Flexible Bayesian semiparametric mixed-effects model for skewed longitudinal data.

BACKGROUND: In clinical trials and epidemiological research, mixed-effects models are commonly used to examine population-level and subject-specific trajectories of biomarkers over time. Despite their increasing popularity and application, the specification of these models necessitates a great deal of care when analysing longitudinal data with non-linear patterns and asymmetry. Parametric (linear) mixed-effect models may not capture these complexities flexibly and adequately. Additionally, assuming a Gaussian distribution for random effects and/or model errors may be overly restrictive, as it lacks robustness against deviations from symmetry. METHODS: This paper presents a semiparametric mixed-effects model with flexible distributions for complex longitudinal data in the Bayesian paradigm. The non-linear time effect on the longitudinal response was modelled using a spline approach. The multivariate skew-t distribution, which is a more flexible distribution, is utilized to relax the normality assumptions associated with both random-effects and model errors. RESULTS: To assess the effectiveness of the proposed methods in various model settings, simulation studies were conducted. We then applied these models on chronic kidney disease (CKD) data and assessed the relationship between covariates and estimated glomerular filtration rate (eGFR). First, we compared the proposed semiparametric partially linear mixed-effect (SPPLM) model with the fully parametric one (FPLM), and the results indicated that the SPPLM model outperformed the FPLM model. We then further compared four different SPPLM models, each assuming different distributions for the random effects and model errors. The model with a skew-t distribution exhibited a superior fit to the CKD data compared to the Gaussian model. The findings from the application revealed that hypertension, diabetes, and follow-up time had a substantial association with kidney function, specifically leading to a decrease in GFR estimates. CONCLUSIONS: The application and simulation studies have demonstrated that our work has made a significant contribution towards a more robust and adaptable methodology for modeling intricate longitudinal data. We achieved this by proposing a semiparametric Bayesian modeling approach with a spline smoothing function and a skew-t distribution.

Spatial mapping of colorectal cancer screening uptake and associated factors.

OBJECTIVE: Over the past decades, it has been understood that the availability of screening tests has contributed to a steady decline in incidence of colorectal cancer (CRC). However, it is also seen that there is a geographic disparity in the use of such tests across small areas. The aim of this study is to examine small-area level barrier factors that may impact CRC screening uptake and to delineate coldspot (low uptake of screening) counties in Florida. METHODS: Data on the percentages of county-level CRC screening uptakes in 2016 and county-level barrier factors for screening were obtained from the Florida Department of Health, Division of Public Health Statistics & Performance Management. Bayesian spatial beta models were used to produce posterior probability of deceedance to identify coldspots for CRC screening rates. RESULTS: Unadjusted screening rates using sigmoidoscopy or colonoscopy test ranged from 56.8 to 85%. Bayesian spatial beta models were fitted to the proportion data. At an ecological level, we found that an increasing rate of CRC screening uptake for either of the test types (colon/rectum exam, stool-based test) was strongly associated with a higher health insurance coverage, and lower percentage of population that speak English less than very well (immigration) at county level. Eleven coldspot counties out of 67 total were also identified. CONCLUSION: This study suggests that health insurance disparities in the use of CRC screening tests are an important factor that may need more attention for resource allocation and health policy targeting small areas with low uptake of screening.

Colorectal Cancer Risk Perceptions Among Black Men in Florida.

PURPOSE: We examined colorectal cancer (CRC) risk perceptions among Black men in relation to socio-demographic characteristics, disease prevention factors, and personal/family history of CRC. METHODS: A self-administered cross-sectional survey was conducted in five major cities in Florida between April 2008 and October 2009. Descriptive statistics and multivariable logistic regression were performed. RESULTS: Among 331 eligible men, we found a higher proportion of CRC risk perceptions were exhibited among those aged ≥ 60 years (70.5%) and American nativity (59.1%). Multivariable analyses found men aged ≥ 60 had three times greater odds of having higher CRC risk perceptions compared to those ≤ 49 years (95% CI = 1.51-9.19). The odds of higher CRC risk perception for obese participants were more than four times (95% CI = 1.66-10.00) and overweight were more than twice the odds (95% CI = 1.03-6.31) as compared to healthy weight/underweight participants. Men using the Internet to search for health information also had greater odds of having higher CRC risk perceptions (95% CI = 1.02-4.00). Finally, men with a personal/family history of CRC were ninefold more likely to have higher CRC risk perceptions (95% CI = 2.02-41.79). CONCLUSION: Higher CRC risk perceptions were associated with older age, being obese/overweight, using the Internet as a health information source, and having a personal/family history of CRC. Culturally resonate health promotion interventions are sorely needed to elevate CRC risk perceptions for increasing intention to screen among Black men.

Nightmare disorder and low back pain in veterans: cross-sectional association and effect over time.

Low back pain (LBP) disproportionately impacts US military veterans compared with nonveterans. Although the effect of psychological conditions on LBP is regularly studied, there is little published to date investigating nightmare disorder (NMD) and LBP. The purpose of this study was to (1) investigate whether an association exists between NMD and LBP and (2) estimate the effect of NMD diagnosis on time to LBP. We used a retrospective cohort design with oversampling of those with NMD from the Veterans Health Administration (n = 15 983). We used logistic regression to assess for a cross-sectional association between NMD and LBP and survival analysis to estimate the effect of NMD on time to LBP, up to 60-month follow-up, conditioning on age, sex, race, index year, Charlson Comorbidity Index, depression, anxiety, insomnia, combat exposure, and prisoner of war history to address confounding. Odds ratios (with 95% confidence intervals [CIs]) indicated a cross-sectional association of 1.35 (1.13 to 1.60) and 1.21 (1.02 to 1.42) for NMD and LBP within 6 months and 12 months pre- or post-NMD diagnosis, respectively. Hazard ratios (HRs) indicated the effect of NMD on time to LBP that was time-dependent-HR (with 95% CIs) 1.27 (1.02 to 1.59), 1.23 (1.03 to 1.48), 1.19 (1.01 to 1.40), and 1.10 (0.94 to 1.29) in the first 3, 6, 9, and 12 months post-diagnosis, respectively-approximating the null (1.00) at >12 months. The estimated effect of NMD on LBP suggests that improved screening for NMD among veterans may help clinicians and researchers predict (or intervene to reduce) risk of future back pain.

Geographic variation and association of risk factors with incidence of colorectal cancer at small-area level.

PURPOSE: Examining spatial distribution of colorectal cancer (CRC) incidence or mortality is helpful for developing cancer control and prevention programs or for generating hypotheses. Such an investigation involves describing the spatial variation of risk factors for CRC and identifying hotspots. The aim of this study is to identify county-level risk factors that may be associated with the incidence of CRC and to map hotspots for CRC in Florida. METHODS: County-level CRC cases, recorded in 2018, were obtained from the Florida Department of Health, Division of Public Health Statistics & Performance Management (DPHSM). Data on county-level risk factors were also obtained from the same source. We used Bayesian spatial models for relative incidence rates and produced posterior predictive that indicates excess risk (hotspots) for CRC. RESULTS: The county-level unadjusted incidence rates range from .462 to 3.142. After fitting a Bayesian spatial model to the data, the results show that a decreasing risk of CRC is strongly associated with an increasing median income, higher percentage of Black population, and higher percentage of sedentary life at county level. Using exceedance probability, it is also observed that there are clustering and hotspots of high CRC incidence rates in Charlotte County in South Florida, Hernando, Sumter and Seminole counties in central Florida and Union and Washington counties in north Florida. CONCLUSION: Among few county-level variables that significantly explained the spatial variation of CRC, income disparity may need more attention for resource allocation and developing preventive intervention in high-risk areas for CRC.

Bayesian censored piecewise regression mixture models with skewness.

This paper presents censored mixture regression models with piecewise growth curves for assessing longitudinal data that exhibit multiphasic features. Such features may include censoring, skewness, measurement errors in covariates, and mixtures of unobserved subpopulations. In the process of describing those features, identification of differential effects of predictors on a response variable for a heterogeneous population (subpopulations) has recently been highly sought. Regression mixture models are key methods for assessing differential effects of predictors. In this article, we extend regression mixture models with normal distribution to incorporate (i) skew-normal distribution, (ii) left-censoring, (iii) measurement errors, and (iv) piecewise growth mixture modeling for describing multiphasic trajectories over time where the observed observations come from a mixture of unobserved subgroups. The proposed methods are illustrated using real data from an AIDS clinical study and a Bayesian approach.

Multilevel modeling, prevalence, and predictors of hypertension in Ghana: Evidence from Wave 2 of the World Health Organization's Study on global AGEing and adult health.

BACKGROUND AND AIMS: Hypertension is a major public health issue, an important risk factor for cardiovascular diseases and stroke, especially in developing countries where the rates remain unacceptably high. In Africa, hypertension is the leading driver of cardiovascular disease and stroke deaths. Identification of critical risk factors of hypertension can help formulate targeted public health programs and policies aimed at reducing the prevalence and its associated morbidity, disability, and mortality. This study attempts to develop multilevel regression, an in-depth statistical model to identify critical risk factors of hypertension. METHODS: This study used data on 4667 individuals aged ≥18 years from the nationally representative World Health Organization Study on global AGEing and adult health (SAGE) Ghana Wave 2 conducted in 2014/2015. Multilevel regression modeling was employed to identify critical risk factors for hypertension based on systolic blood pressure (SBP) (ie, SBP > 140 mmHg). Of the 4667, 27.3% were hypertensive. Final data on 4381 individuals residing in 3790 households were analyzed using multilevel models, and results were presented as adjusted odds ratios (aOR) and their associated 95% confidence intervals (CI). RESULTS: Risk factors for hypertension identified were age (aOR) = 5.4, 95% CI: 4.11-7.09), obesity (aOR = 1.51, 95% CI: 1.19-1.91), marital status (aOR = 0.75, 95% CI: 0.64-0.89), perceived health state (moderate; aOR = 1.38, 95% CI: 1.15-1.65 and bad/very bad; aOR = 1.35, 95% CI: 1.0-1.83), and difficulty with self-care (aOR = 1.64, 95% CI: 1.1-2.44). We found unobserved significant differences in the likelihood of hypertension prevalence between different households. CONCLUSION: Addressing the problem of obesity, targeting specific interventions to those aged over 50 years, and improvement in the general health of Ghanaians are paramount to reducing the prevalence and its associated morbidity, disability, and mortality. Lifestyle modification in the form of dietary intake, knowledge provision supported with strong public health message, and political will could be beneficial to the management and prevention of hypertension.

Geostatistical analysis, web-based mapping, and environmental determinants of under-5 stunting: evidence from the 2014 Ghana Demographic and Health Survey.

BACKGROUND: Stunting rates in children younger than 5 years are among the most important health indicators globally. At the national level, malnutrition accounts for about 40% of under-5 deaths in Ghana. Disease risk mapping provides opportunities for disease surveillance and targeted interventions. We aimed to estimate and map under-5 stunting prevalence in Ghana, with the goal of identifying communities at higher risk where interventions and further research can be targeted. METHODS: For this modelling study, we used data from the 2014 Ghana Demographic and Health Survey. Analyses were done on 2734 children residing in 415 geographical clusters. The outcome variable was the number of stunted children younger than 5 years in each sampled cluster. We employed a Bayesian geostatistical model to investigate both measured and unmeasured spatial risk factors for child stunting, comparing the performance of non-spatial (adjusting for selected covariates without spatial correlation), spatial (including spatial correlation), and null spatial (without the selected covariates) models. We then visualised the stunting prevalence across Ghana by mapping the predicted prevalence and exceedance probabilities to resolutions as refined as 5 km × 5 km. FINDINGS: In 2014, 535 (19·6%) of 2734 children surveyed in Ghana were stunted. Elevation (log odds mean -0·0017, 95% credible interval -0·0034 to -0·0001), precipitation (0·0403, 0·0192 to 0·0615), and aridity (-3·7013, -6·5478 to -0·8723) were environmental and climatic factors associated with stunting in the non-spatial model, but were not significant in the spatial model. Substantial geographical variations in prevalence of childhood stunting were found. The predicted mean stunting prevalence was 27·7% (SD 3·7%) with predicted prevalence ranging from 4·2% to 45·1% across Ghana. Children residing in parts of the Northern region were at highest risk of stunting, whereas parts of the Greater Accra, Brong-Ahafo, Ashanti, and Eastern regions showed some of the lowest prevalence. INTERPRETATION: There are substantial geographical differences in childhood stunting across Ghana. Our prevalence maps can be used as an effective tool to identify communities that require targeted interventions by programme managers and implementers, as part of an overall strategy to reduce the burden of malnutrition in a country with limited public health resources. FUNDING: None.

Geospatial analysis, web-based mapping and determinants of prostate cancer incidence in Georgia counties: evidence from the 2012-2016 SEER data.

BACKGROUND: Prostate cancer (CaP) cases are high in the United States. According to the American Cancer Society, there are an estimated number of 174,650 CaP new cases in 2019. The estimated number of deaths from CaP in 2019 is 31,620, making CaP the second leading cause of cancer deaths among American men with lung cancer been the first. Our goal is to estimate and map prostate cancer relative risk, with the ultimate goal of identifying counties at higher risk where interventions and further research can be targeted. METHODS: The 2012-2016 Surveillance, Epidemiology, and End Results (SEER) Program data was used in this study. Analyses were conducted on 159 Georgia counties. The outcome variable is incident prostate cancer. We employed a Bayesian geospatial model to investigate both measured and unmeasured spatial risk factors for prostate cancer. We visualised the risk of prostate cancer by mapping the predicted relative risk and exceedance probabilities. We finally developed interactive web-based maps to guide optimal policy formulation and intervention strategies. RESULTS: Number of persons above age 65 years and below poverty, higher median family income, number of foreign born and unemployed were risk factors independently associated with prostate cancer risk in the non-spatial model. Except for the number of foreign born, all these risk factors were also significant in the spatial model with the same direction of effects. Substantial geographical variations in prostate cancer incidence were found in the study. The predicted mean relative risk was 1.20 with a range of 0.53 to 2.92. Individuals residing in Towns, Clay, Union, Putnam, Quitman, and Greene counties were at increased risk of prostate cancer incidence while those residing in Chattahoochee were at the lowest risk of prostate cancer incidence. CONCLUSION: Our results can be used as an effective tool in the identification of counties that require targeted interventions and further research by program managers and policy makers as part of an overall strategy in reducing the prostate cancer burden in Georgia State and the United States as a whole.

Compressive sensing based maximum-minimum subband energy detection for cognitive radios.

To satisfy the growing spectrum demands of emerging wireless applications, cognitive radios have been considered as a viable option. It enables dynamic spectrum access opportunistically using wideband spectrum sensing (WSS) methods to discover the temporarily free frequency bands. WSS requires a high-speed analog-to-digital converter (ADC), which has high power consumption and hardware complexity. Improving the power consumption and hardware complexity of the ADC is one of the existing challenges in energy-constrained applications. To alleviate this problem, we propose compressive sensing (CS) in maximum-minimum subband energy detection method to sense the wideband spectrum by utilizing the sparse nature of spectrum occupancy with the minimal possible number of measurements. The CS method uses Fourier Transform and chaotic sequence in designing the measurement matrix to achieve both determinacy and randomness. The Bayesian method is used to reconstruct the signal from the available measurements. From the reconstructed signal, the maximum-minimum subband energy detection (ED) method is used to decide whether the primary user (PU) is absent or present in a particular frequency band. The simulation results show that the proposed CS-based maximum-minimum subband energy detection approach improves the probability of detection by 7.5% compared to the conventional maximum-minimum subband energy detection method of spectrum sensing. The proposed spectrum sensing method is simple and robust to noise uncertainty and signal strength variations.

Bayesian semiparametric growth models for measurement error and missing data in CD4/CD8 ratio: Application to AIDS Study.

In clinical research and practice, there is often an interest in assessing the effect of time varying predictors, such as CD4/CD8 ratio, on immune recovery following antiretroviral therapy. Such predictors are measured with errors, and ignoring those measurement errors during data analysis may lead to biased results. Though parametric methods have been used for reducing biases, they usually depend on untestable assumptions. To relax those assumptions, this paper presents semiparametric mixed-effect models which deal with predictors having measurement errors and missing values. We develop a fully Bayesian approach for fitting these models and discriminating between patients who are potentially progressors or nonprogressors to severe disease condition (AIDS). The proposed methods are demonstrated using real data from an AIDS clinical study.

Macroeconomic and distributional impacts of exchange rate devaluation in Ethiopia: A computable general equilibrium approach.

In this paper, we simulate the macroeconomic and distributional impacts of exchange rate devaluation in Ethiopia using a dynamic single country Computable General Equilibrium model. We find that although devaluation helps exports to be more competitive in the short term, thereby increasing export earnings, over the long term the policy is found to have a contractionary and inflationary impact in a developing country like Ethiopia. It also comes at the cost of a reduction in household welfare and investment. In terms of distributional impact, the policy simulation result suggests that devaluation disproportionately affects urban households than rural households in Ethiopia given the nature of their consumption basket.

Global 3-D Simulations of the Triple Oxygen Isotope Signature Δ17O in Atmospheric CO2.

The triple oxygen isotope signature Δ17O in atmospheric CO2, also known as its "17O excess," has been proposed as a tracer for gross primary production (the gross uptake of CO2 by vegetation through photosynthesis). We present the first global 3-D model simulations for Δ17O in atmospheric CO2 together with a detailed model description and sensitivity analyses. In our 3-D model framework we include the stratospheric source of Δ17O in CO2 and the surface sinks from vegetation, soils, ocean, biomass burning, and fossil fuel combustion. The effect of oxidation of atmospheric CO on Δ17O in CO2 is also included in our model. We estimate that the global mean Δ17O (defined as Δ 17 O = ln ( δ 17 O + 1 ) - λ RL · ln ( δ 18 O + 1 ) with λ RL = 0.5229) of CO2 in the lowest 500 m of the atmosphere is 39.6 per meg, which is ∼20 per meg lower than estimates from existing box models. We compare our model results with a measured stratospheric Δ17O in CO2 profile from Sodankylä (Finland), which shows good agreement. In addition, we compare our model results with tropospheric measurements of Δ17O in CO2 from Göttingen (Germany) and Taipei (Taiwan), which shows some agreement but we also find substantial discrepancies that are subsequently discussed. Finally, we show model results for Zotino (Russia), Mauna Loa (United States), Manaus (Brazil), and South Pole, which we propose as possible locations for future measurements of Δ17O in tropospheric CO2 that can help to further increase our understanding of the global budget of Δ17O in atmospheric CO2.

Evaluating construct equivalence of youth depression measures across multiple measures and multiple studies.

Construct equivalence of measures across studies is necessary for synthesizing results when combining data in meta-analysis or integrative data analysis. We discuss several assumptions required for construct equivalence, and review methods using individual-level data and item response theory (IRT) analysis for detecting or adjusting for violations of these assumptions. We apply IRT to data from 7 measures of depressive symptoms for 4,283 youth from 16 randomized prevention trials. Findings indicate that these data violate assumptions of conditional independence. Bifactor IRT models find that depression measures contain substantial reporter variance, and indicate that a single common factor model would be substantially biased. Separate analyses of ratings by youth find stronger evidence for construct equivalence, but factor invariance across sex and age does not hold. We conclude that data synthesis studies employing measures of youth depression should analyze results separately by reporter, explore more complex approaches to integrate these different perspectives, and explore methods that adjust for sex and age differences in item functioning. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

Determination of the triple oxygen and carbon isotopic composition of CO2 from atomic ion fragments formed in the ion source of the 253 Ultra high-resolution isotope ratio mass spectrometer.

RATIONALE: Determination of δ17 O values directly from CO2 with traditional gas source isotope ratio mass spectrometry is not possible due to isobaric interference of 13 C16 O16 O on 12 C17 O16 O. The methods developed so far use either chemical conversion or isotope equilibration to determine the δ17 O value of CO2 . In addition, δ13 C measurements require correction for the interference from 12 C17 O16 O on 13 C16 O16 O since it is not possible to resolve the two isotopologues. METHODS: We present a technique to determine the δ17 O, δ18 O and δ13 C values of CO2 from the fragment ions that are formed upon electron ionization in the ion source of the Thermo Scientific 253 Ultra high-resolution isotope ratio mass spectrometer (hereafter 253 Ultra). The new technique is compared with the CO2 -O2 exchange method and the 17 O-correction algorithm for δ17 O and δ13 C values, respectively. RESULTS: The scale contractions for δ13 C and δ18 O values are slightly larger for fragment ion measurements than for molecular ion measurements. The δ17 O and Δ17 O values of CO2 can be measured on the 17 O+ fragment with an internal error that is a factor 1-2 above the counting statistics limit. The ultimate precision depends on the signal intensity and on the total time that the 17 O+ beam is monitored; a precision of 14 ppm (parts per million) (standard error of the mean) was achieved in 20 hours at the University of Göttingen. The Δ17 O measurements with the O-fragment method agree with the CO2 -O2 exchange method over a range of Δ17 O values of -0.3 to +0.7‰. CONCLUSIONS: Isotope measurements on atom fragment ions of CO2 can be used as an alternative method to determine the carbon and oxygen isotopic composition of CO2 without chemical processing or corrections for mass interferences.

Measurement of 18 O18 O and 17 O18 O in atmospheric O2 using the 253 Ultra mass spectrometer and applications to stratospheric and tropospheric air samples.

RATIONALE: The doubly substituted isotopologues (e.g., 18 O18 O, 17 O18 O) in atmospheric O2 are potential tracers for ozone photochemistry and atmospheric temperatures. Their low abundances and isobaric interference are the major analytical challenges. The 253 Ultra high-resolution stable isotope ratio mass spectrometer is suitable for resolving isobaric interferences. METHODS: O2 from air is purified using gas chromatography on a packed column filled with molecular sieve 5 Å and cooled to -78°C. The δ17 O, δ18 O, Δ17 O, Δ35 and Δ36 values are measured on the extracted O2 with the 253 Ultra at medium mass resolution (M/ΔM ~10000) using Faraday detectors for the singly substituted isotopologues and ion counters for the doubly substituted isotopologues. RESULTS: Interferences from isobars, mainly 35 Cl for 17 O18 O and H35 Cl and 36 Ar for 18 O18 O, are sufficiently resolved to enable high-precision determination of Δ35 and Δ36 . The Δ35 and Δ36 values of O2 after photochemical isotope equilibration at -63°C and heating to 850°C agree with the theoretical prediction. The stratospheric Δ35 and Δ36 values are close to isotopic equilibrium at the ambient temperatures. However, the values for tropospheric O2 differ from those expected at equilibrium. CONCLUSIONS: The 253 Ultra allows interference-free clumped isotope measurements of O2 at medium mass resolution. The Δ35 and Δ36 signatures in atmospheric O2 are mainly governed by O3 photochemistry, temperature and atmospheric transport. Tropospheric O2 is isotopically well mixed and retains a significant stratospheric signature.

Heterogeneous growth bent-cable models for time-to-event and longitudinal data: application to AIDS studies.

The major limitations of growth curve mixture models for HIV/AIDS data are the usual assumptions of normality and monophasic curves within latent classes. This article addresses these limitations by using non-normal skewed distributions and multiphasic patterns for outcomes of prospective studies. For such outcomes, new skew-t (ST) distributions are proposed for modeling heterogeneous growth trajectories, which exhibit not abrupt but gradual multiphasic changes from a declining trend to an increasing trend over time. We assess these clinically important features of longitudinal HIV/AIDS data using the bent-cable framework within a context of a joint modeling of time-to-event process and response process. A real dataset from an AIDS clinical study is used to illustrate the proposed methods.

Joint bent-cable Tobit models for longitudinal and time-to-event data.

In this article, we show how to estimate a transition period for the evolvement of drug resistance to antiretroviral (ARV) drug or other related treatments in the framework of developing a Bayesian method for jointly analyzing time-to-event and longitudinal data. For HIV/AIDS longitudinal data, developmental trajectories of viral loads tend to show a gradual change from a declining trend after initiation of treatment to an increasing trend without an abrupt change. Such characteristics of trajectories are also associated with a time-to-event process. To assess these clinically important features, we develop a joint bent-cable Tobit model for the time-to-event and left-censored response variable with skewness and phasic developments. Random effects are used to determine the stochastic dependence between the time-to-event process and response process. The proposed method is illustrated using real data from an AIDS clinical study.

Bayesian two-part bent-cable Tobit models with skew distributions: Application to AIDS studies.

This paper presents a new development of a bent-cable two-part Tobit model to identify both phasic patterns and mixture of advancing (to AIDS) and non-advancing patients of HIV. In identification of such phasic patterns, estimation of a transition period for the development of drug resistance to antiretroviral (ARV) drug or therapy is carried out using longitudinal data that have a gradual change from a declining phase to an increasing phase. In addition to phasic changes, there are also problems of skewness and left-censoring in the response variable because of a lower limit of detection. A relatively large percentage of data below limit of detection are recorded more than expected under an assumed skew-distribution. To properly accommodate these features, we present an extension of the random effects bent-cable Tobit model that incorporates a mixture of true undetectable observations and those values from a skew-normal distribution for a response with left-censoring, skewness and phasic patterns. The proposed methods are illustrated using real data from an AIDS clinical study.

Joint two-part Tobit models for longitudinal and time-to-event data.

In this article, we show how Tobit models can address problems of identifying characteristics of subjects having left-censored outcomes in the context of developing a method for jointly analyzing time-to-event and longitudinal data. There are some methods for handling these types of data separately, but they may not be appropriate when time to event is dependent on the longitudinal outcome, and a substantial portion of values are reported to be below the limits of detection. An alternative approach is to develop a joint model for the time-to-event outcome and a two-part longitudinal outcome, linking them through random effects. This proposed approach is implemented to assess the association between the risk of decline of CD4/CD8 ratio and rates of change in viral load, along with discriminating between patients who are potentially progressors to AIDS from patients who do not. We develop a fully Bayesian approach for fitting joint two-part Tobit models and illustrate the proposed methods on simulated and real data from an AIDS clinical study.