Penalized survival models for the analysis of alternating recurrent event data.

Recurrent event data are widely encountered in clinical and observational studies. Most methods for recurrent events treat the outcome as a point process and, as such, neglect any associated event duration. This generally leads to a less informative and potentially biased analysis. We propose a joint model for the recurrent event rate (of incidence) and duration. The two processes are linked through a bivariate normal frailty. For example, when the event is hospitalization, we can treat the time to admission and length-of-stay as two alternating recurrent events. In our method, the regression parameters are estimated through a penalized partial likelihood, and the variance-covariance matrix of the frailty is estimated through a recursive estimating formula. Moreover, we develop a likelihood ratio test to assess the dependence between the incidence and duration processes. Simulation results demonstrate that our method provides accurate parameter estimation, with a relatively fast computation time. We illustrate the methods through an analysis of hospitalizations among end-stage renal disease patients.

Investigating hospital heterogeneity with a competing risks frailty model.

Survival analysis is used in the medical field to identify the effect of predictive variables on time to a specific event. Generally, not all variation of survival time can be explained by observed covariates. The effect of unobserved variables on the risk of a patient is called frailty. In multicenter studies, the unobserved center effect can induce frailty on its patients, which can lead to selection bias over time when ignored. For this reason, it is common practice in multicenter studies to include a random frailty term modeling center effect. In a more complex event structure, more than one type of event is possible. Independent frailty variables representing center effect can be incorporated in the model for each competing event. However, in the medical context, events representing disease progression are likely related and correlation is missed when assuming frailties to be independent. In this work, an additive gamma frailty model to account for correlation between frailties in a competing risks model is proposed, to model frailties at center level. Correlation indicates a common center effect on both events and measures how closely the risks are related. Estimation of the model using the expectation-maximization algorithm is illustrated. The model is applied to a data set from a multicenter clinical trial on breast cancer from the European Organisation for Research and Treatment of Cancer (EORTC trial 10854). Hospitals are compared by employing empirical Bayes estimates methodology together with corresponding confidence intervals.

Parametric overdispersed frailty models for current status data.

Frailty models have a prominent place in survival analysis to model univariate and multivariate time-to-event data, often complicated by the presence of different types of censoring. In recent years, frailty modeling gained popularity in infectious disease epidemiology to quantify unobserved heterogeneity using Type I interval-censored serological data or current status data. In a multivariate setting, frailty models prove useful to assess the association between infection times related to multiple distinct infections acquired by the same individual. In addition to dependence among individual infection times, overdispersion can arise when the observed variability in the data exceeds the one implied by the model. In this article, we discuss parametric overdispersed frailty models for time-to-event data under Type I interval-censoring, building upon the work by Molenberghs et al. (2010) and Hens et al. (2009). The proposed methodology is illustrated using bivariate serological data on hepatitis A and B from Flanders, Belgium anno 1993-1994. Furthermore, the relationship between individual heterogeneity and overdispersion at a stratum-specific level is studied through simulations. Although it is important to account for overdispersion, one should be cautious when modeling both individual heterogeneity and overdispersion based on current status data as model selection is hampered by the loss of information due to censoring.

A comparison of bivariate, multivariate random-effects, and Poisson correlated gamma-frailty models to meta-analyze individual patient data of ordinal scale diagnostic tests.

Individual patient data (IPD) meta-analyses are increasingly common in the literature. In the context of estimating the diagnostic accuracy of ordinal or semi-continuous scale tests, sensitivity and specificity are often reported for a given threshold or a small set of thresholds, and a meta-analysis is conducted via a bivariate approach to account for their correlation. When IPD are available, sensitivity and specificity can be pooled for every possible threshold. Our objective was to compare the bivariate approach, which can be applied separately at every threshold, to two multivariate methods: the ordinal multivariate random-effects model and the Poisson correlated gamma-frailty model. Our comparison was empirical, using IPD from 13 studies that evaluated the diagnostic accuracy of the 9-item Patient Health Questionnaire depression screening tool, and included simulations. The empirical comparison showed that the implementation of the two multivariate methods is more laborious in terms of computational time and sensitivity to user-supplied values compared to the bivariate approach. Simulations showed that ignoring the within-study correlation of sensitivity and specificity across thresholds did not worsen inferences with the bivariate approach compared to the Poisson model. The ordinal approach was not suitable for simulations because the model was highly sensitive to user-supplied starting values. We tentatively recommend the bivariate approach rather than more complex multivariate methods for IPD diagnostic accuracy meta-analyses of ordinal scale tests, although the limited type of diagnostic data considered in the simulation study restricts the generalization of our findings.

Correlated versus uncorrelated frailty Cox models: A comparison of different estimation procedures.

In many studies in medicine, including clinical trials and epidemiological investigations, data are clustered into groups such as health centers or herds in veterinary medicine. Such data are usually analyzed by hierarchical regression models to account for possible variation between groups. When such variation is large, it is of potential interest to explore whether additionally the effect of a within-group predictor varies between groups. In survival analysis, this may be investigated by including two frailty terms at group level in a Cox proportional hazards model. Several estimation methods have been proposed to estimate this type of frailty Cox models. We review four of these methods, apply them to real data from veterinary medicine, and compare them using a simulation study.

A competing risks model with binary time varying covariates for estimation of breast cancer risks in BRCA1 families.

Mammographic screening and prophylactic surgery such as risk-reducing salpingo oophorectomy can potentially reduce breast cancer risks among mutation carriers of BRCA families. The evaluation of these interventions is usually complicated by the fact that their effects on breast cancer may change over time and by the presence of competing risks. We introduce a correlated competing risks model to model breast and ovarian cancer risks within BRCA1 families that accounts for time-varying covariates. Different parametric forms for the effects of time-varying covariates are proposed for more flexibility and a correlated gamma frailty model is specified to account for the correlated competing events.We also introduce a new ascertainment correction approach that accounts for the selection of families through probands affected with either breast or ovarian cancer, or unaffected. Our simulation studies demonstrate the good performances of our proposed approach in terms of bias and precision of the estimators of model parameters and cause-specific penetrances over different levels of familial correlations. We applied our new approach to 498 BRCA1 mutation carrier families recruited through the Breast Cancer Family Registry. Our results demonstrate the importance of the functional form of the time-varying covariate effect when assessing the role of risk-reducing salpingo oophorectomy on breast cancer. In particular, under the best fitting time-varying covariate model, the overall effect of risk-reducing salpingo oophorectomy on breast cancer risk was statistically significant in women with BRCA1 mutation.

Modelling time varying heterogeneity in recurrent infection processes: an application to serological data.

Frailty models are often used in survival analysis to model multivariate time-to-event data. In infectious disease epidemiology, frailty models have been proposed to model heterogeneity in the acquisition of infection and to accommodate association in the occurrence of multiple types of infection. Although traditional frailty models rely on the assumption of lifelong immunity after recovery, refinements have been made to account for reinfections with the same pathogen. Recently, Abrams and Hens quantified the effect of misspecifying the underlying infection process on the basic and effective reproduction number in the context of bivariate current status data on parvovirus B19 and varicella zoster virus. Furthermore, Farrington, Unkel and their co-workers introduced and applied time varying shared frailty models to paired bivariate serological data. In this paper, we consider an extension of the proposed frailty methodology by Abrams and Hens to account for age-dependence in individual heterogeneity through the use of age-dependent shared and correlated gamma frailty models. The methodology is illustrated by using two data applications.

Analysis of the Factors Affecting the Interval between Blood Donations Using Log-Normal Hazard Model with Gamma Correlated Frailties.

BACKGROUND: Time to donating blood plays a major role in a regular donor to becoming continues one. The aim of this study was to determine the effective factors on the interval between the blood donations. METHODS: In a longitudinal study in 2008, 864 samples of first-time donors in Shahrekord Blood Transfusion Center,  capital city of Chaharmahal and Bakhtiari Province, Iran were selected by a systematic sampling and were followed up for five years. Among these samples, a subset of 424 donors who had at least two successful blood donations were chosen for this study and the time intervals between their donations were measured as response variable. Sex, body weight, age, marital status, education, stay and job were recorded as independent variables. Data analysis was performed based on log-normal hazard model with gamma correlated frailty. In this model, the frailties are sum of two independent components assumed a gamma distribution. The analysis was done via Bayesian approach using Markov Chain Monte Carlo algorithm by OpenBUGS. Convergence was checked via Gelman-Rubin criteria using BOA program in R. RESULTS: Age, job and education were significant on chance to donate blood (P<0.05). The chances of blood donation for the higher-aged donors, clericals, workers, free job, students and educated donors were higher and in return, time intervals between their blood donations were shorter. CONCLUSIONS: Due to the significance effect of some variables in the log-normal correlated frailty model, it is necessary to plan educational and cultural program to encourage the people with longer inter-donation intervals to donate more frequently.