K-means for shared frailty models

Background The purpose of this research was to see how the k-means algorithm can be applied to survival analysis with single events per subject for defining groups, which can then be modeled in a shared frailty model to further allow the capturing the unmeasured confounding not already explained by the covariates in the model. Methods For this purpose we developed our own k-means survival grouping algorithm to handle this approach. We compared a regular shared frailty model with a regular grouping variable and a shared frailty model with a k-means grouping variable in simulations as well as analysis on a real dataset. Results We found that in both simulations as well as real data showed that our k-means clustering is no different than the typical frailty clustering even under different situations of varied case rates and censoring. It appeared our k-means algorithm could be a trustworthy mechanism of creating groups from data when no grouping term exists for including in a frailty term in a survival model or comparing to an existing grouping variable available in the current data to use in a frailty model.

Generalized Lindley Shared Frailty Based on Reversed Hazard Rate

Due to the unavailability of complete data in various circumstances in biological, epidemiological, and medical studies, the analysis of censored data is very common among practitioners. But the analysis of bivariate censored data is not a regular mechanism because it is not necessary to always have independent data. Observed and unobserved covariates affect the variables under study. So, heterogeneity is present in the data. Ignoring observed and unobserved covariates may have objectionable consequences. But it is not easy to find that whether there is any effect of the unobserved covariate or not. Shared frailty models are the viable choice to counter such scenarios. However, due to certain restrictions such as the identifiability condition and the requirement that their Laplace transform exists, finding a frailty distribution can be difficult. As a result, in this paper, we introduce a new frailty distribution generalized Lindley (GL) for reversed hazard rate (RHR) setup that outperforms the gamma frailty distribution. So, our main motive is to establish a new frailty distribution under the RHR setup. By assuming exponential Gumbel (EG) and generalized inverted exponential (GIE) baseline distributions, we propose a new class of shared frailty models based on RHR. We estimate the parameters in these frailty models and use the Bayesian paradigm of the Markov Chain Monte Carlo (MCMC) technique. Model selection criteria have been performed for the comparison of models. We analyze Australian twin data and suggest a better model.

Semiparametric estimation for nonparametric frailty models using nonparametric maximum likelihood approach

A consequence of using a parametric frailty model with nonparametric baseline hazard for analyzing clustered time-to-event data is that its regression coefficient estimates could be sensitive to the underlying frailty distribution. Recently, there has been a proposal for specifying both the baseline hazard and the frailty distribution nonparametrically, and estimating the unknown parameters by the maximum penalized likelihood method. Instead, in this paper, we propose the nonparametric maximum likelihood method for a general class of nonparametric frailty models, i.e. models where the frailty distribution is completely unspecified but the baseline hazard can be either parametric or nonparametric. The implementation of the estimation procedure can be based on a combination of either the Broyden–Fletcher–Goldfarb–Shanno or expectation-maximization algorithm and the constrained Newton algorithm with multiple support point inclusion. Simulation studies to investigate the performance of estimation of a regression coefficient by several different model-fitting methods were conducted. The simulation results show that our proposed regression coefficient estimator generally gives a reasonable bias reduction when the number of clusters is increased under various frailty distributions. Our proposed method is also illustrated with two data examples.

613Monitoring chronic kidney disease evolution using frailty models

Background Frailty models improves traditional survival models such that a latent multiplicative effect is introduced on the risk function, representing non-observed characteristics such as genetic and behavioral. The aim of this study is to explore this kind of model on chronic kidney disease (CKD) monitoring for intermediary outcomes. Methods Using a retrospective cohort comprising 778 patients with diagnosed CKD, parametric survival models were adjusted for the months until decay of renal function ≥5mL as outcome. Models included diabetes, hypertension and CKDEPI as covariates. Latent effect were incorporated, with Gamma distribution, to the best model. Results Just diabetes presented relevant effect on outcome. Best model were Weibull. Without frailty component, estimated diabetes parameter was 0.70 (CI95% 0.54; 0.89), indicating diabetic patients present outcome 30% earlier than non-diabetic. When incorporating the Gamma fragility to the models, the effect was 0.75, (CI95% 0.61, 0.92), or 25% faster on diabetes. The 5 percent points difference between parameters on both models represent, on average, a 20-day difference, having the survival median time of 13 months as reference. It’s possible to address individual specific frailty, an important feature for clinical follow-up. Conclusion Including frailty on modeling made possible to know that in average diabetic patients would experience a fast decay in renal function earlier than what a traditional survival model could evidence. This may be crucial for clinical decision making. All models were adjusted using commercial software. Key message Modern clinical epidemiology must foster use of modern statistics

Impact of recurrent sexually transmitted infections on HIV seroconversion: Results from multi-state frailty models

After several decades of research, South Africa is still considered to be the epicentre of HIV epidemic. The country also has the highest burden of sexually transmitted infections (STIs) which have been frequently linked to increasing rates of HIV transmission due to biological and behavioural associations between these two pathogeneses. We investigated the cumulative impact of recurrent STIs on subsequent HIV seroconversion among a cohort of South African women. We used the ‘ frailty’ models which can account for the heterogeneity due to the recurrent STIs in a longitudinal setting. The lowest HIV incidence rate was 5.0/100 person-year among women who had no baseline STI and remained negative during the follow-up. This estimate was three times higher among those who had recurrent STIs in the follow-up period regardless of their STI status at baseline (15.8 and 14.0/100 person-year for women with and without STI diagnosis at baseline, respectively). Besides younger age and certain partnership characteristics, our data provided compelling evidence for the impact of recurrent STI. diagnoses on increasing rates of HIV. At the population-level, 65% of HIV infections collectively associated with recurrent STIs. These results have significant clinical and epidemiological implications and may play critical role in the trajectory of the infections in the region.