RESUMEN
Fitting penalized models for the purpose of merging the estimation and model selection problem has become commonplace in statistical practice. Of the various regularization strategies that can be leveraged to this end, the use of the l0 norm to penalize parameter estimation poses the most daunting model fitting task. In fact, this particular strategy requires an end user to solve a non-convex NP-hard optimization problem irregardless of the underlying data model. For this reason, the use of the l0 norm as a regularization strategy has been woefully under utilized. To obviate this difficulty, a strategy to solve such problems that is generally accessible by the statistical community is developed. The approach can be adopted to solve l0 norm penalized problems across a very broad class of models, can be implemented using existing software, and is computationally efficient. The performance of the method is demonstrated through in-depth numerical experiments and through using it to analyze several prototypical data sets.
RESUMEN
When screening a population for infectious diseases, pooling individual specimens (e.g., blood, swabs, urine, etc.) can provide enormous cost savings when compared to testing specimens individually. In the biostatistics literature, testing pools of specimens is commonly known as group testing or pooled testing. Although estimating a population-level prevalence with group testing data has received a large amount of attention, most of this work has focused on applications involving a single disease, such as human immunodeficiency virus. Modern methods of screening now involve testing pools and individuals for multiple diseases simultaneously through the use of multiplex assays. Hou et al. (2017, Biometrics, 73, 656-665) and Hou et al. (2020, Biostatistics, 21, 417-431) recently proposed group testing protocols for multiplex assays and derived relevant case identification characteristics, including the expected number of tests and those which quantify classification accuracy. In this article, we describe Bayesian methods to estimate population-level disease probabilities from implementing these protocols or any other multiplex group testing protocol which might be carried out in practice. Our estimation methods can be used with multiplex assays for two or more diseases while incorporating the possibility of test misclassification for each disease. We use chlamydia and gonorrhea testing data collected at the State Hygienic Laboratory at the University of Iowa to illustrate our work. We also provide an online R resource practitioners can use to implement the methods in this article.
Asunto(s)
Infecciones por Chlamydia , Enfermedades Transmisibles , Humanos , Infecciones por Chlamydia/diagnóstico , Infecciones por Chlamydia/epidemiología , Infecciones por Chlamydia/prevención & control , Teorema de Bayes , Prevalencia , Enfermedades Transmisibles/diagnóstico , Enfermedades Transmisibles/epidemiología , ProbabilidadRESUMEN
The proportional hazards (PH) model is, arguably, the most popular model for the analysis of lifetime data arising from epidemiological studies, among many others. In such applications, analysts may be faced with censored outcomes and/or studies which institute enrollment criterion leading to left truncation. Censored outcomes arise when the event of interest is not observed but rather is known relevant to an observation time(s). Left truncated data occur in studies that exclude participants who have experienced the event prior to being enrolled in the study. If not accounted for, both of these features can lead to inaccurate inferences about the population under study. Thus, to overcome this challenge, herein we propose a novel unified PH model that can be used to accommodate both of these features. In particular, our approach can seamlessly analyze exactly observed failure times along with interval-censored observations, while aptly accounting for left truncation. To facilitate model fitting, an expectation-maximization algorithm is developed through the introduction of carefully structured latent random variables. To provide modeling flexibility, a monotone spline representation is used to approximate the cumulative baseline hazard function. The performance of our methodology is evaluated through a simulation study and is further illustrated through the analysis of two motivating data sets; one that involves child mortality in Nigeria and the other prostate cancer.
Asunto(s)
Algoritmos , Masculino , Niño , Humanos , Modelos de Riesgos Proporcionales , Simulación por ComputadorRESUMEN
BACKGROUND: There is a need to match characteristics of tobacco users with cessation treatments and risks of tobacco attributable diseases such as lung cancer. The rate in which the body metabolizes nicotine has proven an important predictor of these outcomes. Nicotine metabolism is primarily catalyzed by the enzyme cytochrone P450 (CYP2A6) and CYP2A6 activity can be measured as the ratio of two nicotine metabolites: trans-3'-hydroxycotinine to cotinine (NMR). Measurements of these metabolites are only possible in current tobacco users and vary by biofluid source, timing of collection, and protocols; unfortunately, this has limited their use in clinical practice. The NMR depends highly on genetic variation near CYP2A6 on chromosome 19 as well as ancestry, environmental, and other genetic factors. Thus, we aimed to develop prediction models of nicotine metabolism using genotypes and basic individual characteristics (age, gender, height, and weight). RESULTS: We identified four multiethnic studies with nicotine metabolites and DNA samples. We constructed a 263 marker panel from filtering genome-wide association scans of the NMR in each study. We then applied seven machine learning techniques to train models of nicotine metabolism on the largest and most ancestrally diverse dataset (N=2239). The models were then validated using the other three studies (total N=1415). Using cross-validation, we found the correlations between the observed and predicted NMR ranged from 0.69 to 0.97 depending on the model. When predictions were averaged in an ensemble model, the correlation was 0.81. The ensemble model generalizes well in the validation studies across ancestries, despite differences in the measurements of NMR between studies, with correlations of: 0.52 for African ancestry, 0.61 for Asian ancestry, and 0.46 for European ancestry. The most influential predictors of NMR identified in more than two models were rs56113850, rs11878604, and 21 other genetic variants near CYP2A6 as well as age and ancestry. CONCLUSIONS: We have developed an ensemble of seven models for predicting the NMR across ancestries from genotypes and age, gender and BMI. These models were validated using three datasets and associate with nicotine dosages. The knowledge of how an individual metabolizes nicotine could be used to help select the optimal path to reducing or quitting tobacco use, as well as, evaluating risks of tobacco use.
Asunto(s)
Cotinina , Nicotina , Cotinina/metabolismo , Estudio de Asociación del Genoma Completo , Genotipo , Humanos , Nicotina/metabolismo , Fumar/genética , Fumar/metabolismoRESUMEN
In screening applications involving low-prevalence diseases, pooling specimens (e.g., urine, blood, swabs, etc.) through group testing can be far more cost effective than testing specimens individually. Estimation is a common goal in such applications and typically involves modeling the probability of disease as a function of available covariates. In recent years, several authors have developed regression methods to accommodate the complex structure of group testing data but often under the assumption that covariate effects are linear. Although linearity is a reasonable assumption in some applications, it can lead to model misspecification and biased inference in others. To offer a more flexible framework, we propose a Bayesian generalized additive regression approach to model the individual-level probability of disease with potentially misclassified group testing data. Our approach can be used to analyze data arising from any group testing protocol with the goal of estimating multiple unknown smooth functions of covariates, standard linear effects for other covariates, and assay classification accuracy probabilities. We illustrate the methods in this article using group testing data on chlamydia infection in Iowa.
Asunto(s)
Infecciones por Chlamydia , Teorema de Bayes , Infecciones por Chlamydia/diagnóstico , Humanos , Tamizaje Masivo , Prevalencia , Análisis de RegresiónRESUMEN
Background: Substance use disorder (SUD) is a heterogeneous disorder. Adapting machine learning algorithms to allow for the parsing of intrapersonal and interpersonal heterogeneity in meaningful ways may accelerate the discovery and implementation of clinically actionable interventions in SUD research.Objectives: Inspired by a study of heavy drinkers that collected daily drinking and substance use (ABQ DrinQ), we develop tools to estimate subject-specific risk trajectories of heavy drinking; estimate and perform inference on patient characteristics and time-varying covariates; and present results in easy-to-use Jupyter notebooks. Methods: We recast support vector machines (SVMs) into a Bayesian model extended to handle mixed effects. We then apply these methods to ABQ DrinQ to model alcohol use patterns. ABQ DrinQ consists of 190 heavy drinkers (44% female) with 109,580 daily observations. Results: We identified male gender (point estimate; 95% credible interval: -0.25;-0.29,-0.21), older age (-0.03;-0.03,-0.03), and time varying usage of nicotine (1.68;1.62,1.73), cannabis (0.05;0.03,0.07), and other drugs (1.16;1.01,1.35) as statistically significant factors of heavy drinking behavior. By adopting random effects to capture the subject-specific longitudinal trajectories, the algorithm outperforms traditional SVM (classifies 84% of heavy drinking days correctly versus 73%). Conclusions: We developed a mixed effects variant of SVM and compare it to the traditional formulation, with an eye toward elucidating the importance of incorporating random effects to account for underlying heterogeneity in SUD data. These tools and examples are packaged into a repository for researchers to explore. Understanding patterns and risk of substance use could be used for developing individualized interventions.
Asunto(s)
Trastornos Relacionados con Sustancias , Máquina de Vectores de Soporte , Teorema de Bayes , Femenino , Humanos , Masculino , Trastornos Relacionados con Sustancias/epidemiologíaRESUMEN
Group testing involves pooling individual specimens (e.g., blood, urine, swabs, etc.) and testing the pools for the presence of disease. When the proportion of diseased individuals is small, group testing can greatly reduce the number of tests needed to screen a population. Statistical research in group testing has traditionally focused on applications for a single disease. However, blood service organizations and large-scale disease surveillance programs are increasingly moving towards the use of multiplex assays, which measure multiple disease biomarkers at once. Tebbs and others (2013, Two-stage hierarchical group testing for multiple infections with application to the Infertility Prevention Project. Biometrics69, 1064-1073) and Hou and others (2017, Hierarchical group testing for multiple infections. Biometrics73, 656-665) were the first to examine hierarchical group testing case identification procedures for multiple diseases. In this article, we propose new non-hierarchical procedures which utilize two-dimensional arrays. We derive closed-form expressions for the expected number of tests per individual and classification accuracy probabilities and show that array testing can be more efficient than hierarchical procedures when screening individuals for multiple diseases at once. We illustrate the potential of using array testing in the detection of chlamydia and gonorrhea for a statewide screening program in Iowa. Finally, we describe an R/Shiny application that will help practitioners identify the best multiple-disease case identification algorithm.
Asunto(s)
Algoritmos , Bioensayo , Enfermedades Transmisibles/diagnóstico , Tamizaje Masivo , Modelos Teóricos , Bioensayo/métodos , Bioensayo/normas , Infecciones por Chlamydia/diagnóstico , Gonorrea/diagnóstico , Humanos , Iowa , Tamizaje Masivo/métodos , Tamizaje Masivo/normasRESUMEN
High-volume testing of clinical specimens for sexually transmitted diseases is performed frequently by a process known as group testing. This algorithmic process involves testing portions of specimens from separate individuals together as one unit (or "group") to detect diseases. Retesting is performed on groups that test positively in order to differentiate between positive and negative individual specimens. The overall goal is to use the least number of tests possible across all individuals without sacrificing diagnostic accuracy. One of the most efficient group testing algorithms is array testing. In its simplest form, specimens are arranged into a grid-like structure so that row and column groups can be formed. Positive-testing rows/columns indicate which specimens to retest. With the growing use of multiplex assays, the increasing number of diseases tested by these assays, and the availability of subject-specific risk information, opportunities exist to make this testing process even more efficient. We propose specific specimen arrangements within an array that can reduce the number of retests needed when compared with other array testing algorithms. We examine how to calculate operating characteristics, including the expected number of tests and the SD for the number of tests, and then subsequently find a best arrangement. Our methods are illustrated for chlamydia and gonorrhea detection with the Aptima Combo 2 Assay. We also provide R functions to make our research accessible to laboratories.
Asunto(s)
Infecciones por Chlamydia , Gonorrea , Enfermedades de Transmisión Sexual , Algoritmos , Chlamydia trachomatis , Humanos , Sensibilidad y EspecificidadRESUMEN
When screening for infectious diseases, group testing has proven to be a cost efficient alternative to individual level testing. Cost savings are realized by testing pools of individual specimens (eg, blood, urine, saliva, and so on) rather than by testing the specimens separately. However, a common concern that arises in group testing is the so-called "dilution effect." This occurs if the signal from a positive individual's specimen is diluted past an assay's threshold of detection when it is pooled with multiple negative specimens. In this article, we propose a new statistical framework for group testing data that merges estimation and case identification, which are often treated separately in the literature. Our approach considers analyzing continuous biomarker levels (eg, antibody levels, antigen concentrations, and so on) from pooled samples to estimate both a binary regression model for the probability of disease and the biomarker distributions for cases and controls. To increase case identification accuracy, we then show how estimates of the biomarker distributions can be used to select diagnostic thresholds on a pool-by-pool basis. Our proposals are evaluated through numerical studies and are illustrated using hepatitis B virus data collected on a prison population in Ireland.
Asunto(s)
Enfermedades Transmisibles , Biomarcadores , Humanos , Irlanda , Tamizaje MasivoRESUMEN
INTRODUCTION: The nicotine metabolite ratio and nicotine equivalents are measures of metabolism rate and intake. Genome-wide prediction of these nicotine biomarkers in multiethnic samples will enable tobacco-related biomarker, behavioral, and exposure research in studies without measured biomarkers. AIMS AND METHODS: We screened genetic variants genome-wide using marginal scans and applied statistical learning algorithms on top-ranked genetic variants, age, ethnicity and sex, and, in additional modeling, cigarettes per day (CPD), (in additional modeling) to build prediction models for the urinary nicotine metabolite ratio (uNMR) and creatinine-standardized total nicotine equivalents (TNE) in 2239 current cigarette smokers in five ethnic groups. We predicted these nicotine biomarkers using model ensembles and evaluated external validity using dependence measures in 1864 treatment-seeking smokers in two ethnic groups. RESULTS: The genomic regions with the most selected and included variants for measured biomarkers were chr19q13.2 (uNMR, without and with CPD) and chr15q25.1 and chr10q25.3 (TNE, without and with CPD). We observed ensemble correlations between measured and predicted biomarker values for the uNMR and TNE without (with CPD) of 0.67 (0.68) and 0.65 (0.72) in the training sample. We observed inconsistency in penalized regression models of TNE (with CPD) with fewer variants at chr15q25.1 selected and included. In treatment-seeking smokers, predicted uNMR (without CPD) was significantly associated with CPD and predicted TNE (without CPD) with CPD, time-to-first-cigarette, and Fagerström total score. CONCLUSIONS: Nicotine metabolites, genome-wide data, and statistical learning approaches developed novel robust predictive models for urinary nicotine biomarkers in multiple ethnic groups. Predicted biomarker associations helped define genetically influenced components of nicotine dependence. IMPLICATIONS: We demonstrate development of robust models and multiethnic prediction of the uNMR and TNE using statistical and machine learning approaches. Variants included in trained models for nicotine biomarkers include top-ranked variants in multiethnic genome-wide studies of smoking behavior, nicotine metabolites, and related disease. Association of the two predicted nicotine biomarkers with Fagerström Test for Nicotine Dependence items supports models of nicotine biomarkers as predictors of physical dependence and nicotine exposure. Predicted nicotine biomarkers may facilitate tobacco-related disease and treatment research in samples with genomic data and limited nicotine metabolite or tobacco exposure data.
Asunto(s)
Productos de Tabaco , Tabaquismo , Biomarcadores , Humanos , Nicotina , Fumar/genética , Tabaquismo/genéticaRESUMEN
Due to reductions in both time and cost, group testing is a popular alternative to individual-level testing for disease screening. These reductions are obtained by testing pooled biospecimens (eg, blood, urine, swabs, etc.) for the presence of an infectious agent. However, these reductions come at the expense of data complexity, making the task of conducting disease surveillance more tenuous when compared to using individual-level data. This is because an individual's disease status may be obscured by a group testing protocol and the effect of imperfect testing. Furthermore, unlike individual-level testing, a given participant could be involved in multiple testing outcomes and/or may never be tested individually. To circumvent these complexities and to incorporate all available information, we propose a Bayesian generalized linear mixed model that accommodates data arising from any group testing protocol, estimates unknown assay accuracy probabilities and accounts for potential heterogeneity in the covariate effects across population subgroups (eg, clinic sites, etc.); this latter feature is of key interest to practitioners tasked with conducting disease surveillance. To achieve model selection, our proposal uses spike and slab priors for both fixed and random effects. The methodology is illustrated through numerical studies and is applied to chlamydia surveillance data collected in Iowa.
Asunto(s)
Teorema de Bayes , Humanos , Iowa , Modelos LinealesRESUMEN
The proportional hazards (PH) model is arguably one of the most popular models used to analyze time to event data arising from clinical trials and longitudinal studies. In many such studies, the event time is not directly observed but is known relative to periodic examination times; i.e., practitioners observe either current status or interval-censored data. The analysis of data of this structure is often fraught with many difficulties since the event time of interest is unobserved. Further exacerbating this issue, in some such studies the observed data also consists of instantaneous failures; i.e., the event times for several study units coincide exactly with the time at which the study begins. In light of these difficulties, this work focuses on developing a mixture model, under the PH assumptions, which can be used to analyze interval-censored data subject to instantaneous failures. To allow for modeling flexibility, two methods of estimating the unknown cumulative baseline hazard function are proposed; a fully parametric and a monotone spline representation are considered. Through a novel data augmentation procedure involving latent Poisson random variables, an expectation-maximization (EM) algorithm is developed to complete model fitting. The resulting EM algorithm is easy to implement and is computationally efficient. Moreover, through extensive simulation studies the proposed approach is shown to provide both reliable estimation and inference. The motivation for this work arises from a randomized clinical trial aimed at assessing the effectiveness of a new peanut allergen treatment in attaining sustained unresponsiveness in children.
Asunto(s)
Algoritmos , Distribución de Poisson , Modelos de Riesgos Proporcionales , Simulación por Computador , HumanosRESUMEN
Infectious disease testing frequently takes advantage of two tools-group testing and multiplex assays-to make testing timely and cost effective. Until the work of Tebbs et al. (2013) and Hou et al. (2017), there was no research available to understand how best to apply these tools simultaneously. This recent work focused on applications where each individual is considered to be identical in terms of the probability of disease. However, risk-factor information, such as past behavior and presence of symptoms, is very often available on each individual to allow one to estimate individual-specific probabilities. The purpose of our paper is to propose the first group testing algorithms for multiplex assays that take advantage of individual risk-factor information as expressed by these probabilities. We show that our methods significantly reduce the number of tests required while preserving accuracy. Throughout this paper, we focus on applying our methods with the Aptima Combo 2 Assay that is used worldwide for chlamydia and gonorrhea screening.
Asunto(s)
Algoritmos , Enfermedades Transmisibles/diagnóstico , Tamizaje Masivo/métodos , Infecciones por Chlamydia/diagnóstico , Femenino , Gonorrea/diagnóstico , Humanos , Masculino , Probabilidad , Factores de RiesgoRESUMEN
For disease screening, group (pooled) testing can be a cost-saving alternative to one-at-a-time testing, with savings realized through assaying pooled biospecimen (eg, urine, blood, saliva). In many group testing settings, practitioners are faced with the task of conducting disease surveillance. That is, it is often of interest to relate individuals' true disease statuses to covariate information via binary regression. Several authors have developed regression methods for group testing data, which is challenging due to the effects of imperfect testing. That is, all testing outcomes (on pools and individuals) are subject to misclassification, and individuals' true statuses are never observed. To further complicate matters, individuals may be involved in several testing outcomes. For analyzing such data, we provide a novel regression methodology which generalizes and extends the aforementioned regression techniques and which incorporates regularization. Specifically, for model fitting and variable selection, we propose an adaptive elastic net estimator under the logistic regression model which can be used to analyze data from any group testing strategy. We provide an efficient algorithm for computing the estimator along with guidance on tuning parameter selection. Moreover, we establish the asymptotic properties of the proposed estimator and show that it possesses "oracle" properties. We evaluate the performance of the estimator through Monte Carlo studies and illustrate the methodology on a chlamydia data set from the State Hygienic Laboratory in Iowa City.
Asunto(s)
Interpretación Estadística de Datos , Tamizaje Masivo/métodos , Algoritmos , Infecciones por Chlamydia/diagnóstico , Simulación por Computador , Humanos , Tamizaje Masivo/economía , Tamizaje Masivo/estadística & datos numéricos , Método de Montecarlo , Análisis de RegresiónRESUMEN
Group testing is an indispensable tool for laboratories when testing high volumes of clinical specimens for infectious diseases. An important decision that needs to be made prior to implementation is determining what group sizes to use. In best practice, an objective function is chosen and then minimized to determine an optimal set of these group sizes, known as the optimal testing configuration (OTC). There are a few options for objective functions, and they differ based on how the expected number of tests, assay characteristics, and testing constraints are taken into account. These varied options have led to a recent controversy in the literature regarding which of two different objective functions is better. In our paper, we examine these objective functions over a number of realistic situations for infectious disease testing. We show that this controversy may be much ado about nothing because the OTCs and corresponding results (eg, number of tests and accuracy) are largely the same for standard testing algorithms in a wide variety of situations.
Asunto(s)
Algoritmos , Enfermedades Transmisibles/diagnóstico , Pruebas Diagnósticas de Rutina/estadística & datos numéricos , Tamizaje Masivo/estadística & datos numéricos , HumanosRESUMEN
For analyzing current status data, a flexible partially linear proportional hazards model is proposed. Modeling flexibility is attained through using monotone splines to approximate the baseline cumulative hazard function, as well as B-splines to accommodate nonlinear covariate effects. To facilitate model fitting, a computationally efficient and easy to implement expectation-maximization algorithm is developed through a two-stage data augmentation process involving carefully structured latent Poisson random variables. Asymptotic normality and the efficiency of the spline estimator of the regression coefficients are established, and the spline estimators of the nonparametric components are shown to possess the optimal rate of convergence under suitable regularity conditions. The finite-sample performance of the proposed approach is evaluated through Monte Carlo simulation and it is further illustrated using uterine fibroid data arising from a prospective cohort study on early pregnancy.
Asunto(s)
Algoritmos , Estado de Salud , Leiomioma/epidemiología , Modelos de Riesgos Proporcionales , Adulto , Simulación por Computador , Femenino , Humanos , Método de Montecarlo , Distribución de Poisson , EmbarazoRESUMEN
In this work, we delineate an altered study design of a pre-existing clinical trial that is currently being implemented in the Department of Pediatrics at the University of North Carolina at Chapel Hill. The purpose of the ongoing investigation of the desensitized pediatric cohort is to address the effectiveness of sublingual immunotherapy in achieving sustained unresponsiveness (SU) as assessed by repeated double-blind placebo-controlled food challenges (DBPCFC). With scarce published literature characterizing SU, the length of time off-therapy that would represent clinically meaningful benefit remains undefined. We use the new design features to assess time to loss of SU, an important efficacy endpoint, that to our knowledge, no prior study has investigated. Our work has two-fold objectives: first is to propose and discuss aspects of the altered design that would allow us to study SU and second is to explore methodology to evaluate the time to loss of SU and its association with risk factors in the context of the data originating from the trial. The salient feature of the new design is the allocation scheme of study subjects to staggered sampling timepoints when a subsequent DBPCFC is administered. Due to this feature, the time to loss of SU is either left or right censored. Additionally, some participants at study entry fail the DBPCFC, leading to what can be construed as an instantaneous failure. Through in-depth numerical studies, we examine the performance and power of a recently proposed mixture proportional hazards model specifically designed for the analysis of interval-censored data subject to instantaneous failures.
Asunto(s)
Alérgenos/uso terapéutico , Hipersensibilidad al Cacahuete/terapia , Ensayos Clínicos Controlados Aleatorios como Asunto/métodos , Inmunoterapia Sublingual/métodos , Resultado del Tratamiento , Alérgenos/administración & dosificación , Alérgenos/inmunología , Arachis/inmunología , Niño , Ensayos Clínicos Fase II como Asunto/métodos , Interpretación Estadística de Datos , Método Doble Ciego , Femenino , Humanos , Masculino , Modelos EstadísticosRESUMEN
Screening procedures for infectious diseases, such as HIV, often involve pooling individual specimens together and testing the pools. For diseases with low prevalence, group testing (or pooled testing) can be used to classify individuals as diseased or not while providing considerable cost savings when compared to testing specimens individually. The pooling literature is replete with group testing case identification algorithms including Dorfman testing, higher-stage hierarchical procedures, and array testing. Although these algorithms are usually evaluated on the basis of the expected number of tests and classification accuracy, most evaluations in the literature do not account for the continuous nature of the testing responses and thus invoke potentially restrictive assumptions to characterize an algorithm's performance. Commonly used case identification algorithms in group testing are considered and are evaluated by taking a different approach. Instead of treating testing responses as binary random variables (i.e., diseased/not), evaluations are made by exploiting an assay's underlying continuous biomarker distributions for positive and negative individuals. In doing so, a general framework to describe the operating characteristics of group testing case identification algorithms is provided when these distributions are known. The methodology is illustrated using two HIV testing examples taken from the pooling literature.
RESUMEN
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.
RESUMEN
Group testing, where individuals are tested initially in pools, is widely used to screen a large number of individuals for rare diseases. Triggered by the recent development of assays that detect multiple infections at once, screening programs now involve testing individuals in pools for multiple infections simultaneously. Tebbs, McMahan, and Bilder (2013, Biometrics) recently evaluated the performance of a two-stage hierarchical algorithm used to screen for chlamydia and gonorrhea as part of the Infertility Prevention Project in the United States. In this article, we generalize this work to accommodate a larger number of stages. To derive the operating characteristics of higher-stage hierarchical algorithms with more than one infection, we view the pool decoding process as a time-inhomogeneous, finite-state Markov chain. Taking this conceptualization enables us to derive closed-form expressions for the expected number of tests and classification accuracy rates in terms of transition probability matrices. When applied to chlamydia and gonorrhea testing data from four states (Region X of the United States Department of Health and Human Services), higher-stage hierarchical algorithms provide, on average, an estimated 11% reduction in the number of tests when compared to two-stage algorithms. For applications with rarer infections, we show theoretically that this percentage reduction can be much larger.