A simple and robust parametric shared frailty model for recurrent events with the competing risk of death: An application to the Carvedilol Prospective Randomized Cumulative Survival trial

Many non-fatal events can be considered recurrent in that they can occur repeatedly over time, and some researchers may be interested in the trajectory and relative risk of non-fatal events. With the competing risk of death, the treatment effect on the mean number of recurrent events is non-identifiable since the observed mean is a function of both the recurrent event and terminal event processes. In this paper, we assume independence between the non-fatal and the terminal event process, conditional on the shared frailty, to fit a parametric model that recovers the trajectory of, and identifies the effect of treatment on, the non-fatal event process in the presence of the competing risk of death. Simulation studies are conducted to verify the reliability of our estimators. We illustrate the method and perform model diagnostics using the Carvedilol Prospective Randomized Cumulative Survival trial which involves heart-failure events.

Analysis of Recurrent Times-to-Clinical Malaria Episodes and Plasmodium falciparum Parasitemia: A Joint Modeling Approach Applied to a Cohort Data

Background

Recurrent clinical malaria episodes due to Plasmodium falciparum parasite infection are common in endemic regions. With each infection, acquired immunity develops, making subsequent disease episodes less likely. To capture the effect of acquired immunity to malaria, it may be necessary to model recurrent clinical disease episodes jointly with P. falciparum parasitemia data. A joint model of longitudinal parasitemia and time-to-first clinical malaria episode (single-event joint model) may be inaccurate because acquired immunity is lost when subsequent episodes are excluded. This study's informativeness assessed whether joint modeling of recurrent clinical malaria episodes and parasitemia is more accurate than a single-event joint model where the subsequent episodes are ignored.

Methods

The single event joint model comprised Cox Proportional Hazards (PH) sub-model for time-to-first clinical malaria episode and Negative Binomial (NB) mixed-effects sub-model for the longitudinal parasitemia. The recurrent events joint model extends the survival sub-model to a Gamma shared frailty model to include all recurrent clinical episodes. The models were applied to cohort data from Malawi. Simulations were also conducted to assess the performance of the model under different conditions.

Results

The recurrent events joint model, which yielded higher hazard ratios of clinical malaria, was more precise and in most cases produced smaller standard errors than the single-event joint model; hazard ratio (HR) = 1.42, [95% confidence interval [CI]: 1.22, 2.03] vs. HR = 1.29, [95% CI:1.60, 2.45] among participants who reported not to use LLINs every night compared to those who used the nets every night; HR = 0.96, [ 95% CI: 0.94, 0.98] vs. HR = 0.81, [95% CI: 0.75, 0.88] for each 1-year increase in participants' age; and HR = 1.36, [95% CI: 1.05, 1.75] vs. HR = 1.10, [95% CI: 0.83, 4.11] for observations during the rainy season compared to the dry season.

Conclusion

The recurrent events joint model in this study provides a way of estimating the risk of recurrent clinical malaria in a cohort where the effect of immunity on malaria disease acquired due to P. falciparum parasitemia with aging is captured. The simulation study has shown that if correctly specified, the recurrent events joint model can give risk estimates with low bias.

A shared frailty model for multivariate longitudinal data on adverse event of radiation therapy

Oral mucositis is an inflammatory adverse event when treating head and neck cancer patients with radiation therapy (RT). The severity of its occurrence is believed to mainly depend on its site and the distribution of a cumulative radiation dose in the mouth area. The motivating study investigating differences in radiosensitivities (mucositis progression) at distinct sites where the severity of mucositis is assessed regularly at eight distinct sites on an ordinal scale results in multivariate longitudinal data and thus poses certain challenges. To deal with the multivariate longitudinal data in this particular setting, we take a time-to-event approach focusing on the first occurrence of severe mucositis at the distinct sites using the fact that the site-specific cumulative radiation dose thought to be the main driver of oral mucositis develops over time. Thereby, we may address multivariate longitudinal processes in a simpler and more compact fashion. In this article, to find out differences in mucositis progression at eight distinct sites we propose a shared frailty model for multivariate parallel processes within individuals. The shared frailty model directly incorporating 'process indicators' as covariates turns out to adequately explain the differences in the parallel processes (here, mucositis progressions at distinct sites) while taking individual effects into account. The parallel result with the one from the previous analysis based on the same data but conducted with an alternative statistical methodology shows adequacy of the proposed approach.

General Semiparametric Shared Frailty Model: Estimation and Simulation with frailtySurv

The R package frailtySurv for simulating and fitting semi-parametric shared frailty models is introduced. Package frailtySurv implements semi-parametric consistent estimators for a variety of frailty distributions, including gamma, log-normal, inverse Gaussian and power variance function, and provides consistent estimators of the standard errors of the parameters' estimators. The parameters' estimators are asymptotically normally distributed, and therefore statistical inference based on the results of this package, such as hypothesis testing and confidence intervals, can be performed using the normal distribution. Extensive simulations demonstrate the flexibility and correct implementation of the estimator. Two case studies performed with publicly available datasets demonstrate applicability of the package. In the Diabetic Retinopathy Study, the onset of blindness is clustered by patient, and in a large hard drive failure dataset, failure times are thought to be clustered by the hard drive manufacturer and model.