Abstract
We present mexhaz, an R package for fitting flexible hazard-based regression models with the possibility to add time-dependent effects of covariates and to account for a twolevel hierarchical structure in the data through the inclusion of a normally distributed random intercept (i.e., a log-normally distributed shared frailty). Moreover, mexhazbased models can be fitted within the excess hazard setting by allowing the specification of an expected hazard in the model. These models are of common use in the context of the analysis of population-based cancer registry data. Follow-up time can be entered in the right-censored or counting process input style, the latter allowing models with delayed entries. The logarithm of the baseline hazard can be flexibly modeled with B-splines or restricted cubic splines of time. Parameters estimation is based on likelihood maximization: in deriving the contribution of each observation to the cluster-specific conditional likelihood, Gauss-Legendre quadrature is used to calculate the cumulative hazard; the cluster-specific marginal likelihoods are then obtained by integrating over the random effects distribution, using adaptive Gauss-Hermite quadrature. Functions to compute and plot the predicted (excess) hazard and (net) survival (possibly with cluster-specific predictions in the case of random effect models) are provided. We illustrate the use of the different options of the mexhaz package and compare the results obtained with those of other available R packages.
Highlights
In the context of the analysis of time-to-event data, parametric and semi-parametric hazard regression models are widely used when the interest lies in estimating the impact of covariates mexhaz: Mixed-Effect Excess Hazard Regression Models in R on the time to occurrence of the event of interest
We focus here on the two main extensions proposed in our package, namely the possibility to include time-dependent effects and a random effect, in comparison with two existing tools proposed in R by default, mgcv (Wood 2017) and nlme (Pinheiro, Bates, and R Core Team 2021)
The mexhaz package combines different tools to model time-to-event data based on maximum likelihood theory, from flexible parametric models up to flexible parametric excess hazard
Summary
In the context of the analysis of time-to-event data, parametric and semi-parametric hazard regression models are widely used when the interest lies in estimating the impact of covariates mexhaz: Mixed-Effect Excess Hazard Regression Models in R on the time to occurrence of the event of interest. One possibility to take advantage of parametric models without making unrealistic assumptions on the shape of the hazard (and on the corresponding survival) is to use flexible functions, such as fractional polynomials or regression splines. The correct modeling of the data might require the inclusion of time-dependent effects of some of the covariates. It has been shown in many studies that the effects of covariates such as age may vary with time since diagnosis, especially in cancer epidemiology, so that the proportional hazard assumption does no longer hold (Quantin et al 1999; Bossard et al 2007)
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