Joint Frailty Mixing Model for Recurrent Event Data with an Associated Terminal Event: Application to Hospital Readmission Data

Recurrent events like repeated hospitalization, cancer tumour recurrences, and many others occur frequently. The follow-up on recurrent events may be stopped by a terminal event like death. It is obvious that if the frequencies of recurrent events are more, then it may lead to a terminal event and in this case terminal event becomes ‘dependent’. In this article, we study a joint modelling and analysis of recurrent events with a dependent terminal event. Here, the proportional intensity model for the recurrent events process and the proportional hazard model for the terminal event time are taken. To account for the association between recurrent events and terminal events, mixing frailty or random effect is studied rather than available pure frailty. In our case, the distribution of frailty is introduced as a mixture of folded normal distribution and gamma distribution rather than using pure gamma distribution. An estimation procedure in the joint frailty model is applied to estimate the parameters of the model. This method is close to the method of minimum chi-square rather than a complicated one. An extensive simulation study has been performed to estimate the model parameters and the performances are evaluated based on bias and MSE criteria. Further from an application point of view, the method is illustrated to a hospital readmission data for colorectal cancer patients

Multivariate Joint Models and Dynamic Predictions

The joint modeling of longitudinal and time-to-event data is an active area of statistical research that has received a lot of attention. The standard joint models, referred to as univariate joint models, allow simultaneous modeling of a single longitudinal outcome and a single time-to-event under an assumption of independent censoring. The majority of the joint modeling research in the last two decades has focused on extending and improving the univariate joint models. While many of the practical applications involve data on multivariate longitudinal outcomes and multiple timeto- events possibly informatively censored by some other terminal time-to-event, the developments of joint models to analyze such complex data structure have not received deserved attention. One other area of statistical joint modeling methods that remained understudied is the joint analysis of multivariate longitudinal outcomes and multiple ordered time-to-events. The joint models for recurrent events in existing literature can be applied to analyze ordered time-to-events of the same type under an assumption that all occurrences of the time-to-event are homogeneously influenced by the covariates. However, in problems of ordered time-to-events of different types or of the same kind where different occurrences may be impacted differently by the covariates, the current methods may not be applied. Given the limitations in the existing body of joint modeling literature, this research work aims to present joint modeling extensions with the potentials of filling in the noted literature gaps. In Chapter 2 of this dissertation, we presented a shared parameters Bayesian latent trait joint frailty model for analyzing multivariate longitudinal outcomes and multiple unordered non-terminal time-to-events in the presence of a terminal event inducing dependent right censoring. We adopted a semiparametric latent trait generalized mixed-effects approach to define the longitudinal submodel. Semiparametric hazard regression models are used to model the non-terminal and terminal time-to-event risks with multivariate non-terminal event frailties to account for the inter-event associations. Chapter 4 introduces an extension of the joint model presented in Chapter 2 for multivariate longitudinal outcomes and multiple ordered time-to-events. For both the proposed models, Bayesian approaches of parameter estimation are discussed, and Bayesian Monte Carlo Markov Chain (MCMC) dynamic prediction algorithms for longitudinal outcomes and time-to-event risks are outlined. The finite sample performances of the parameter estimation methods and dynamic prediction algorithms are studied through statistical simulations for both the proposed models. Before presenting the joint frailty model for multiple ordered time-to-events in Chapter 4, we revisited a long-studied problem of estimating the survival functions for multiple ordered time-to-events in Chapter 3. Given the complexities and unbecomingness under certain assumptions of the current methods, we discussed two straightforward and easy to compute approaches of estimating survival functions of multiple ordered time-to-events. The first approach is non-parametric, based on Kaplan-Meier survival estimates, and assumes independence between the consecutive event times to estimate the marginal survival curves. The second approach is fully parametric, assumes the consecutive event gap times to be log-normally distributed, and estimates the marginal and conditional survival functions when the consecutive event times may not be expected to be independent. Simulations studies were performed to evaluate the finite sample properties of both the non-parametric and parametric approaches at different sample sizes and censoring rates. In addition to the extensive simulation studies, we have demonstrated applications of all the proposed joint models, and survival function estimation approaches using statewide surveillance data from South Carolina (SC) HIV/AIDS patients

Effect of sacubitril/valsartan on recurrent events in the prospective comparison of ARNI with ACEI to determine impact on global mortality and morbidity in heart failure trial (PARADIGM-HF)

Aims: Recurrent hospitalizations are a major part of the disease burden in heart failure (HF), but conventional analyses consider only the first event. We compared the effect of sacubitril/valsartan vs. enalapril on recurrent events, incorporating all HF hospitalizations and cardiovascular (CV) deaths in PARADIGM-HF, using a variety of statistical approaches advocated for this type of analysis. Methods and results: In PARADIGM-HF, a total of 8399 patients were randomized and followed for a median of 27 months. We applied various recurrent event analyses, including a negative binomial model, the Wei, Lin and Weissfeld (WLW), and Lin, Wei, Ying and Yang (LWYY) methods, and a joint frailty model, all adjusted for treatment and region. Among a total of 3181 primary endpoint events (including 1251 CV deaths) during the trial, only 2031 (63.8%) were first events (836 CV deaths). Among a total of 1195 patients with at least one HF hospitalization, 410 (34%) had at least one further HF hospitalization. Sacubitril/valsartan compared with enalapril reduced the risk of recurrent HF hospitalization using the negative binomial model [rate ratio (RR) 0.77, 95% confidence interval (CI) 0.67–0.89], the WLW method [hazard ratio (HR) 0.79, 95% CI 0.71–0.89], the LWYY method (RR 0.78, 95% CI 0.68–0.90), and the joint frailty model (HR 0.75, 95% CI 0.66–0.86) (all P < 0.001). The effect of sacubitril/valsartan vs. enalapril on recurrent HF hospitalizations/CV death was similar. Conclusions: In PARADIGM-HF, approximately one third of patients with a primary endpoint (time-to-first) experienced a further event. Compared with enalapril, sacubitril/valsartan reduced both first and recurrent events. The treatment effect size was similar, regardless of the statistical approach applied

An overall strategy based on regression models to estimate relative survival and model the effects of prognostic factors in cancer survival studies.

Relative survival provides a measure of the proportion of patients dying from the disease under study without requiring the knowledge of the cause of death. We propose an overall strategy based on regression models to estimate the relative survival and model the effects of potential prognostic factors. The baseline hazard was modelled until 10 years follow-up using parametric continuous functions. Six models including cubic regression splines were considered and the Akaike Information Criterion was used to select the final model. This approach yielded smooth and reliable estimates of mortality hazard and allowed us to deal with sparse data taking into account all the available information. Splines were also used to model simultaneously non-linear effects of continuous covariates and time-dependent hazard ratios. This led to a graphical representation of the hazard ratio that can be useful for clinical interpretation. Estimates of these models were obtained by likelihood maximization. We showed that these estimates could be also obtained using standard algorithms for Poisson regression

Incidence of HIV-related anal cancer remains increased despite long-term combined antiretroviral treatment: results from the french hospital database on HIV.

PURPOSE: To study recent trends in the incidence of anal cancer in HIV-infected patients receiving long-term combined antiretroviral treatment (cART) compared with the general population. PATIENTS AND METHODS: From the French Hospital Database on HIV, we identified 263 cases of invasive anal squamous cell carcinoma confirmed histologically between 1992 and 2008. We compared incidence rates of anal cancer across four calendar periods: 1992-1996 (pre-cART period), 1997-2000 (early cART period), and 2001-2004 and 2005-2008 (recent cART periods). Standardized incidence ratios (SIRs) were calculated by using general population incidence data from the French Network of Cancer Registries. RESULTS: In HIV-infected patients, the hazard ratio (HR) in the cART periods versus the pre-cART period was 2.5 (95% CI, 1.28 to 4.98). No difference was observed across the cART calendar periods (HR, 0.9; 95% CI, 0.6 to 1.3). In 2005-2008, HIV-infected patients compared with the general population had an excess risk of anal cancer, with SIRs of 109.8 (95% CI, 84.6 to 140.3), 49.2 (95% CI, 33.2 to 70.3), and 13.1 (95% CI, 6.8 to 22.8) for men who have sex with men (MSM), other men, and women, respectively. Among patients with CD4 cell counts above 500/μL for at least 2 years, SIRs were 67.5 (95% CI, 41.2 to 104.3) when the CD4 nadir was less than 200/μL for more than 2 years and 24.5 (95% CI, 17.1 to 34.1) when the CD4 nadir was more than 200/μL. CONCLUSION: Relative to that in the general population, the risk of anal cancer in HIV-infected patients is still extremely high, even in patients with high current CD4 cell counts. cART appears to have no preventive effect on anal cancer, particularly in MSM

Tutorial in Joint Modeling and Prediction: A Statistical Software for Correlated Longitudinal Outcomes, Recurrent Events and a Terminal Event

Extensions in the field of joint modeling of correlated data and dynamic predictions improve the development of prognosis research. The R package frailtypack provides estimations of various joint models for longitudinal data and survival events. In particular, it fits models for recurrent events and a terminal event (frailtyPenal), models for two survival outcomes for clustered data (frailtyPenal), models for two types of recurrent events and a terminal event (multivPenal), models for a longitudinal biomarker and a terminal event (longiPenal) and models for a longitudinal biomarker, recurrent events and a terminal event (trivPenal). The estimators are obtained using a standard and penalized maximum likelihood approach, each model function allows to evaluate goodness-of-fit analyses and provides plots of baseline hazard functions. Finally, the package provides individual dynamic predictions of the terminal event and evaluation of predictive accuracy. This paper presents the theoretical models with estimation techniques, applies the methods for predictions and illustrates frailtypack functions details with examples