Recurrent events analysis with piece-wise exponential additive mixed models

Abstract

Recurrent events analysis plays an important role in many applications, including the study of chronic diseases or recurrence of infections. Historically, many models for recurrent events have been variants of the Cox model. In this article we introduce and describe the application of the piece-wise exponential Additive Mixed Model (PAMM) for recurrent events analysis and illustrate how PAMMs can be used to flexibly model the dependencies in recurrent events data. Simulations confirm that PAMMs provide unbiased estimates as well as equivalence to the Cox model when proportional hazards are assumed. Applications to recurrence of staphylococcus aureus and malaria in children illustrate the estimation of seasonality, bivariate non-linear effects, multiple timescales and relaxation of the proportional hazards assumption via time-varying effects. The R package pammtools is extended to facilitate estimation and visualization of PAMMs for recurrent events data.

A flexible approach to modelling stillbirths using the foetuses at risk approach

“…In analyses where we assumed that hazards were proportional, the two modelling approaches yielded identical results in both univariate and multivariable analyses, indicating that the estimation of the baseline hazard in PAMMs made little practical difference. This is consistent with the findings of a previous simulation study, which compared the two methods when the proportional hazards assumption was true 25 . Since PAMMs use penalization, there is less risk of overfitting than other parametric models, and based on the above agreement between models, minimal downside to estimating the baseline hazard.…”

“…This is consistent with the findings of a previous simulation study, which compared the two methods when the proportional hazards assumption was true. 25 Since PAMMs use penalization, there is less risk of overfitting than other parametric models, and based on the above agreement between models, minimal downside to estimating the baseline hazard. This penalised estimation allows one to include a diverse set of effects in the model, such as those demonstrated above, without making strong assumptions about the data generating mechanism.…”

Gametocyte production in incident P. falciparum infections: a longitudinal study in a low transmission setting under intensive vector control

“…The parameters in the model were estimated by a penalized maximum likelihood method within a competing risks framework. More specifically, and also similarly described elsewhere (Kopper Philipp; Ramjith, 2021; Ramjith et al, 2021; Bender Andreas, 2018) the hazard function at time t is defined as where events k = 1, 2 indicate gametocyte initiation and clearance of infection prior to gametocyte initiation respectively, exp ( β 0,k + f 0,k ( t j )) is the baseline hazard function at time t j for each of the events respectively, and t j is a chosen value of time within the interval (in our case τ j = τ j , the right boundary) that was used to make the hazard depend on time while being constant over time within the interval. Note that other choices of t j within the interval ( τ j− 1 , τ j ) can be made.…”

“…GAMMs allows for the modelling of complex non-linear relationships using smoothing splines (Belias et al, 2022) without the need for parametric assumptions of the shapes of the trajectories. GAMMs are extensively used in areas such as ecology (Pedersen et al, 2019), and have been used to model other infectious disease processes with complex non-linear effects and interactions, such as seasonality (Ramjith et al, 2021). While under-utilized in malaria epidemiology, Rodriguez-Barraquer (Rodriguez-Barraquer et al, 2018) used GAMMs to model the malaria incidence, parasite prevalence and density over age and exposure.…”

“…GAMMs allow for the modelling of complex non-linear relationships using smoothing splines (Belias et al, 2022) without the need for parametric assumptions of the shapes of the trajectories. GAMMs are extensively used in areas such as ecology (Pedersen et al, 2019), and have been used to model other infectious disease processes with complex non-linear effects and interactions, such as seasonality (Ramjith et al, 2021). As a result of the limited number of infections and failure to determine the complexity of infection in a substantial number of infections, especially in low-density infections (Early et al, 2019), we were unable to assess the impact of covariates on gametocyte production in a multivariate model.…”