A semiparametric Bayesian proportional hazards model for interval censored data with frailty effects

Bayesian inference for Cox proportional hazard models with partial likelihoods, nonlinear covariate effects and correlated observations

We propose a flexible and scalable approximate Bayesian inference methodology for the Cox Proportional Hazards model with partial likelihood. The model we consider includes nonlinear covariate effects and correlated survival times. The proposed method is based on nested approximations and adaptive quadrature, and the computational burden of working with the log-partial likelihood is mitigated through automatic differentiation and Laplace approximation. We provide two simulation studies to show the accuracy of the proposed approach, compared with the existing methods. We demonstrate the practical utility of our method and its computational advantages over Markov Chain Monte Carlo methods through the analysis of Kidney infection times, which are paired, and the analysis of Leukemia survival times with a semi-parametric covariate effect and spatial variation.

Evaluation of the protective efficacy of a spatial repellent to reduce malaria incidence in children in western Kenya compared to placebo: study protocol for a cluster-randomized double-blinded control trial (the AEGIS program)

BACKGROUND

Spatial repellents are widely used for prevention of mosquito bites and evidence is building on their public health value, but their efficacy against malaria incidence has never been evaluated in Africa. To address this knowledge gap, a trial to evaluate the efficacy of Mosquito Shield™, a spatial repellent incorporating transfluthrin, was developed for implementation in Busia County, western Kenya where long-lasting insecticidal net coverage is high and baseline malaria transmission is moderate to high year-round.

METHODS

This trial is designed as a cluster-randomized, placebo-controlled, double-blinded clinical trial. Sixty clusters will be randomly assigned in a 1:1 ratio to receive spatial repellent or placebo. A total of 6120 children aged ≥6 months to 10 years of age will be randomly selected from the study clusters, enrolled into an active cohort (baseline, cohort 1, and cohort 2), and sampled monthly to determine time to first infection by smear microscopy. Each cohort following the implementation of the intervention will be split into two groups, one to estimate direct effect of the spatial repellent and the other to estimate degree of diversion of mosquitoes and malaria transmission to unprotected persons. Malaria incidence in each cohort will be estimated and compared (primary indicator) to determine benefit of using a spatial repellent in a high, year-round malaria transmission setting. Mosquitoes will be collected monthly using CDC light traps to determine if there are entomological correlates of spatial repellent efficacy that may be useful for the evaluation of new spatial repellents. Quarterly human landing catches will assess behavioral effects of the intervention.

DISCUSSION

Findings will serve as the first cluster-randomized controlled trial powered to detect spatial repellent efficacy to reduce malaria in sub-Saharan Africa where transmission rates are high, insecticide-treated nets are widely deployed, and mosquitoes are resistant to insecticides. Results will be submitted to the World Health Organization Vector Control Advisory Group for assessment of public health value towards an endorsement to recommend inclusion of spatial repellents in malaria control programs.

TRIAL REGISTRATION

ClinicalTrials.gov NCT04766879 . Registered February 23, 2021.

Semiparametric analysis of clustered interval-censored survival data using soft Bayesian additive regression trees (SBART)

Popular parametric and semiparametric hazards regression models for clustered survival data are inappropriate and inadequate when the unknown effects of different covariates and clustering are complex. This calls for a flexible modeling framework to yield efficient survival prediction. Moreover, for some survival studies involving time to occurrence of some asymptomatic events, survival times are typically interval censored between consecutive clinical inspections. In this article, we propose a robust semiparametric model for clustered interval-censored survival data under a paradigm of Bayesian ensemble learning, called soft Bayesian additive regression trees or SBART (Linero and Yang, 2018), which combines multiple sparse (soft) decision trees to attain excellent predictive accuracy. We develop a novel semiparametric hazards regression model by modeling the hazard function as a product of a parametric baseline hazard function and a nonparametric component that uses SBART to incorporate clustering, unknown functional forms of the main effects, and interaction effects of various covariates. In addition to being applicable for left-censored, right-censored, and interval-censored survival data, our methodology is implemented using a data augmentation scheme which allows for existing Bayesian backfitting algorithms to be used. We illustrate the practical implementation and advantages of our method via simulation studies and an analysis of a prostate cancer surgery study where dependence on the experience and skill level of the physicians leads to clustering of survival times. We conclude by discussing our method's applicability in studies involving high-dimensional data with complex underlying associations.

A Gamma-frailty proportional hazards model for bivariate interval-censored data

Correlated survival data naturally arise from many clinical and epidemiological studies. For the analysis of such data, the Gamma-frailty proportional hazards (PH) model is a popular choice because the regression parameters have marginal interpretations and the statistical association between the failure times can be explicitly quantified via Kendall's tau. Despite their popularity, Gamma-frailty PH models for correlated interval-censored data have not received as much attention as analogous models for right-censored data. In this work, a Gamma-frailty PH model for bivariate interval-censored data is presented and an easy to implement expectation-maximization (EM) algorithm for model fitting is developed. The proposed model adopts a monotone spline representation for the purposes of approximating the unknown conditional cumulative baseline hazard functions, significantly reducing the number of unknown parameters while retaining modeling flexibility. The EM algorithm was derived from a data augmentation procedure involving latent Poisson random variables. Extensive numerical studies illustrate that the proposed method can provide reliable estimation and valid inference, and is moreover robust to the misspecification of the frailty distribution. To further illustrate its use, the proposed method is used to analyze data from an epidemiological study of sexually transmitted infections.

Effects of whole body vibration exercises on bone mineral density of women with postmenopausal osteoporosis without medications: novel findings and literature review

OBJECTIVES

The aim of this study was to review the literature about the effect of whole body vibration exercise in the BMD in patients with postmenopausal osteoporosis without medications.

METHODS

A systematic review was performed.

RESULTS

The frequency of the mechanical vibration used in the protocols has varied from 12 to 90 Hz. The time used in the protocols varied from 2 up to 22 months. Techniques with X-rays were used in nine of the twelve publications analyzed, the Dual energy X-ray absorptiometry (DEXA) in eight studies and the High resolution peripheral quantitative computed tomography (HR-pQCT) in one publication. The concentration of some biomarkers was determined, as the sclerostin, the bone alkaline phosphatase, N-telopeptide X and 25-hydroxyvitamin D. Among the twelve articles analyzed, seven of them have shown an improvement of the BMD of some bone of postmenopausal women exposed to whole body vibration exercises not associated to medications; as well as modifications in biomarkers.

Semi-parametric frailty model for clustered interval-censored data

Abstract:

The shared frailty model is a popular tool to analyze correlated right-censored time-to-event data. In the shared frailty model, the latent frailty is assumed to be shared by the members of a cluster and is assigned a parametric distribution, typically a gamma distribution due to its conjugacy. In the case of interval-censored time-to-event data, the inclusion of frailties results in complicated intractable likelihoods. Here, we propose a flexible frailty model for analyzing such data by assuming a smooth semi-parametric form for the conditional time-to-event distribution and a parametric or a flexible form for the frailty distribution. The results of a simulation study suggest that the estimation of regression parameters is robust to misspecification of the frailty distribution (even when the frailty distribution is multimodal or skewed). Given sufficiently large sample sizes and number of clusters, the flexible approach produces smooth and accurate posterior estimates for the baseline survival function and for the frailty density, and it can correctly detect and identify unusual frailty density forms. The methodology is illustrated using dental data from the Signal Tandmobiel[Formula: see text] study.

Flexible Bayesian survival modeling with semiparametric time-dependent and shape-restricted covariate effects

Presently, there are few options with available software to perform a fully Bayesian analysis of time-to-event data wherein the hazard is estimated semi- or non-parametrically. One option is the piecewise exponential model, which requires an often unrealistic assumption that the hazard is piecewise constant over time. The primary aim of this paper is to construct a tractable semiparametric alternative to the piecewise exponential model that assumes the hazard is continuous, and to provide modifiable, user-friendly software that allows the use of these methods in a variety of settings. To accomplish this aim, we use a novel model formulation for the log-hazard based on a low-rank thin plate linear spline that readily facilitates adjustment for covariates with time-dependent and proportional hazards effects, possibly subject to shape restrictions. We investigate the performance of our model choices via simulation. We then analyze colorectal cancer data from a clinical trial comparing the effectiveness of two novel treatment regimes relative to the standard of care for overall survival. We estimate a time-dependent hazard ratio for each novel regime relative to the standard of care while adjusting for the effect of aspartate transaminase, a biomarker of liver function, that is subject to a non-decreasing shape restriction.

A Bayesian Approach for the Cox Proportional Hazards Model with Covariates Subject to Detection Limit

The research on biomarkers has been limited in its effectiveness because biomarker levels can only be measured within the thresholds of assays and laboratory instruments, a challenge referred to as a detection limit (DL) problem. In this paper, we propose a Bayesian approach to the Cox proportional hazards model with explanatory variables subject to lower, upper, or interval DLs. We demonstrate that by formulating the time-to-event outcome using the Poisson density with counting process notation, implementing the proposed approach in the OpenBUGS and JAGS is straightforward. We have conducted extensive simulations to compare the proposed Bayesian approach to the other four commonly used methods and to evaluate its robustness with respect to the distribution assumption of the biomarkers. The proposed Bayesian approach and other methods were applied to an acute lung injury study, in which a panel of cytokine biomarkers was studied for the biomarkers’ association with ventilation-free survival.

Software for semiparametric shared gamma and log-normal frailty models: An overview

In survival analysis individuals are followed over some period and the time until the transition from an initial to a final state is of particular interest. An important tool for analyzing potential risk factors of this transition is the Cox proportional hazards model. This model requires homogeneity in the study population and independence between the observations. An extension of the Cox model to deal with both, unobserved heterogeneity and clustered survival data, are frailty models [1]. Different software are available for the analysis of shared frailty models such as coxph, coxme, phmm, frailtyPenal, SPGAM or SPLN3. This makes it difficult for the user to find the appropriate tool for the specific problem under investigation. To compare the performance of the aforementioned software a large simulation study was conducted. Advantages and limitations of the software are discussed in detail.

Parametric frailty models for clustered data with arbitrary censoring: application to effect of male circumcision on HPV clearance

Background

In epidemiological studies, subjects are often followed for a period during which study outcomes are measured at selected time points, such as by diagnostic testing performed on biological samples collected at each visit. Although test results may indicate the presence or absence of a disease or condition, they cannot provide information on when exactly it occurred. Such study designs generate arbitrarily censored time-to-event data, which can include left, interval and right censoring. Adding to this complexity, the data may be clustered such that observations within the same cluster are not independent, such as time to recovery of an infectious disease of family or community members. This data structure is observed when evaluating circumcision's effect on clearance of penile high risk human papillomavirus (HR-HPV) infections using data collected from the male circumcision(MC) trial conducted in Rakai, Uganda, where the multiple infections within individual and HPV testings performed at trial follow-up visits gave rise to the clustered data with arbitrary censoring.

Methods

We describe the use of parametric proportional hazards frailty models and accelerated failure time frailty models to examine the relationship between explanatory variables and the survival outcomes that are subject to arbitrary censoring, while accounting for the correlation within clusters. Standard software such as SAS can be used for parameter estimation.

Results

Circumcision's effect on HPV infection was a secondary end point in the Rakai MC trial, and HPV genotyping was conducted for penile samples of a subset of trial participants collected at enrollment, 6, 12 and 24-month follow up visits. At enrollment, 36.7% intervention arm men (immediate circumcision) and 36.6% control arm men (delayed circumcision at 2 years) were infected with HR-HPV, with the number of infections per man being 1-5. The proposed models were used to examine whether MC facilitated clearance of the prevalent infections. Results show that clearance of multiple infections within each man is highly correlated, and clearance was 60% faster if a man was circumcised.

Conclusions

Parametric frailty models provide viable ways to study the relationship between exposure variables and clustered survival outcome that is subject to arbitrary censoring, as is often observed in HPV epidemiology studies.