A marginal cure rate proportional hazards model for spatial survival data

Spatial Survival Model for COVID-19 in México

A spatial survival analysis was performed to identify some of the factors that influence the survival of patients with COVID-19 in the states of Guerrero, México, and Chihuahua. The data that we analyzed correspond to the period from 28 February 2020 to 24 November 2021. A Cox proportional hazards frailty model and a Cox proportional hazards model were fitted. For both models, the estimation of the parameters was carried out using the Bayesian approach. According to the DIC, WAIC, and LPML criteria, the spatial model was better. The analysis showed that the spatial effect influences the survival times of patients with COVID-19. The spatial survival analysis also revealed that age, gender, and the presence of comorbidities, which vary between states, and the development of pneumonia increase the risk of death from COVID-19.

Bayesian transformation model for spatial partly interval-censored data

The transformation model with partly interval-censored data offers a highly flexible modeling framework that can simultaneously support multiple common survival models and a wide variety of censored data types. However, the real data may contain unexplained heterogeneity that cannot be entirely explained by covariates and may be brought on by a variety of unmeasured regional characteristics. Due to this, we introduce the conditionally autoregressive prior into the transformation model with partly interval-censored data and take the spatial frailty into account. An efficient Markov chain Monte Carlo method is proposed to handle the posterior sampling and model inference. The approach is simple to use and does not include any challenging Metropolis steps owing to four-stage data augmentation. Through several simulations, the suggested method's empirical performance is assessed and then the method is used in a leukemia study.

Bridged parametric survival models: General paradigm and speed improvements

BACKGROUND AND OBJECTIVE

With the recent surge in availability of large biomedical databases mostly derived from electronic health records, the need for the development of scalable marginal survival models with faster implementation cannot be more timely. The presence of clustering renders computational complexity, especially when the number of clusters is high. Marginalizing conditional survival models can violate the proportional hazards assumption for some frailty distributions, disrupting the connection to a conditional model. While theoretical connections between proportional hazard and accelerated failure time models exist, a computational framework to produce both for either marginal or conditional perspectives is lacking. Our objective is to provide fast, scalable bridged-survival models contained in a unified framework from which the effects and standard errors for the conditional hazard ratio, the marginal hazard ratio, the conditional acceleration factor, and the marginal acceleration factor can be estimated, and related to one another in a transparent fashion. Methods We formulate a Weibull parametric frailty likelihood for clustered survival times that can directly estimate the four estimands. Under a nonlinear mixed model specification with positive stable frailties powered by Gaussian quadrature, we put forth a novel closed form of the integrated likelihood that lowered the computational threshold for fitting these models. The method is illustrated on a real dataset generated from electronic health records examining tooth-loss.

RESULTS

Our novel closed form of the integrated likelihood significantly lowered the computational threshold for fitting these models by a factor of 12 (36 compared to 3 min) for the R package parfm, and a factor of 2400 for Gaussian Quadrature (4.6 days compared to 3 min) in SAS. Moreover, each of these estimands are connected by simple relationships of the parameters and the proportional hazards assumption is preserved for the marginal model. Our framework provides a flow of analysis enabling the fit of any/all of the 4 perspective-parameterization combinations. Conclusions We see the potential usefulness of our framework of bridged parametric survival models fitted with the Static-Stirling closed form likelihood. Bridged-survival models provide insights on subject-specific and population-level survival effects when their relation is transparent. SAS and R codes, along with implementation details on a pseudo data are provided.

BAREB: A Bayesian repulsive biclustering model for periodontal data

Preventing periodontal diseases (PD) and maintaining the structure and function of teeth are important goals for personal oral care. To understand the heterogeneity in patients with diverse PD patterns, we develop a Bayesian repulsive biclustering method that can simultaneously cluster the PD patients and their tooth sites after taking the patient- and site-level covariates into consideration. BAREB uses the determinantal point process prior to induce diversity among different biclusters to facilitate parsimony and interpretability. Since PD progression is hypothesized to be spatially referenced, BAREB factors in the spatial dependence among tooth sites. In addition, since PD is the leading cause for tooth loss, the missing data mechanism is nonignorable. Such nonrandom missingness is incorporated into BAREB. For the posterior inference, we design an efficient reversible jump Markov chain Monte Carlo sampler. Simulation studies show that BAREB is able to accurately estimate the biclusters, and compares favorably to alternatives. For real world application, we apply BAREB to a dataset from a clinical PD study, and obtain desirable and interpretable results. A major contribution of this article is the Rcpp implementation of our methodology, available in the R package BAREB.

A Bayesian piecewise survival cure rate model for spatially clustered data

This paper proposes a Bayesian hierarchical cure rate survival model for spatially clustered time to event data. We consider a mixture cure rate model with covariates and a flexible (semi)parametric baseline survival distribution for uncured individuals. The spatial correlation structure is introduced in the form of frailties which follow a Multivariate Conditionally Autoregressive distribution on a pre-specified map. We obtain the usual posterior estimates, smoothed by regional level maps of spatial frailties and cure rates. A simulation study demonstrates that the parameters of the models with spatially correlated frailties have smaller relative biases and MSE than the ones obtained using simple frailty models. We apply our methodology to Hodgkin lymphoma cancer survival times for patients diagnosed in the state of Connecticut.