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1.  Bayesian Semiparametric Mixture Tobit Models with Left-Censoring, Skewness and Covariate Measurement Errors 
Statistics in medicine  2013;32(22):3881-3898.
Common problems to many longitudinal HIV/AIDS, cancer, vaccine and environmental exposure studies are the presence of a lower limit of quantification of an outcome with skewness and time-varying covariates with measurement errors. There has been relatively little work published simultaneously dealing with these features of longitudinal data. In particular, left-censored data falling below a limit of detection (LOD) may sometimes have a proportion larger than expected under a usually assumed log-normal distribution. In such cases, alternative models which can account for a high proportion of censored data should be considered. In this article, we present an extension of the Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for an outcome with possible left-censoring and skewness, and covariates with substantial measurement error. To quantify the covariate process, we offer a flexible nonparametric mixed-effects model within the Tobit framework. A Bayesian modeling approach is used to assess the simultaneous impact of left-censoring, skewness and measurement error in covariates on inference. The proposed methods are illustrated using real data from an AIDS clinical study.
doi:10.1002/sim.5799
PMCID: PMC3773307  PMID: 23553914
measurement error; mixed-effects models; mixture Tobit models; skew distributions
2.  Bayesian Inference for Skew-Normal Mixture Models With Left-Censoring 
Assays to measure concentration of antibody after vaccination are often subject to left-censoring due to a lower detection limit (LDL), leading to a high proportion of observations below the detection limit. Not accounting for such left-censoring appropriately can lead to biased parameter estimates. To properly adjust for left-censoring and a high proportion of observations at LDL, this paper proposes a mixture model combining a point mass below LDL and a Tobit model with skew-elliptical error distribution. We show that skew-elliptical distributions, where the skew-normal and skew-t are special cases, have great flexibility for simultaneously handling left-censoring, skewness and heaviness in the tails of a distribution of a response variable with left-censored data. A Bayesian procedure is used to estimate model parameters. Two real datasets from a study of measles vaccine and an HIV/AIDS study are used to illustrate the proposed models.
doi:10.1080/10543406.2013.813517
PMCID: PMC3985432  PMID: 23957513
Bayesian inference; Censoring; Mixed-effects models; Skew-normal distribution; Tobit model
3.  Effect of combining mosquito repellent and insecticide treated net on malaria prevalence in Southern Ethiopia: a cluster-randomised trial 
Parasites & Vectors  2014;7:132.
Background
A mosquito repellent has the potential to prevent malaria infection, but there has been few studies demonstrating the effectiveness of combining this strategy with the highly effective long-lasting insecticidal nets (LLINs). This study aimed to determine the effect of combining community-based mosquito repellent with LLINs in the reduction of malaria.
Methods
A community-based clustered-randomised trial was conducted in 16 rural villages with 1,235 households in southern Ethiopia between September and December of 2008. The villages were randomly assigned to intervention (mosquito repellent and LLINs, eight villages) and control (LLINs alone, eight villages) groups. Households in the intervention villages received mosquito repellent (i.e., Buzz-Off® petroleum jelly, essential oil blend) applied every evening. The baseline survey was followed by two follow-up surveys, at one month interval. The primary outcome was detection of Plasmodium falciparum, Plasmodium vivax, or both parasites, through microscopic examination of blood slides. Analysis was by intention to treat. Baseline imbalances and clustering at individual, household and village levels were adjusted using a generalized linear mixed model.
Results
3,078 individuals in intervention and 3,004 in control group were enrolled into the study. Compared with the control arm, the combined use of mosquito repellent and LLINs significantly reduced malaria infection of all types over time [adjusted Odds Ratio (aOR) = 0.66; 95% CI = 0.45-0.97]. Similarly, a substantial reduction in P. falciparum malaria infection during the follow-up surveys was observed in the intervention group (aOR = 0.53, 95% CI = 0.31-0.89). The protective efficacy of using mosquito repellent and LLINs against malaria infection of both P. falciparum/P. vivax and P. falciparum was 34% and 47%, respectively.
Conclusions
Daily application of mosquito repellent during the evening followed by the use of LLINs during bedtime at community level has significantly reduced malaria infection. The finding has strong implication particularly in areas where malaria vectors feed mainly in the evening before bedtime.
Trial registration
ClinicalTrials.gov identifier: NCT01160809.
doi:10.1186/1756-3305-7-132
PMCID: PMC3986599  PMID: 24678612
4.  Impact of Maternal Thyroperoxidase Status on Fetal Body and Brain Size 
Journal of Thyroid Research  2014;2014:872410.
The obstetric consequences of abnormal thyroid function during pregnancy have been established. Less understood is the influence of maternal thyroid autoantibodies on infant outcomes. The objective of this study was to examine the influence of maternal thyroperoxidase (TPO) status on fetal/infant brain and body growth. Six-hundred thirty-one (631) euthyroid pregnant women were recruited from prenatal clinics in Tampa Bay, Florida, and the surrounding area between November 2007 and December 2010. TPO status was determined during pregnancy and fetal/infant brain and body growth variables were assessed at delivery. Regression analysis revealed maternal that TPO positivity was significantly associated with smaller head circumference, reduced brain weight, and lower brain-to-body ratio among infants born to TPO+ white, non-Hispanic mothers only, distinguishing race/ethnicity as an effect modifier in the relationship. No significant differences were noted in body growth measurements among infants born to TPO positive mothers of any racial/ethnic group. Currently, TPO antibody status is not assessed as part of the standard prenatal care laboratory work-up, but findings from this study suggest that fetal brain growth may be impaired by TPO positivity among certain populations; therefore autoantibody screening among high-risk subgroups may be useful for clinicians to determine whether prenatal thyroid treatment is warranted.
doi:10.1155/2014/872410
PMCID: PMC3929063  PMID: 24624307
5.  Simultaneous Bayesian inference for skew-normal semiparametric nonlinear mixed-effects models with covariate measurement errors 
Bayesian analysis (Online)  2011;7(1):189-210.
Longitudinal data arise frequently in medical studies and it is a common practice to analyze such complex data with nonlinear mixed-effects (NLME) models which enable us to account for between-subject and within-subject variations. To partially explain the variations, covariates are usually introduced to these models. Some covariates, however, may be often measured with substantial errors. It is often the case that model random error is assumed to be distributed normally, but the normality assumption may not always give robust and reliable results, particularly if the data exhibit skewness. Although there has been considerable interest in accommodating either skewness or covariate measurement error in the literature, there is relatively little work that considers both features simultaneously. In this article, our objectives are to address simultaneous impact of skewness and covariate measurement error by jointly modeling the response and covariate processes under a general framework of Bayesian semiparametric nonlinear mixed-effects models. The method is illustrated in an AIDS data example to compare potential models which have different distributional specifications. The findings from this study suggest that the models with a skew-normal distribution may provide more reasonable results if the data exhibit skewness and/or have measurement errors in covariates.
doi:10.1214/12-BA706
PMCID: PMC3584628  PMID: 23459161
Bayesian approach; Covariate measurement errors; HIV/AIDS; Joint models; Longitudinal data; Semiparametric nonlinear mixed-effects models; Skew-normal distribution
6.  Bayesian Semiparametric Nonlinear Mixed-Effects Joint Models for Data with Skewness, Missing Responses, and Measurement Errors in Covariates 
Biometrics  2011;68(3):943-953.
Summary
It is a common practice to analyze complex longitudinal data using semiparametric nonlinear mixed-effects (SNLME) models with a normal distribution. Normality assumption of model errors may unrealistically obscure important features of subject variations. To partially explain between- and within-subject variations, covariates are usually introduced in such models, but some covariates may often be measured with substantial errors. Moreover, the responses may be missing and the missingness may be nonignorable. Inferential procedures can be complicated dramatically when data with skewness, missing values, and measurement error are observed. In the literature, there has been considerable interest in accommodating either skewness, incompleteness or covariate measurement error in such models, but there has been relatively little study concerning all three features simultaneously. In this article, our objective is to address the simultaneous impact of skewness, missingness, and covariate measurement error by jointly modeling the response and covariate processes based on a flexible Bayesian SNLME model. The method is illustrated using a real AIDS data set to compare potential models with various scenarios and different distribution specifications.
doi:10.1111/j.1541-0420.2011.01719.x
PMCID: PMC3460696  PMID: 22150787
Bayesian analysis; Covariate measurement errors; Longitudinal data; Missing data; Random-effects models; Skew distributions
7.  Inherited Variants in Mitochondrial Biogenesis Genes May Influence Epithelial Ovarian Cancer Risk 
Background
Mitochondria contribute to oxidative stress, a phenomenon implicated in ovarian carcinogenesis. We hypothesized that inherited variants in mitochondrial-related genes influence epithelial ovarian cancer (EOC) susceptibility.
Methods
Through a multi-center study of 1,815 Caucasian EOC cases and 1,900 controls, we investigated associations between EOC risk and 128 single nucleotide polymorphisms (SNPs) from 22 genes/regions within the mitochondrial genome (mtDNA) and 2,839 nuclear-encoded SNPs localized to 138 genes involved in mitochondrial biogenesis (BIO, n=35), steroid hormone metabolism (HOR, n=13), and oxidative phosphorylation (OXP, n=90) pathways. Unconditional logistic regression was used to estimate odds ratios (OR) and 95% confidence intervals (CI) between genotype and case status. Overall significance of each gene and pathway was evaluated using Fisher’s method to combine SNP-level evidence. At the SNP-level, we investigated whether lifetime ovulation, hormone replacement therapy (HRT), and cigarette smoking were confounders or modifiers of associations.
Results
Inter-individual variation involving BIO was most strongly associated with EOC risk (empirical P=0.050), especially for NRF1, MTERF, PPARGC1A, ESRRA, and CAMK2D. Several SNP-level associations strengthened after adjustment for non-genetic factors, particularly for MTERF. Statistical interactions with cigarette smoking and HRT use were observed with MTERF and CAMK2D SNPs, respectively. Overall variation within mtDNA, HOR, and OXP was not statistically significant (empirical P >0.10).
Conclusion
We provide novel evidence to suggest that variants in mitochondrial biogenesis genes may influence EOC susceptibility.
Impact
A deeper understanding of the complex mechanisms implicated in mitochondrial biogenesis and oxidative stress may aid in developing strategies to reduce morbidity and mortality from EOC.
doi:10.1158/1055-9965.EPI-10-1224
PMCID: PMC3111851  PMID: 21447778
polymorphisms; oxidative stress; genetic susceptibility; mitochondria; ovarian cancer
8.  Simultaneous Bayesian Inference for Linear, Nonlinear and Semiparametric Mixed-Effects Models with Skew-Normality and Measurement Errors in Covariates 
In recent years, various mixed-effects models have been suggested for estimating viral decay rates in HIV dynamic models for complex longitudinal data. Among those models are linear mixed-effects (LME), nonlinear mixed-effects (NLME), and semiparametric nonlinear mixed-effects (SNLME) models. However, a critical question is whether these models produce coherent estimates of viral decay rates, and if not, which model is appropriate and should be used in practice. In addition, one often assumes that a model random error is normally distributed, but the normality assumption may be unrealistic, particularly if the data exhibit skewness. Moreover, some covariates such as CD4 cell count may be often measured with substantial errors. This paper addresses these issues simultaneously by jointly modeling the response variable with skewness and a covariate process with measurement errors using a Bayesian approach to investigate how estimated parameters are changed or different under these three models. A real data set from an AIDS clinical trial study was used to illustrate the proposed models and methods. It was found that there was a significant incongruity in the estimated decay rates in viral loads based on the three mixed-effects models, suggesting that the decay rates estimated by using Bayesian LME or NLME joint models should be interpreted differently from those estimated by using Bayesian SNLME joint models. The findings also suggest that the Bayesian SNLME joint model is preferred to other models because an arbitrary data truncation is not necessary; and it is also shown that the models with a skew-normal distribution and/or measurement errors in covariate may achieve reliable results when the data exhibit skewness.
doi:10.2202/1557-4679.1292
PMCID: PMC3404555  PMID: 22848189
Bayesian analysis; covariate measurement errors; HIV dynamics; mixed-effects joint models; skew-normal distribution
9.  Prognostic Performance of Metabolic Indexes in Predicting Onset of Type 1 Diabetes 
Diabetes Care  2010;33(12):2508-2513.
OBJECTIVE
In this investigation we evaluated nine metabolic indexes from intravenous glucose tolerance tests (IVGTTs) and oral glucose tolerance tests (OGTTs) in an effort to determine their prognostic performance in predicting the development of type 1 diabetes in those with moderate risk, as defined by familial relation to a type 1 diabetic individual, a positive test for islet cell antibodies and insulin autoantibody, but normal glucose tolerance.
RESEARCH DESIGN AND METHODS
Subjects (n = 186) who had a projected risk of 25–50% for developing type 1 diabetes within 5 years were followed until clinical diabetes onset or the end of the study as part of the Diabetes Prevention Trial–Type 1. Prognostic performance of the metabolic indexes was determined using receiver operating characteristic (ROC) curve and survival analyses.
RESULTS
Two-hour glucose from an OGTT most accurately predicted progression to disease compared with all other metabolic indicators with an area under the ROC curve of 0.67 (95% CI 0.59–0.76), closely followed by the ratio of first-phase insulin response (FPIR) to homeostasis model assessment of insulin resistance (HOMA-IR) with an area under the curve value of 0.66. The optimal cutoff value for 2-h glucose (114 mg/dl) maintained sensitivity and specificity values >0.60. The hazard ratio for those with 2-h glucose ≥114 mg/dl compared with those with 2-h glucose <114 mg/dl was 2.96 (1.67–5.22).
CONCLUSIONS
The ratio of FPIR to HOMA-IR from an IVGTT provided accuracy in predicting the development of type 1 diabetes similar to that of 2-h glucose from an OGTT, which, because of its lower cost, is preferred. The optimal cutoff value determined for 2-h glucose provides additional guidance for clinicians to identify subjects for potential prevention treatments before the onset of impaired glucose tolerance.
doi:10.2337/dc10-0802
PMCID: PMC2992179  PMID: 20807869
10.  LIN28B polymorphisms influence susceptibility to epithelial ovarian cancer 
Cancer research  2011;71(11):3896-3903.
Defective miRNA biogenesis contributes to the development and progression of epithelial ovarian cancer (EOC). In this study, we examined the hypothesis that single nucleotide polymorphisms (SNPs) in miRNA biogenesis genes may influence EOC risk. In an initial investigation, 318 SNPs in 18 genes were evaluated among 1,815 EOC cases and 1,900 controls, followed up by a replicative joint meta-analysis of data from an additional 2,172 cases and 3,052 controls. Of 23 SNPs from 9 genes associated with risk (empirical P<0.05) in the initial investigation, the meta-analysis replicated 6 SNPs from the DROSHA, FMR1, LIN28, and LIN28B genes, including rs12194974 (G>A), a SNP in a putative transcription factor binding site in the LIN28B promoter region (summary OR=0.90, 95% CI: 0.82–0.98; P=0.015) which has been recently implicated in age of menarche and other phenotypes. Consistent with reports that LIN28B over-expression in EOC contributes to tumorigenesis by repressing tumor suppressor let-7 expression, we provide data from luciferase reporter assays and quantitative RT-PCR to suggest that the inverse association among rs12194974 A allele carriers may be due to reduced LIN28B expression. Our findings suggest that variants in LIN28B and possibly other miRNA biogenesis genes may influence EOC susceptibility.
doi:10.1158/0008-5472.CAN-10-4167
PMCID: PMC3107389  PMID: 21482675
miRNA processing; inherited susceptibility; ovarian cancer; genetic variants
11.  Prostate cancer health and cultural beliefs of black men: The Florida Prostate Cancer Disparity Project 
Infectious Agents and Cancer  2011;6(Suppl 2):S10.
Background
Since behavioral factors are significant determinants of population health, addressing prostate cancer (CaP)-related health beliefs and cultural beliefs are key weapons to fight this deadly disease. This study investigated the health beliefs and cultural beliefs of black men relative to CaP, and the key socio-demographic correlates of these beliefs.
Methods
The study design was a cross-sectional survey of 2,864 Florida black men, age 40 to 70, on their perceived susceptibility, perceived severity, attitude, outcomes beliefs, perceived behavioral control, CaP fatalism, religiosity, temporal orientation, and acculturation relative to CaP screening and prevention.
Results
The men reported favorable attitude and positive outcome beliefs, but moderate perceived behavioral control, CaP susceptibility and CaP severity. They also had low level of acculturation, did not hold fatalistic beliefs about CaP, had high religious coping skills and had high future time perspective. Several demographic variables were found to be associated with health beliefs and cultural beliefs.
Discussion
Our study provides rich data with regard to the health and cultural beliefs that might serve to inform the development of CaP control initiative for US-born and foreign-born black men.
doi:10.1186/1750-9378-6-S2-S10
PMCID: PMC3194180  PMID: 21992652
12.  BAYESIAN ANALYSIS OF REPEATED EVENTS USING EVENT-DEPENDENT FRAILTY MODELS: AN APPLICATION TO BEHAVIORAL OBSERVATION DATA 
In social interaction studies, one commonly encounters repeated displays of behaviors along with their duration data. Statistical methods for the analysis of such data use either parametric (e.g., Weibull) or semi-nonparametric (e.g., Cox) proportional hazard models, modified to include random effects (frailty) which account for the correlation of repeated occurrences of behaviors within a unit (dyad). However, dyad-specific random effects by themselves are not able to account for the ordering of event occurrences within dyads. The occurrence of an event (behavior) can make further occurrences of the same behavior to be more or less likely during an interaction. This paper develops event-dependent random effects models for analyzing repeated behaviors data using a Bayesian approach. The models are illustrated by a dataset relating to emotion regulation in families with children who have behavioral or emotional problems.
doi:10.1080/03610920902737118
PMCID: PMC2808641  PMID: 20161593
Bayesian inference; emotion regulation; random effects; social interaction; survival model
13.  Bayesian Hierarchical Duration Model for Repeated Events : An Application to Behavioral Observations 
Journal of applied statistics  2009;36(11):1267-1279.
This paper presents a continuous-time Bayesian model for analyzing durations of behavior displays in social interactions. Duration data of social interactions are often complex because of repeated behaviors (events) at individual or group (e.g., dyad) level, multiple behaviors (multistates), and several choices of exit from a current event (competing risks). A multilevel, multistate model is proposed to adequately characterize the behavioral processes. The model incorporates dyad-specific and transition-specific random effects to account for heterogeneity among dyads and interdependence among competing risks. The proposed method is applied to child-parent observational data derived from the School Transitions Project to assess the relation of emotional expression in child-parent interaction to risk for early and persisting child conduct problems.
doi:10.1080/02664760802587032
PMCID: PMC2832316  PMID: 20209032
competing risks; event history; survival; multilevel models; multistates; Bayesian inference; semi-Markov models
14.  Adaptive Designs for Randomized Trials in Public Health 
In this article, we present a discussion of two general ways in which the traditional randomized trial can be modified or adapted in response to the data being collected. We use the term adaptive design to refer to a trial in which characteristics of the study itself, such as the proportion assigned to active intervention versus control, change during the trial in response to data being collected. The term adaptive sequence of trials refers to a decision-making process that fundamentally informs the conceptualization and conduct of each new trial with the results of previous trials. Our discussion below investigates the utility of these two types of adaptations for public health evaluations. Examples are provided to illustrate how adaptation can be used in practice. From these case studies, we discuss whether such evaluations can or should be analyzed as if they were formal randomized trials, and we discuss practical as well as ethical issues arising in the conduct of these new-generation trials.
doi:10.1146/annurev.publhealth.031308.100223
PMCID: PMC2778326  PMID: 19296774
multilevel trials; multistage trials; growth mixture models; encouragement designs; CACE modeling; principal stratification

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