i.e. account for) both potential time-dependent treatment effects and unobserved heterogeneity. This motivates the need to consider using flexible parametric shared frailty models that can optimally capture both the time-dependent effects and unobserved heterogeneity, to improve drug safety estimates

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Conclusion