Nonproportional random effects modelling of a neonatal unit operational patient pathways

Modelling patient flow in health care systems is considered to be vital in understanding the operational and clinical functions of the system and may therefore prove to be useful in improving the functionality of the health care system, and most importantly provide an evidence based approach for decision making, particularly in the management of the system. In this paper, we introduce a nonproportional cumulative odds random effects model for patient pathways by violating the proportional assumption of the cumulative odds model. Using the probability integral transform, we have extended this to cases where the random effects are not normal, specifically gamma and exponentially distributions. Some of the advantages of this is that these models depict changes in wellbeing (frailties) of patients as they move from one stage of care to the other in time. This is an hybrid extension of our earlier work by jointly including pathways and covariates to explain probability of transition and discharge, which could easily be used to predict the outcome of the treatment. The models here show that the inclusion of pathways render patients characteristics as insignificant. Thus, pathways provide a source of useful information about transition and discharge than patient characteristics, especially when the model is applied to a London University Neonatal Unit dataset. Bootstrapping was then used to investigate the stability, consistency and generalizability of estimated parameters from the models.     

Bayesian structural equation modeling for the health index

There are many factors which could influence the level of health of an individual. These factors are interactive and their overall effects on health are usually measured by an index which is called as health index. The health index could also be used as an indicator to describe the health level of a community. Since the health index is important, many research have been done to study its determinant. The main purpose of this study is to model the health index of an individual based on classical structural equation modeling (SEM) and Bayesian SEM. For estimation of the parameters in the measurement and structural equation models, the classical SEM applies the robust-weighted least-square approach, while the Bayesian SEM implements the Gibbs sampler algorithm. The Bayesian SEM approach allows the user to use the prior information for updating the current information on the parameter. Both methods are applied to the data gathered from a survey conducted in Hulu Langat, a district in Malaysia. Based on the classical and the Bayesian SEM, it is found that demographic status and lifestyle are significantly related to the health index. However, mental health has no significant relation to the health index.     

A latent variable model for analyzing mixed longitudinal (k,l)-inflated count and ordinal responses

A random effects model for analyzing mixed longitudinal count and ordinal data is presented where the count response is inflated in two points (k and l) and an (k,l)-Inflated Power series distribution is used as its distribution. A full likelihood-based approach is used to obtain maximum likelihood estimates of parameters of the model. For data with non-ignorable missing values models with probit model for missing mechanism are used.The dependence between longitudinal sequences of responses and inflation parameters are investigated using a random effects approach. Also, to investigate the correlation between mixed ordinal and count responses of each individuals at each time, a shared random effect is used. In order to assess the performance of the model, a simulation study is performed for a case that the count response has (k,l)-Inflated Binomial distribution. Performance comparisons of count-ordinal random effect model, Zero-Inflated ordinal random effects model and (k,l)-Inflated ordinal random effects model are also given. The model is applied to a real social data set from the first two waves of the national longitudinal study of adolescent to adult health (Add Health study). In this data set, the joint responses are the number of days in a month that each individual smoked as the count response and the general health condition of each individual as the ordinal response. For the count response there is incidence of excess values of 0 and 30.     

A finite mixture model for multivariate counts under endogenous selectivity

We describe a selection model for multivariate counts, where association between the primary outcomes and the endogenous selection source is modeled through outcome-specific latent effects which are assumed to be dependent across equations. Parametric specifications of this model already exist in the literature; in this paper, we show how model parameters can be estimated in a finite mixture context. This approach helps us to consider overdispersed counts, while allowing for multivariate association and endogeneity of the selection variable. In this context, attention is focused both on bias in estimated effects when exogeneity of selection (treatment) variable is assumed, as well as on consistent estimation of the association between the random effects in the primary and in the treatment effect models, when the latter is assumed endogeneous. The model behavior is investigated through a large scale simulation experiment. An empirical example on health care utilization data is provided.     

A Bayesian approach of joint models for clustered zero-inflated count data with skewness and measurement errors

Count data with excess zeros are widely encountered in the fields of biomedical, medical, public health and social survey, etc. Zero-inflated Poisson (ZIP) regression models with mixed effects are useful tools for analyzing such data, in which covariates are usually incorporated in the model to explain inter-subject variation and normal distribution is assumed for both random effects and random errors. However, in many practical applications, such assumptions may be violated as the data often exhibit skewness and some covariates may be measured with measurement errors. In this paper, we deal with these issues simultaneously by developing a Bayesian joint hierarchical modeling approach. Specifically, by treating intercepts and slopes in logistic and Poisson regression as random, a flexible two-level ZIP regression model is proposed, where a covariate process with measurement errors is established and a skew-t-distribution is considered for both random errors and random effects. Under the Bayesian framework, model selection is carried out using deviance information criterion (DIC) and a goodness-of-fit statistics is also developed for assessing the plausibility of the posited model. The main advantage of our method is that it allows for more robustness and correctness for investigating heterogeneity from different levels, while accommodating the skewness and measurement errors simultaneously. An application to Shanghai Youth Fitness Survey is used as an illustrate example. Through this real example, it is showed that our approach is of interest and usefulness for applications.     

Assessing conditional independence for log-linear poisson models with random effects

In the context of regression rnodels with random effects, repeated response are traditionally assumed to be mutually independent conditional on the random effects. In order to asseess the validity of such an assumption and its impact on parameter inference, we propose an estimating equation methodology where both random eifects and within-subject correlation are modeled. This fllows a subsequent analysis on the statistical sianificance of the conditional correlation. We illustrate this method with the epilepsy data of Thall and Vail (1990), and find our method useh in a proper representation for khe random effect modeling.     

Fitting bivariate multilevel models to assess long-term changes in body mass index and cigarette smoking

Using data from the National Health interview Survey from 1997 to 2006, we present a multilevel analysis of change in body mass index (BMI) and number of cigarettes smoked per day in the USA. Smoking and obesity are the leading causes of preventable mortality and morbidity in the USA and most parts of the developed world. A two-stage bivariate model of changes in obesity and number of cigarette smoked per day is proposed. At the within subject stage, an individual's BMI status and the number of cigarette smoked per day are jointly modeled as a function of an individual growth trajectory plus a random error. At the between-subject stage, the parameters of the individual growth trajectories are allowed to vary as a function of differences between subjects with respect to demographic and behavioral characteristics and with respect to the four regions of the USA (Northeast, West, South and North central). Our two-stage modeling techniques are more informative than standard regression because they characterize both group-level (nomothetic) and individual-level (idiographic) effects, yielding a more complete understanding of the phenomena under study.     

Bayesian tests on components of the compound symmetry covariance matrix

Complex dependency structures are often conditionally modeled, where random effects parameters are used to specify the natural heterogeneity in the population. When interest is focused on the dependency structure, inferences can be made from a complex covariance matrix using a marginal modeling approach. In this marginal modeling framework, testing covariance parameters is not a boundary problem. Bayesian tests on covariance parameter(s) of the compound symmetry structure are proposed assuming multivariate normally distributed observations. Innovative proper prior distributions are introduced for the covariance components such that the positive definiteness of the (compound symmetry) covariance matrix is ensured. Furthermore, it is shown that the proposed priors on the covariance parameters lead to a balanced Bayes factor, in case of testing an inequality constrained hypothesis. As an illustration, the proposed Bayes factor is used for testing (non-)invariant intra-class correlations across different group types (public and Catholic schools), using the 1982 High School and Beyond survey data.     

AN APPROACH FOR JOINTLY MODELING MULTIVARIATE LONGITUDINAL MEASUREMENTS AND DISCRETE TIME-TO-EVENT DATA

In many medical studies, patients are followed longitudinally and interest is on assessing the relationship between longitudinal measurements and time to an event. Recently, various authors have proposed joint modeling approaches for longitudinal and time-to-event data for a single longitudinal variable. These joint modeling approaches become intractable with even a few longitudinal variables. In this paper we propose a regression calibration approach for jointly modeling multiple longitudinal measurements and discrete time-to-event data. Ideally, a two-stage modeling approach could be applied in which the multiple longitudinal measurements are modeled in the first stage and the longitudinal model is related to the time-to-event data in the second stage. Biased parameter estimation due to informative dropout makes this direct two-stage modeling approach problematic. We propose a regression calibration approach which appropriately accounts for informative dropout. We approximate the conditional distribution of the multiple longitudinal measurements given the event time by modeling all pairwise combinations of the longitudinal measurements using a bivariate linear mixed model which conditions on the event time. Complete data are then simulated based on estimates from these pairwise conditional models, and regression calibration is used to estimate the relationship between longitudinal data and time-to-event data using the complete data. We show that this approach performs well in estimating the relationship between multivariate longitudinal measurements and the time-to-event data and in estimating the parameters of the multiple longitudinal process subject to informative dropout. We illustrate this methodology with simulations and with an analysis of primary biliary cirrhosis (PBC) data.     

The generalized inverse Lindley distribution: A new inverse statistical model for the study of upside-down bathtub data

ABSTRACT

In this article, a two-parameter generalized inverse Lindley distribution capable of modeling a upside-down bathtub-shaped hazard rate function is introduced. Some statistical properties of proposed distribution are explicitly derived here. The method of maximum likelihood, least square, and maximum product spacings are used for estimating the unknown model parameters and also compared through the simulation study. The approximate confidence intervals, based on a normal and a log-normal approximation, are also computed. Two algorithms are proposed for generating a random sample from the proposed distribution. A real data set is modeled to illustrate its applicability, and it is shown that our distribution fits much better than some other existing inverse distributions.     

Fairness of the national health service in Italy: a bivariate correlated random effects model

The primary purpose of this paper is to comprehensively assess households’ burden due to health payments. Starting from the fairness approach developed by the World Health Organization, we analyse the burden of healthcare payments on Italian households by modeling catastrophic payments and impoverishment due to healthcare expenditures. For this purpose, we propose to extend the analysis of fairness in financing contribution through a generalized linear mixed models by introducing a bivariate correlated random effects model, where association between the outcomes is modeled through individual- and outcome-specific latent effects which are assumed to be correlated. We discuss model parameter estimation in a finite mixture context. By using such model specification, the fairness of the Italian national health service is investigated.     

Semiparametric models of longitudinal and time-to-event data with applications to HIV viral dynamics and CD4 counts

We propose a semiparametric approach based on proportional hazards and copula method to jointly model longitudinal outcomes and the time-to-event. The dependence between the longitudinal outcomes on the covariates is modeled by a copula-based times series, which allows non-Gaussian random effects and overcomes the limitation of the parametric assumptions in existing linear and nonlinear random effects models. A modified partial likelihood method using estimated covariates at failure times is employed to draw statistical inference. The proposed model and method are applied to analyze a set of progression to AIDS data in a study of the association between the human immunodeficiency virus viral dynamics and the time trend in the CD4/CD8 ratio with measurement errors. Simulations are also reported to evaluate the proposed model and method.     

Regression analysis of health care charges with heteroscedasticity

We examine the effects of a prospective drug utilization review and patients' characteristics on total in-patient and out-patient health care charges. Our analysis of charges is complicated by the fact that the total health care charges are skewed. A log-transformation of these charges can normalize their distribution but may not stabilize their variance. To handle these problems, we propose a linear regression model with a non-constant variance (heteroscedasticity). Using results from a fitted linear regression model for log-transformed charges, we also discuss interpreting the regression coefficients in the original scale and estimating the total health care charges to individual patients. Employing these methods, we analyse total health care charges for drug utilization review patients with hypertension and identify patients' factors that are related to their total health care charges.     

A Comparative Study of Approaches for Predicting Prostate Cancer from Longitudinal Data

Disease prediction based on longitudinal data can be done using various modeling approaches. Alternative approaches are compared using data from a longitudinal study to predict the onset of disease. The data are modeled using linear mixed-effects models. Posterior probabilities of group membership are computed starting with the first observation and sequentially adding observations until the subject is classified as developing the disease or until the last measurement is used. Individuals are classified by computing posterior probabilities using the marginal distributions of the mixed-effects models, the conditional distributions (conditional on the group-specific random effects), and the distributions of the random effects.     

Models for surveillance data under reporting delay: applications to US veteran first-time suicide attempters

Surveillance data provide a vital source of information for assessing the spread of a health problem or disease of interest and for planning for future health-care needs. However, the use of surveillance data requires proper adjustments of the reported caseload due to underreporting caused by reporting delays within a limited observation period. Although methods are available to address this classic statistical problem, they are largely focused on inference for the reporting delay distribution, with inference about caseload of disease incidence based on estimates for the delay distribution. This approach limits the complexity of models for disease incidence to provide reliable estimates and projections of incidence. Also, many of the available methods lack robustness since they require parametric distribution assumptions. We propose a new approach to overcome such limitations by allowing for separate models for the incidence and the reporting delay in a distribution-free fashion, but with joint inference for both modeling components, based on functional response models. In addition, we discuss inference about projections of future disease incidence to help identify significant shifts in temporal trends modeled based on the observed data. This latter issue on detecting ‘change points’ is not sufficiently addressed in the literature, despite the fact that such warning signs of potential outbreak are critically important for prevention purposes. We illustrate the approach with both simulated and real data, with the latter involving data for suicide attempts from the Veteran Healthcare Administration.     

On familial Poisson mixed models with multi-dimensional random effects

When a generalized linear mixed model with multiple (two or more) sources of random effects is considered, the inferences may vary depending on the nature of the random effects. In this paper, we consider a familial Poisson mixed model where each of the count responses of a family are influenced by two independent unobservable familial random effects with two distinct components of dispersion. A generalized quasilikelihood (GQL) approach is discussed for the estimation of the dispersion components as well as the regression effects of the model. A simulation study is conducted to examine the relative performance of the GQL approach as opposed to a simpler method of moments. Furthermore, the GQL estimation methodology is illustrated by using health care utilization data that follow a Poisson mixed model with one component of dispersion and by using simulated asthma data that follow a Poisson mixed model with two sources of random effects with two distinct components of dispersion.     

Statistical aspects in comparative benefit-risk assessment: challenges and opportunities for pharmaceutical statisticians

Benefit-risk assessment is a fundamental element of drug development with the aim to strengthen decision making for the benefit of public health. Appropriate benefit-risk assessment can provide useful information for proactive intervention in health care settings, which could save lives, reduce litigation, improve patient safety and health care outcomes, and furthermore, lower overall health care costs. Recent development in this area presents challenges and opportunities to statisticians in the pharmaceutical industry. We review the development and examine statistical issues in comparative benefit-risk assessment. We argue that a structured benefit-risk assessment should be a multi-disciplinary effort involving experts in clinical science, safety assessment, decision science, health economics, epidemiology and statistics. Well planned and conducted analyses with clear consideration on benefit and risk are critical for appropriate benefit-risk assessment. Pharmaceutical statisticians should extend their knowledge to relevant areas such as pharmaco-epidemiology, decision analysis, modeling, and simulation to play an increasingly important role in comparative benefit-risk assessment.     

Copula regression spline models for binary outcomes

We introduce a framework for estimating the effect that a binary treatment has on a binary outcome in the presence of unobserved confounding. The methodology is applied to a case study which uses data from the Medical Expenditure Panel Survey and whose aim is to estimate the effect of private health insurance on health care utilization. Unobserved confounding arises when variables which are associated with both treatment and outcome are not available (in economics this issue is known as endogeneity). Also, treatment and outcome may exhibit a dependence which cannot be modeled using a linear measure of association, and observed confounders may have a non-linear impact on the treatment and outcome variables. The problem of unobserved confounding is addressed using a two-equation structural latent variable framework, where one equation essentially describes a binary outcome as a function of a binary treatment whereas the other equation determines whether the treatment is received. Non-linear dependence between treatment and outcome is dealt using copula functions, whereas covariate-response relationships are flexibly modeled using a spline approach. Related model fitting and inferential procedures are developed, and asymptotic arguments presented.     

Interlitter Response Variability in a Threshold Dose-Response Model

In this article, we extend a previously formulated threshold dose-response model with random litter effects that was applied to a data set from a developmental toxicity study. The dose-response pattern of the data indicates that a threshold dose level may exist. Additionally, there is noticeable variation between the responses across the dose levels. With threshold estimation being critical, the assumed variability structure should adequately model the variation while not taking away from the estimation of the threshold as well as the other parameters directly involved in the dose-response relationship. In the prior formulation, the random effect was modeled assuming identical variation in the interlitter response probabilities across all dose levels, that is, the model had a single parameter to account for the interlitter variability. In this new model, the random effect is modeled as having different response variability across dose levels, that is, multiple interlitter variability parameters. We performed the likelihood ratio test (LRT) to compare our extended model to the previous model. We conducted a simulation study to compare the bias of each model when fit to data generated with the underlying parametric structure of the opposing model. The extended threshold dose-response model with multiple response variation was less biased.     

Joint models for mixed categorical outcomes: a study of HIV risk perception and disease status in Mozambique

Two types of bivariate models for categorical response variables are introduced to deal with special categories such as ‘unsure’ or ‘unknown’ in combination with other ordinal categories, while taking additional hierarchical data structures into account. The latter is achieved by the use of different covariance structures for a trivariate random effect. The models are applied to data from the INSIDA survey, where interest goes to the effect of covariates on the association between HIV risk perception (quadrinomial with an ‘unknown risk’ category) and HIV infection status (binary). The final model combines continuation-ratio with cumulative link logits for the risk perception, together with partly correlated and partly shared trivariate random effects for the household level. The results indicate that only age has a significant effect on the association between HIV risk perception and infection status. The proposed models may be useful in various fields of application such as social and biomedical sciences, epidemiology and public health.