Marginal proportional hazards models for clustered interval-censored data with time-dependent covariates.

The Botswana Combination Prevention Project was a cluster-randomized HIV prevention trial whose follow-up period coincided with Botswana's national adoption of a universal test and treat strategy for HIV management. Of interest is whether, and to what extent, this change in policy modified the preventative effects of the study intervention. To address such questions, we adopt a stratified proportional hazards model for clustered interval-censored data with time-dependent covariates and develop a composite expectation maximization algorithm that facilitates estimation of model parameters without placing parametric assumptions on either the baseline hazard functions or the within-cluster dependence structure. We show that the resulting estimators for the regression parameters are consistent and asymptotically normal. We also propose and provide theoretical justification for the use of the profile composite likelihood function to construct a robust sandwich estimator for the variance. We characterize the finite-sample performance and robustness of these estimators through extensive simulation studies. Finally, we conclude by applying this stratified proportional hazards model to a re-analysis of the Botswana Combination Prevention Project, with the national adoption of a universal test and treat strategy now modeled as a time-dependent covariate.

Boosting multivariate structured additive distributional regression models.

We develop a model-based boosting approach for multivariate distributional regression within the framework of generalized additive models for location, scale, and shape. Our approach enables the simultaneous modeling of all distribution parameters of an arbitrary parametric distribution of a multivariate response conditional on explanatory variables, while being applicable to potentially high-dimensional data. Moreover, the boosting algorithm incorporates data-driven variable selection, taking various different types of effects into account. As a special merit of our approach, it allows for modeling the association between multiple continuous or discrete outcomes through the relevant covariates. After a detailed simulation study investigating estimation and prediction performance, we demonstrate the full flexibility of our approach in three diverse biomedical applications. The first is based on high-dimensional genomic cohort data from the UK Biobank, considering a bivariate binary response (chronic ischemic heart disease and high cholesterol). Here, we are able to identify genetic variants that are informative for the association between cholesterol and heart disease. The second application considers the demand for health care in Australia with the number of consultations and the number of prescribed medications as a bivariate count response. The third application analyses two dimensions of childhood undernutrition in Nigeria as a bivariate response and we find that the correlation between the two undernutrition scores is considerably different depending on the child's age and the region the child lives in.

Association of dietary mineral mixture with depressive symptoms: A combination of Bayesian approaches.

The relationships between mixtures of multiple minerals and depression have not been explored. Therefore, we analyzed the relationship between the mixture of nine dietary minerals [calcium (Ca), phosphorus, magnesium (Mg), iron (Fe), zinc, copper (Cu), sodium, potassium (K), and selenium (Se)] and depressive symptoms in the general population. We screened 20,342 participants from the National Health and Nutrition Examination Survey (NHANES) 2007-2018. We fitted the general linear regression, Bayesian kernel machine regression (BKMR), and Bayesian semiparametric regression models to explore associations and interactions. We obtained the relative importance of dietary minerals by calculating posterior inclusion probabilities (PIPs). The dietary intakes of minerals were obtained using the 24-h dietary recall interview, and depressive symptoms were assessed using the Patient Health Questionnaire-9 (PHQ-9). The linear analysis showed that nine minerals were negatively associated with PHQ-9 scores. The BKMR analysis showed a negative association between the dietary mineral mixture and PHQ-9 scores, with Se having the largest PIP at 1.0000, followed by K (0.7784). We also observed potential interactions between Ca and Fe, Se and Fe, and K and Mg. Among them, the interaction of Ca and Fe had the largest PIP of 0.986. In addition, the overall effect was more pronounced in females than males, and Cu's PIP (0.8376) was higher in females. Two sensitivity analyses showed that our results were robust. Our study provides a basis for formulating nutritional intervention programs for depression in the future.

A log-binomial Bayesian geoadditive semiparametric analysis of geographical inequalities in caesarean births in Ghana.

BACKGROUND: Caesarean section is a clinical intervention aimed to save the lives of women and their newborns. In Ghana, studies have reported inequalities in use among women of different socioeconomic backgrounds. However, geographical differentials at the district level where health interventions are implemented, have not been systematically studied. This study examined geographical inequalities in caesarean births at the district level in Ghana. The study investigated how pregnancy complications and birth risks, access to health care and affluence correlate with geographical inequalities in caesarean section uptake. METHODS: The data for the analysis was derived from the 2017 Ghana Maternal Health Survey. The log-binomial Bayesian Geoadditive Semiparametric regression technique was used to examine the extent of geographical clustering in caesarean births at the district level and their spatial correlates. RESULTS: In Ghana, 16.0% (95% CI = 15.3, 16.8) of births were via caesarean section. Geospatial analysis revealed a strong spatial dependence in caesarean births, with a clear north-south divide. Low frequencies of caesarean births were observed among districts in the northern part of the country, while those in the south had high frequencies. The predominant factor associated with the spatial differentials was affluence rather than pregnancy complications and birth risk and access to care. CONCLUSIONS: Strong geographical inequalities in caesarean births exist in Ghana. Targeted and locally relevant interventions including health education and policy support are required at the district level to address the overuse and underuse of caesarean sections, to correspond to the World Health Organisation recommended optimal threshold of 10% to 15%.

Diagnostic evaluation of pharmacokinetic features of functional markers.

The dynamicity of functional (curve) markers from modern clinical studies offers deeper insights into complex disease physiology. A frequent clinical practice is to examine various 'pharmacokinetic features' of functional markers (definite integral, maximum value, time to maximum, etc.) that reflect important physiological underpinnings. For instance, the current diagnostic procedure for kidney obstruction is to examine several pharmacokinetic features of renogram curves characterizing renal function. Motivated by such clinical practices, we develop a statistical framework for evaluating diagnostic accuracy of pharmacokinetic features using area under the receiver operating characteristic curve (AUC). The major challenge is that functional markers are observed at discrete time points with measurement error. To address this challenge, we develop a two-stage non-parametric AUC estimator based on summary functionals providing unified representation of various pharmacokinetic features and study its asymptotic properties. We also propose a sensible adaptation of a semiparametric regression model that can describe heterogeneity of AUC across different subpopulations, while appropriately handling discreteness and noise in observed functional markers. Here, a novel data-driven approach that balances between bias and efficiency of the regression coefficient estimates is introduced. Finally, the framework is applied to rigorously evaluate pharmacokinetic features of renogram curves potentially useful for detecting kidney obstruction.

A semiparametric model for between-subject attributes: Applications to beta-diversity of microbiome data.

The human microbiome plays an important role in our health and identifying factors associated with microbiome composition provides insights into inherent disease mechanisms. By amplifying and sequencing the marker genes in high-throughput sequencing, with highly similar sequences binned together, we obtain operational taxonomic units (OTUs) profiles for each subject. Due to the high-dimensionality and nonnormality features of the OTUs, the measure of diversity is introduced as a summarization at the microbial community level, including the distance-based beta-diversity between individuals. Analyses of such between-subject attributes are not amenable to the predominant within-subject-based statistical paradigm, such as t-tests and linear regression. In this paper, we propose a new approach to model beta-diversity as a response within a regression setting by utilizing the functional response models (FRMs), a class of semiparametric models for between- as well as within-subject attributes. The new approach not only addresses limitations of current methods for beta-diversity with cross-sectional data, but also provides a premise for extending the approach to longitudinal and other clustered data in the future. The proposed approach is illustrated with both real and simulated data.

Semiparametric multiple inflation count model with application to a smoking cessation study.

Count data are observed by practitioners across various fields. Often, a substantially large proportion of one or some values causes extra variation and may lead to a particular case of mixed structured data. In these cases, a standard count model may lead to poor inference of the parameters involved because of its inability to account for extra variation. Furthermore, we hypothesize a possible nonlinear relationship of a continuous covariate with the logarithm of the mean count and with the probability of belonging to an inflated category. We propose a semiparametric multiple inflation Poisson (MIP) model that considers the two nonlinear link functions. We develop a sieve maximum likelihood estimator (sMLE) for the regression parameters of interest. We establish the asymptotic behavior of the sMLE. Simulations are conducted to evaluate the performance of the proposed sieve MIP (sMIP). Then, we illustrate the methodology on data from a smoking cessation study. Finally, some remarks and opportunities for future research conclude the article.

Variable selection in semiparametric regression models for longitudinal data with informative observation times.

A common issue in longitudinal studies is that subjects' visits are irregular and may depend on observed outcome values which is known as longitudinal data with informative observation times (follow-up). Semiparametric regression modeling for this type of data has received much attention as it provides more flexibility in studying the association between regression factors and a longitudinal outcome. An important problem here is how to select relevant variables and estimate their coefficients in semiparametric regression models when the number of covariates at baseline is large. The current penalization procedures in semiparametric regression models for longitudinal data do not account for informative observation times. We propose a variable selection procedure that is suitable for the estimation methods based on pseudo-score functions. We investigate the asymptotic properties of penalized estimators and conduct simulation studies to illustrate the theoretical results. We also use the procedure for variable selection in semiparametric regression models for the STAR*D dataset from a multistage randomized clinical trial for treating major depressive disorder.

Bayesian analysis for partly linear Cox model with measurement error and time-varying covariate effect.

The Cox proportional hazards model is commonly used to estimate the association between time-to-event and covariates. Under the proportional hazards assumption, covariate effects are assumed to be constant in the follow-up period of study. When measurement error presents, common estimation methods that adjust for an error-contaminated covariate in the Cox proportional hazards model assume that the true function on the covariate is parametric and specified. We consider a semiparametric partly linear Cox model that allows the hazard to depend on an unspecified function of an error-contaminated covariate and an error-free covariate with time-varying effect, which simultaneously relaxes the assumption on the functional form of the error-contaminated covariate and allows for nonconstant effect of the error-free covariate. We take a Bayesian approach and approximate the unspecified function by a B-spline. Simulation studies are conducted to assess the finite sample performance of the proposed approach. The results demonstrate that our proposed method has favorable statistical performance. The proposed method is also illustrated by an application to data from the AIDS Clinical Trials Group Protocol 175.

Selective inference for effect modification via the lasso.

Effect modification occurs when the effect of the treatment on an outcome varies according to the level of other covariates and often has important implications in decision-making. When there are tens or hundreds of covariates, it becomes necessary to use the observed data to select a simpler model for effect modification and then make valid statistical inference. We propose a two-stage procedure to solve this problem. First, we use Robinson's transformation to decouple the nuisance parameters from the treatment effect of interest and use machine learning algorithms to estimate the nuisance parameters. Next, after plugging in the estimates of the nuisance parameters, we use the lasso to choose a low-complexity model for effect modification. Compared to a full model consisting of all the covariates, the selected model is much more interpretable. Compared to the univariate subgroup analyses, the selected model greatly reduces the number of false discoveries. We show that the conditional selective inference for the selected model is asymptotically valid given the rate assumptions in classical semiparametric regression. Extensive simulation studies are conducted to verify the asymptotic results and an epidemiological application is used to demonstrate the method.

Geographical hotspots and correlates of early sexual debut among women in Ghana.

OBJECTIVES: Generalisation of sexual behaviour, including early sexual initiation, does not provide comprehensive knowledge of young people's sexual attitudes, behaviours and challenges, given the high sociocultural diversity and economic inequalities within countries. This study examines geographical hotspots of early sexual initiation, at the district level in Ghana and the factors associated with the observed spatial patterns. METHODS: Data was derived from the 2017 Ghana Maternal Health Survey, covering 21,392 women aged 15-49 years. Early sexual debut denotes first sexual intercourse before attaining the legal age of sexual consent, which in Ghana, is 16 years. The Bayesian geoadditive semiparametric regression technique was used to examine geographical hotspots and correlates of the observed spatial patterns, classified into demographic, socioeconomic and pregnancy outcome factors. RESULTS: The results show that 26.7% (95% CI = 26.1-27.3) of women had their first sexual intercourse before attaining the age of 16 years. Hotspots of early sexual debut was observed predominantly among districts along the mainstream of the Volta Lake, which are also reported hotspots of child trafficking, labour and slavery. Demographic, socioeconomic and pregnancy related factors were identified to be correlated with the observed spatial clustering. CONCLUSION: Policies and interventions such as sexual and reproductive health education should target at-risk population, simultaneously addressing other child abuses perpetuating the practice.

Ghana operates a decentralised health system, where health policies and interventions, including those for sexual and reproductive health are implemented at the district level. Yet, there are no studies that systematically identify districts where sexual behaviours, such as early sexual debut, require attention. This study uses spatial models and data from the 2017 Ghana Maternal Health Survey to identify areas (districts) with high concentration of women who initiated sex before the legal age of consent. Early sexual debut refers to first sexual intercourse before attainment of the legal age (16 years) of sexual consent. Early sexual initiation has been associated with adverse sexual and reproductive health outcomes such as unwanted pregnancies and STIs. The results show that about one in four women reported having early sexual intercourse. High early sexual intercourse was observed to be particularly concentrated among districts along the mainstream of the Volta Lake. With regards to the spatial correlates, for the districts in the Oti region, high early sexual debut was associated with low educational attainment and inability to read. For those in the Bono East and Eastern regions, women who had early sexual debut were more likely to have had a miscarriage, abortion or stillbirth. Younger women, those in co-habiting relationships and those not in union were more likely to have had early sexual debut in the districts in the Ashanti, Central and Northern regions. The findings call for intensification of sexual and reproductive health education in districts along the mainstream of the Volta Lake.

Partially linear single-index generalized mean residual life models.

Mean residual life (MRL) function defines the remaining life expectancy of a subject who has survived to a time point and is an important alternative to the hazard function for characterizing the distribution of a time-to-event variable. Existing MRL models primarily focus on studying the association between risk factors and disease risks using linear model specifications in multiplicative or additive scale. When risk factors have complex correlation structures, nonlinear effects, or interactions, the prefixed linearity assumption may be insufficient to capture the relationship. Single-index modeling framework offers flexibility in reducing dimensionality and modeling nonlinear effects. In this article, we propose a class of partially linear single-index generalized MRL models, the regression component of which consists of both a semiparametric single-index part and a linear regression part. Regression spline technique is employed to approximate the nonparametric single-index function, and parameters are estimated using an iterative algorithm. Double-robust estimators are also proposed to protect against the misspecification of censoring distribution or MRL models. A further contribution of this article is a nonparametric test proposed to formally evaluate the linearity of the single-index function. Asymptotic properties of the estimators are established, and the finite-sample performance is evaluated through extensive numerical simulations. The proposed models and inference approaches are demonstrated by a New York University Langone Health (NYULH) COVID-19 dataset.

Regression analysis of arbitrarily censored survival data under the proportional odds model.

Arbitrarily censored data are referred to as the survival data that contain a mixture of exactly observed, left-censored, interval-censored, and right-censored observations. Existing research work on regression analysis on arbitrarily censored data is relatively sparse and mainly focused on the proportional hazards model and the accelerated failure time model. This article studies the proportional odds (PO) model and proposes a novel estimation approach through an expectation-maximization (EM) algorithm for analyzing such data. The proposed EM algorithm has many appealing properties such as being robust to initial values, easy to implement, converging fast, and providing the variance estimate of the regression parameter estimate in closed form. An informal diagnosis plot is developed for checking the PO model assumption. Our method has shown excellent performance in estimating the regression parameters as well as the baseline survival function in a simulation study. A real-life dataset about metastatic colorectal cancer is analyzed for illustration. An R package regPO has been created for practitioners to implement our method.

Right-Censored Time Series Modeling by Modified Semi-Parametric A-Spline Estimator.

This paper focuses on the adaptive spline (A-spline) fitting of the semiparametric regression model to time series data with right-censored observations. Typically, there are two main problems that need to be solved in such a case: dealing with censored data and obtaining a proper A-spline estimator for the components of the semiparametric model. The first problem is traditionally solved by the synthetic data approach based on the Kaplan-Meier estimator. In practice, although the synthetic data technique is one of the most widely used solutions for right-censored observations, the transformed data's structure is distorted, especially for heavily censored datasets, due to the nature of the approach. In this paper, we introduced a modified semiparametric estimator based on the A-spline approach to overcome data irregularity with minimum information loss and to resolve the second problem described above. In addition, the semiparametric B-spline estimator was used as a benchmark method to gauge the success of the A-spline estimator. To this end, a detailed Monte Carlo simulation study and a real data sample were carried out to evaluate the performance of the proposed estimator and to make a practical comparison.

A semiparametric model for wearable sensor-based physical activity monitoring data with informative device wear.

Wearable sensors provide an exceptional opportunity in collecting real-time behavioral data in free living conditions. However, wearable sensor data from observational studies often suffer from information bias, since participants' willingness to wear the monitoring devices may be associated with the underlying behavior of interest. The aim of this study was to introduce a semiparametric statistical approach for modeling wearable sensor-based physical activity monitoring data with informative device wear. Our simulation study indicated that estimates from the generalized estimating equations showed ignorable bias when device wear patterns were independent of the participants physical activity process, but incrementally more biased when the patterns of device non-wear times were increasingly associated with the physical activity process. The estimates from the proposed semiparametric modeling approach were unbiased both when the device wear patterns were (i) independent or (ii) dependent to the underlying physical activity process. We demonstrate an application of this method using data from the 2003-2004 National Health and Nutrition Examination Survey ($N=4518$), to examine gender differences in physical activity measured using accelerometers. The semiparametric model can be implemented using our R package acc, free software developed for reading, processing, simulating, visualizing, and analyzing accelerometer data, publicly available at the Comprehensive R Archive Network.

Semiparametric estimation of the cure fraction in population-based cancer survival analysis.

With rapid development in medical research, the treatment of diseases including cancer has progressed dramatically and those survivors may die from causes other than the one under study, especially among elderly patients. Motivated by the Surveillance, Epidemiology, and End Results (SEER) female breast cancer study, background mortality is incorporated into the mixture cure proportional hazards (MCPH) model to improve the cure fraction estimation in population-based cancer studies. Here, that patients are "cured" is defined as when the mortality rate of the individuals in diseased group returns to the same level as that expected in the general population, where the population level mortality is presented by the mortality table of the United States. The semiparametric estimation method based on the EM algorithm for the MCPH model with background mortality (MCPH+BM) is further developed and validated via comprehensive simulation studies. Real data analysis shows that the proposed semiparametric MCPH+BM model may provide more accurate estimation in population-level cancer study.

Comparison of nonlinear curves and surfaces.

Estimation of nonlinear curves and surfaces has long been the focus of semiparametric and nonparametric regression analysis. What has been less studied is the comparison of nonlinear functions. In lower-dimensional situations, inference typically involves comparisons of curves and surfaces. The existing comparative procedures are subject to various limitations, and few computational tools have been made available for off-the-shelf use. To address these limitations, two modified testing procedures for nonlinear curve and surface comparisons are proposed. The proposed computational tools are implemented in an R package, with a syntax similar to that of the commonly used model fitting packages. An R Shiny application is provided with an interactive interface for analysts who do not use R. The new tests are consistent against fixed alternative hypotheses. Theoretical details are presented in an appendix. Operating characteristics of the proposed tests are assessed against the existing methods. Applications of the methods are illustrated through real data examples.

Tree-based modeling of time-varying coefficients in discrete time-to-event models.

Hazard models are popular tools for the modeling of discrete time-to-event data. In particular two approaches for modeling time dependent effects are in common use. The more traditional one assumes a linear predictor with effects of explanatory variables being constant over time. The more flexible approach uses the class of semiparametric models that allow the effects of the explanatory variables to vary smoothly over time. The approach considered here is in between these modeling strategies. It assumes that the effects of the explanatory variables are piecewise constant. It allows, in particular, to evaluate at which time points the effect strength changes and is able to approximate quite complex variations of the change of effects in a simple way. A tree-based method is proposed for modeling the piecewise constant time-varying coefficients, which is embedded into the framework of varying-coefficient models. One important feature of the approach is that it automatically selects the relevant explanatory variables and no separate variable selection procedure is needed. The properties of the method are investigated in several simulation studies and its usefulness is demonstrated by considering two real-world applications.

Robust estimation for panel count data with informative observation times and censoring times.

We consider the semiparametric regression of panel count data occurring in longitudinal follow-up studies that concern occurrence rate of certain recurrent events. The analysis of panel count data involves two processes, i.e, a recurrent event process of interest and an observation process controlling observation times. However, the model assumptions of existing methods, such as independent censoring time and Poisson assumption, are restrictive and questionable. In this paper, we propose new joint models for panel count data by considering both informative observation times and censoring times. The asymptotic normality of the proposed estimators are established. Numerical results from simulation studies and a real data example show the advantage of the proposed method.

A Bayesian approach for semiparametric regression analysis of panel count data.

Panel count data commonly arise in epidemiological, social science, and medical studies, in which subjects have repeated measurements on the recurrent events of interest at different observation times. Since the subjects are not under continuous monitoring, the exact times of those recurrent events are not observed but the counts of such events within the adjacent observation times are known. A Bayesian semiparametric approach is proposed for analyzing panel count data under the proportional mean model. Specifically, a nonhomogeneous Poisson process is assumed to model the panel count response over time, and the baseline mean function is approximated by monotone I-splines of Ramsay (Stat Sci 3:425-461, 1988). Our approach allows to estimate the regression parameters and the baseline mean function jointly. The proposed Gibbs sampler is computationally efficient and easy to implement because all of the full conditional distributions either have closed form or are log-concave. Extensive simulations are conducted to evaluate the proposed method and to compare with two other bench methods. The proposed approach is also illustrated by an application to a famous bladder tumor data set (Byar, in: Pavone-Macaluso M, Smith PH, Edsmyn F (eds) Bladder tumors and other topics in urological oncology. Plenum, New York, 1980).