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Non-negative continuous outcomes with a substantial number of zero values and incomplete longitudinal follow-up are quite common in medical costs data. It is thus critical to incorporate the potential dependence of survival status and longitudinal medical costs in joint modeling, where censorship is death-related. Despite the wide use of conventional two-part joint models (CTJMs) to capture zero-inflation, they are limited to conditional interpretations of the regression coefficients in the model’s continuous part. In this paper, we propose a marginalized two-part joint model (MTJM) to jointly analyze semi-continuous longitudinal costs data and survival data. We compare it to the conventional two-part joint model (CTJM) for handling marginal inferences about covariate effects on average costs. We conducted a series of simulation studies to evaluate the superior performance of the proposed MTJM over the CTJM. To illustrate the applicability of the MTJM, we applied the model to a set of real electronic health record (EHR) data recently collected in Iran. We found that the MTJM yielded a smaller standard error, root-mean-square error of estimates, and AIC value, with unbiased parameter estimates. With this MTJM, we identified a significant positive correlation between costs and survival, which was consistent with the simulation results.

Panel counts are often encountered in longitudinal, such as diary, studies where individuals are followed over time and the number of events occurring in time intervals, or panels, is recorded. This article develops methods for situations where, in addition to the counts of events, a mark, denoting a measure of severity of the events, is recorded. In many situations there is an association between the panel counts and their marks. This is the case for our motivating application that studies the effect of two hormone therapy treatments in reducing counts and severities of vasomotor symptoms in women after hysterectomy/ovariectomy. We model the event counts and their severities jointly through the use of shared random effects. We also compare, through simulation, the power of testing for the treatment effect based on such joint modeling and an alternative scoring approach, which is commonly employed. The scoring approach analyzes the compound outcome of counts times weighted severity. We discuss this approach and quantify challenges which may arise in isolating the treatment effect when such a scoring approach is used. We also show that the power of detecting a treatment effect is higher when using the joint model than analysis using the scoring approach. Inference is performed via Markov chain Monte Carlo methods.

Mixture models are frequently used in ecology for the estimation of abundance. These models adopt a hierarchical structure in which the observations are dependent on both a detection probability and abundance at the survey site. Applications are typically to discrete survey count data. Analogous mixture models have not been developed for semi‐continuous sampling data, which are characterised by a large number of zero observations and non‐zero observations measured on a continuous scale. We attempt to bridge the gap between mixture modelling approaches developed for discrete counts and their application to semi‐continuous data. We use survival analysis to derive a relationship between a continuous measure of abundance and the probability of a zero observation, and incorporate this relationship into a two‐part, log‐normal hurdle model, with the biomass represented as a hierarchical model parameter. We apply the model to semi‐continuous marine sampling data collected from a bottom trawl fishery in New Zealand. Despite the simplicity of the parameterisation, the model is able to describe the observations and predict a relative biomass density layer over space. The approach allows mixture models to be applied to semi‐continuous ecological data. By allowing the population density distribution to be properly estimated, the methods presented here can inform the management of anthropogenic impacts on vulnerable species, as well as understanding distributional shifts that may arise due to climate change.

Background Connective tissue growth factor (CTGF), is a secreted matricellular factor that has been linked to increased risk of cardiovascular disease in diabetic subjects. Despite the biological role of CTGF in diabetes, it still remains unclear how CTGF expression is regulated. In this study, we aim to identify the clinical parameters that modulate plasma CTGF levels measured longitudinally in type 1 diabetic patients over a period of 10 years. A number of patients had negligible measured values of plasma CTGF that formed a point mass at zero, whereas others had high positive values of CTGF that were measured on a continuous scale. The observed combination of excessive zero and continuous positively distributed non-zero values in the CTGF outcome is referred to as semicontinuous data. Methods We propose a novel application of a marginalized two-part model (mTP) extended to accommodate longitudinal semicontinuous data in which the marginal mean is expressed in terms of the covariates and estimates of their effect on the mean responses are generated. The continuous component is assumed to follow distributions that stem from the generalized gamma family whereas the binary measure is analyzed using logistic model and both have correlated random effects. Other approaches including the one- and two-part with uncorrelated and correlated random effects models were also applied and their estimates were all compared. Results Our results using the mTP model identified intensive glucose control treatment and smoking as clinical factors that were associated with decreased and increased odds of observing non-zero CTGF values respectively. In addition, hemoglobin A1c, systolic blood pressure, and high density lipoprotein were all shown to be significant risk factors that contribute to increasing CTGF levels. These findings were consistently observed under the mTP model but varied with the distributions for the other models. Accuracy and precision of the mTP model was further validated using simulation studies. Conclusion The mTP model identified new clinical determinants that modulate the levels of CTGF in diabetic subjects. Applicability of this approach can be extended to other biomarkers measured in patient populations that display a combination of negligible zero and non-zero values.

In 2001, the U.S. Office of Personnel Management required all health plans participating in the Federal Employees Health Benefits Program to offer mental health and substance abuse benefits on par with general medical benefits. The initial evaluation found that, on average, parity did not result in either large spending increases or increased service use over the four-year observational period. However, some groups of enrollees may have benefited from parity more than others. To address this question, we propose a Bayesian two-part latent class model to characterize the effect of parity on mental health use and expenditures. Within each class, we fit a two-part random effects model to separately model the probability of mental health or substance abuse use and mean spending trajectories among those having used services. The regression coefficients and random effect covariances vary across classes, thus permitting class-varying correlation structures between the two components of the model. Our analysis identified three classes of subjects: a group of low spenders that tended to be male, had relatively rare use of services, and decreased their spending pattern over time; a group of moderate spenders, primarily female, that had an increase in both use and mean spending after the introduction of parity; and a group of high spenders that tended to have chronic service use and constant spending patterns. By examining the joint 95% highest probability density regions of expected changes in use and spending for each class, we confirmed that parity had an impact only on the moderate spender class.

The problem of small area estimation (SAE) is how to produce reliable estimates of characteristics of interest such as means, counts, quantiles, etc., for areas or domains for which only small samples or no samples are available, and how to assess their precision. The purpose of this paper is to review and discuss some of the new important developments in small area estimation methods. Rao [Small Area Estimation (2003)] wrote a very comprehensive book, which covers all the main developments in this topic until that time. A few review papers have been written after 2003, but they are limited in scope. Hence, the focus of this review is on new developments in the last 7-8 years, but to make the review more self-contained, I also mention shortly some of the older developments. The review covers both designbased and model-dependent methods, with the latter methods further classified into frequentist and Bayesian methods. The style of the paper is similar to the style of my previous review on SAE published in 2002, explaining the new problems investigated and describing the proposed solutions, but without dwelling on theoretical details, which can be found in the original articles. I hope that this paper will be useful both to researchers who like to learn more on the research carried out in SAE and to practitioners who might be interested in the application of the new methods.

Zero-inflated nonnegative continuous (or semicontinuous) data arise frequently in biomedical, economical, and ecological studies. Examples include substance abuse, medical costs, medical care utilization, biomarkers (e.g., CD4 cell counts, coronary artery calcium scores), single cell gene expression rates, and (relative) abundance of microbiome. Such data are often characterized by the presence of a large portion of zero values and positive continuous values that are skewed to the right and heteroscedastic. Both of these features suggest that no simple parametric distribution may be suitable for modeling such type of outcomes. In this paper, we review statistical methods for analyzing zero-inflated nonnegative outcome data. We will start with the cross-sectional setting, discussing ways to separate zero and positive values and introducing flexible models to characterize right skewness and heteroscedasticity in the positive values. We will then present models of correlated zero-inflated nonnegative continuous data, using random effects to tackle the correlation on repeated measures from the same subject and that across different parts of the model. We will also discuss expansion to related topics, for example, zero-inflated count and survival data, nonlinear covariate effects, and joint models of longitudinal zero-inflated nonnegative continuous data and survival. Finally, we will present applications to three real datasets (i.e., microbiome, medical costs, and alcohol drinking) to illustrate these methods. Example code will be provided to facilitate applications of these methods.

The hypobaric decompression sickness data study was conducted by the National Aeronautics and Space Administration to investigate the risk of decompression sickness in hypobaric environments. The quantity of interest is the time to onset of grade IV venous gas emboli, which was mixed case interval censored because of measurement limitations. In the study, some subjects participated in multiple experiments, leading to repeated and correlated measurements on those subjects. In addition, it has been suggested that some subjects had a much lower risk of developing grade IV venous gas emboli than others, i.e. those subjects were immune from the event of interest (or 'cured'). We propose to use two-part models, where the first part describes the probability of cure and the second part describes the survival for susceptible subjects. We use two random effects to account for the correlated nature of measurements. A leverage bootstrap approach is proposed for model diagnosis. A simulation study shows satisfactory performance of the estimation and diagnosis approaches proposed. Model estimation and evaluation of the hypobaric decompression sickness data are carefully investigated.

The current ITU rain attenuation model that is used in the design of satellite-earth communication link was derived using data collected predominantly from temperate regions and has limitations when applied to tropical and equatorial regions that are characterized by heavy rainfall. Elevation and frequency scaling was applied to the rain attenuation data obtained from tropical and equatorial regions to validate the linear relationship for rain rates above 90 mm/h in the TPRA model. Analysis of the data from these regions also confirms the linear relationship between the rain attenuation and rain rates above 90 mm/h. The TPRA model can be considered as an alternative model for a reliable satellite-earth link for use in the tropical and equatorial regions.