Multiple indicator hidden Markov model with an application to medical utilization data

Monthly counts of medical visits across several years for persons identified to have alcoholism problems are modeled using two-state hidden Markov models (HMM) in order to describe the effect of alcoholism treatment on the likelihood of persons to be in a 'healthy' or 'unhealthy' state. The medical visits can be classified into different types leading to multivariate counts of medical visits each month. A multiple indicator HMM is introduced, which simultaneously fits the multivariate Poisson counts by assuming a shared hidden state underlying all of them. The multiple indicator HMM borrows information across different types of medical encounters. A univariate HMM based on the total count across types of medical visits each month is also considered. Comparisons between the multiple indicator HMM and the total count HMM are made, as well as comparisons with more traditional longitudinal models that directly model the counts. A Bayesian framework is used for the estimation of the HMM and implementation is in Winbugs.     

Multilevel modelling of clustered grouped survival data using Cox regression model: an application to ART dental restorations

In some controlled clinical trials in dental research, multiple failure time data from the same patient are frequently observed that result in clustered multiple failure time. Moreover, the treatments are often delivered by more than one operator and thus the multiple failure times are clustered according to a multilevel structure when the operator effects are assumed to be random. In practice, it is often too expensive or even impossible to monitor the study subjects continuously, but they are examined periodically at some regular pre-scheduled visits. Hence, discrete or grouped clustered failure time data are collected. The aim of this paper is to illustrate the use of the Monte Carlo Markov chain (MCMC) approach and non-informative prior in a Bayesian framework to mimic the maximum likelihood (ML) estimation in a frequentist approach in multilevel modelling of clustered grouped survival data. A three-level model with additive variance components model for the random effects is considered in this paper. Both the grouped proportional hazards model and the dynamic logistic regression model are used. The approximate intra-cluster correlation of the log failure times can be estimated when the grouped proportional hazards model is used. The statistical package WinBUGS is adopted to estimate the parameter of interest based on the MCMC method. The models and method are applied to a data set obtained from a prospective clinical study on a cohort of Chinese school children that atraumatic restorative treatment (ART) restorations were placed on permanent teeth with carious lesions. Altogether 284 ART restorations were placed by five dentists and clinical status of the ART restorations was evaluated annually for 6 years after placement, thus clustered grouped failure times of the restorations were recorded. Results based on the grouped proportional hazards model revealed that clustering effect among the log failure times of the different restorations from the same child was fairly strong (corr(child)=0.55) but the effects attributed to the dentists could be regarded as negligible (corr(dentist)=0.03). Gender and the location of the restoration were found to have no effects on the failure times and no difference in failure times was found between small restorations placed on molars and non-molars. Large restorations placed on molars were found to have shorter failure times compared to small restorations. The estimates of the baseline parameters were increasing indicating increasing hazard rates from interval 1 to 6. Results based on the logistic regression models were similar. In conclusion, the use of the MCMC approach and non-informative prior in a Bayesian framework to mimic the ML estimation in a frequentist approach in multilevel modelling of clustered grouped survival data can be easily applied with the use of the software WinBUGS.     

Generalized estimating equations to estimate the ordered stereotype logit model for panel data

By modeling the effects of predictor variables as a multiplicative function of regression parameters being invariant over categories, and category-specific scalar effects, the ordered stereotype logit model is a flexible regression model for ordinal response variables. In this article, we propose a generalized estimating equations (GEE) approach to estimate the ordered stereotype logit model for panel data based on working covariance matrices, which are not required to be correctly specified. A simulation study compares the performance of GEE estimators based on various working correlation matrices and working covariance matrices using local odds ratios. Estimation of the model is illustrated using a real-world dataset. The results from the simulation study suggest that GEE estimation of this model is feasible in medium-sized and large samples and that estimators based on local odds ratios as realized in this study tend to be less efficient compared with estimators based on a working correlation matrix. For low true correlations, the efficiency gains seem to be rather small and if the working covariance structure is too flexible, the corresponding estimator may even be less efficient compared with the GEE estimator assuming independence. Like for GEE estimators more generally, if the true correlations over time are high, then a working covariance structure which is close to the true structure can lead to considerable efficiency gains compared with assuming independence.     

The application of multilevel modelling to dental caries data

Clinical studies of dental caries experience generate multiple outcome data for each participant, with information collected for each individual tooth surface. This paper investigates multilevel modelling as a method of analysis for dental caries data, allowing for full use of the data collected at surface level. Data from a clinical trial of a caries preventive agent in adolescents are modelled. The effect of tooth position within the mouth on the development of dental caries is investigated, with the results showing the importance of differentiating between the upper and lower arches, when modelling the probabilities of caries developing on teeth. Calculation of the intracluster correlation using the threshold model is suggested for use in multilevel logistic regression modelling of caries data. This model, which assumes that a dichotomous outcome is based on an underlying continuous variable with a threshold point where the outcome changes from zero to one, is identified to be appropriate for the analysis of caries which is a continuous process, but is only identified as present in a clinical trial when it has reached a certain level of severity.     

Mixed binary-continuous copula regression models with application to adverse birth outcomes

Bivariate copula regression allows for the flexible combination of two arbitrary, continuous marginal distributions with regression effects being placed on potentially all parameters of the resulting bivariate joint response distribution. Motivated by the risk factors for adverse birth outcomes, many of which are dichotomous, we consider mixed binary-continuous responses that extend the bivariate continuous framework to the situation where one response variable is discrete (more precisely, binary) whereas the other response remains continuous. Utilizing the latent continuous representation of binary regression models, we implement a penalized likelihood–based approach for the resulting class of copula regression models and employ it in the context of modeling gestational age and the presence/absence of low birth weight. The analysis demonstrates the advantage of the flexible specification of regression impacts including nonlinear effects of continuous covariates and spatial effects. Our results imply that racial and spatial inequalities in the risk factors for infant mortality are even greater than previously suggested.     

Mixed linear regression model for longitudinal data: application to an unbalanced anthropometric data set

A longitudinal data set is characterized by a time sequence of two or more observations from each individual. In cohort studies, these data are usually not balanced. A data set related to longitudinal height measurements in children of HIV-infected mothers was recorded at the university hospital of the Federal University in Minas Gerais, Brazil. The objective was to assess the application of the mixed effect model to this unbalanced data set. At six months of age, on average boys were 1.8 cm taller than girls, and seroreverter infants were 2.9 cm taller than their HIV+ peers. At 12 months of age, on average boys were 2.4 cm taller than girls and seroreverter children were 3.5 cm taller than HIV+ ones. In addition to describing longitudinal height behavior, this model also includes the growth rate estimation for this infant population by gender and group.     

Analysis of clustered failure time data with cure fraction using copula

Clustered survival data in the presence of cure has received increasing attention. In this paper, we consider a semiparametric mixture cure model which incorporates a logistic regression model for the cure fraction and a semiparametric regression model for the failure time. We utilize Archimedean copula (AC) models to assess the strength of association for both susceptibility and failure times between susceptible individuals in the same cluster. Instead of using the full likelihood approach, we consider a composite likelihood function and a two-stage estimation procedure for both marginal and association parameters. A Jackknife procedure that takes out one cluster at a time is proposed for the variance estimation of the estimators. Akaike information criterion is applied to select the best model among ACs. Simulation studies are performed to validate our estimating procedures, and two real data sets are analyzed to demonstrate the practical use of our proposed method.     

Multivariate survival analysis with doubly-censored data: application to the assessment of Accutane treatment for fibrodysplasia ossificans progressiva

Fibrodysplasia ossificans progressiva is a rare genetic disorder in which the joints of patients become disabled by the formation of heterotopic bone. Data are available on the status of 11 joints of each of 21 patients before, during and after treatment with Accutane. These are compared with data obtained by questionnaire from 40 untreated patients to determine the efficacy of the treatment. Both left- and right-censoring are present in each group, which, together with the multivariate nature of the data and the time-dependent treatment covariate, makes analysis difficult. We consider two alternative parametric models for incorporating within-subject dependence: a marginal model and a frailty model. Both analyses suggest that Accutane treatment is effective. We discuss and illustrate the differences between the two approaches. We also discuss the extent to which the conclusions are compromised by the observational nature of the study.     

Stein-type shrinkage estimators in gamma regression model with application to prostate cancer data

Gamma regression is applied in several areas such as life testing, forecasting cancer incidences, genomics, rainfall prediction, experimental designs, and quality control. Gamma regression models allow for a monotone and no constant hazard in survival models. Owing to the broad applicability of gamma regression, we propose some novel and improved methods to estimate the coefficients of gamma regression model. We combine the unrestricted maximum likelihood (ML) estimators and the estimators that are restricted by linear hypothesis, and we present Stein-type shrinkage estimators (SEs). We then develop an asymptotic theory for SEs and obtain their asymptotic quadratic risks. In addition, we conduct Monte Carlo simulations to study the performance of the estimators in terms of their simulated relative efficiencies. It is evident from our studies that the proposed SEs outperform the usual ML estimators. Furthermore, some tabular and graphical representations are given as proofs of our assertions. This study is finally ended by appraising the performance of our estimators for a real prostate cancer data.     

A demonstration of modeling count data with an application to physical activity

Objectives

To introduce a new, patient-oriented predictive index as a measure of gain in certainty.

Study design

Algebraic equations.

Results

A new measure is suggested based on error rates in a patient population. The new Predictive Summary Index (PSI) reflects the true total gain in certainty obtained by performing a diagnostic test based on knowledge of disease prevalence, i.e., the overall additional certainty. We show that the overall gain in certainty can be expressed in the form of the following expression: PSI = PPV+NPV-1. PSI is a more comprehensive measure than the post-test probability or the Youden Index (J). The reciprocal of J is interpreted as the number of persons with a given disease who need to be examined in order to detect correctly one person with the disease. The reciprocal of PSI is suggested as the number of persons who need to be examined in order to correctly predict a diagnosis of the disease.

Conclusion

PSI provides more information than J and the predictive values, making it more appropriate in a clinical setting.     

Bayesian hierarchical model for multiple repeated measures and survival data: an application to Parkinson's disease

Multilevel item response theory models have been increasingly used to analyze the multivariate longitudinal data of mixed types (e.g., continuous and categorical) in clinical studies. To address the possible correlation between multivariate longitudinal measures and time to terminal events (e.g., death and dropout), joint models that consist of a multilevel item response theory submodel and a survival submodel have been previously developed. However, in multisite studies, multiple patients are recruited and treated by the same clinical site. There can be a significant site correlation because of common environmental and socioeconomic status, and similar quality of care within site. In this article, we develop and study several hierarchical joint models with the hazard of terminal events dependent on shared random effects from various levels. We conduct extensive simulation study to evaluate the performance of various models under different scenarios. The proposed hierarchical joint models are applied to the motivating deprenyl and tocopherol antioxidative therapy of Parkinsonism study to investigate the effect of tocopherol in slowing Parkinson's disease progression. Copyright © 2014 John Wiley & Sons, Ltd.     

Two-sample test for correlated data under outcome-dependent sampling with an application to self-reported weight loss data

Standard methods for two-sample tests such as the t-test and Wilcoxon rank sum test may lead to incorrect type I errors when applied to longitudinal or clustered data. Recent alternatives of two-sample tests for clustered data often require certain assumptions on the correlation structure and/or noninformative cluster size. In this paper, based on a novel pseudolikelihood for correlated data, we propose a score test without knowledge of the correlation structure or assuming data missingness at random. The proposed score test can capture differences in the mean and variance between two groups simultaneously. We use projection theory to derive the limiting distribution of the test statistic, in which the covariance matrix can be empirically estimated. We conduct simulation studies to evaluate the proposed test and compare it with existing methods. To illustrate the usefulness proposed test, we use it to compare self-reported weight loss data in a friends' referral group, with the data from the Internet self-joining group.     

A copula model for repeated measurements with non-ignorable non-monotone missing outcome

A normal copula-based selection model is proposed for continuous longitudinal data with a non-ignorable non-monotone missing-data process. The normal copula is used to combine the distribution of the outcome of interest and that of the missing-data indicators given the covariates. Parameters in the model are estimated by a pseudo-likelihood method. We first use the GEE with a logistic link to estimate the parameters associated with the marginal distribution of the missing-data indicator given the covariates, assuming that covariates are always observed. Then we estimate other parameters by inserting the estimates from the first step into the full likelihood function. A simulation study is conducted to assess the robustness of the assumed model under different missing-data processes. The proposed method is then applied to one example from a community cohort study to demonstrate its capability to reduce bias.     

A three‐level mixed‐effects location scale model with an application to ecological momentary assessment data

In studies using ecological momentary assessment (EMA), or other intensive longitudinal data collection methods, interest frequently centers on changes in the variances, both within‐subjects and between‐subjects. For this, Hedeker et al. (Biometrics 2008; 64: 627–634) developed an extended two‐level mixed‐effects model that treats observations as being nested within subjects and allows covariates to influence both the within‐subjects and between‐subjects variance, beyond their influence on means. However, in EMA studies, subjects often provide many responses within and across days. To account for the possible systematic day‐to‐day variation, we developed a more flexible three‐level mixed‐effects location scale model that treats observations within days within subjects, and allows covariates to influence the variance at the subject, day, and observation level (over and above their usual effects on means) using a log‐linear representation throughout. We provide details of a maximum likelihood solution and demonstrate how SAS PROC NLMIXED can be used to achieve maximum likelihood estimates in an alternative parameterization of our proposed three‐level model. The accuracy of this approach using NLMIXED was verified by a series of simulation studies. Data from an adolescent mood study using EMA were analyzed to demonstrate this approach. The analyses clearly show the benefit of the proposed three‐level model over the existing two‐level approach. The proposed model has useful applications in many studies with three‐level structures where interest centers on the joint modeling of the mean and variance structure. Copyright © 2012 John Wiley & Sons, Ltd.     

A 3‐level Bayesian mixed effects location scale model with an application to ecological momentary assessment data

Ecological momentary assessment studies usually produce intensively measured longitudinal data with large numbers of observations per unit, and research interest is often centered around understanding the changes in variation of people's thoughts, emotions and behaviors. Hedeker et al developed a 2‐level mixed effects location scale model that allows observed covariates as well as unobserved variables to influence both the mean and the within‐subjects variance, for a 2‐level data structure where observations are nested within subjects. In some ecological momentary assessment studies, subjects are measured at multiple waves, and within each wave, subjects are measured over time. Li and Hedeker extended the original 2‐level model to a 3‐level data structure where observations are nested within days and days are then nested within subjects, by including a random location and scale intercept at the intermediate wave level. However, the 3‐level random intercept model assumes constant response change rate for both the mean and variance. To account for changes in variance across waves, as well as clustering attributable to waves, we propose a more comprehensive location scale model that allows subject heterogeneity at baseline as well as across different waves, for a 3‐level data structure where observations are nested within waves and waves are then further nested within subjects. The model parameters are estimated using Markov chain Monte Carlo methods. We provide details on the Bayesian estimation approach and demonstrate how the Stan statistical software can be used to sample from the desired distributions and achieve consistent estimates. The proposed model is validated via a series of simulation studies. Data from an adolescent smoking study are analyzed to demonstrate this approach. The analyses clearly favor the proposed model and show significant subject heterogeneity at baseline as well as change over time, for both mood mean and variance. The proposed 3‐level location scale model can be widely applied to areas of research where the interest lies in the consistency in addition to the mean level of the responses.     

Bayesian and classical estimation of mixed logit: An application to genetic testing

Discrete choice experiments (DCEs) in health economics have recently used the mixed logit (MXL) model to incorporate preference heterogeneity. These studies typically use a classical approach to estimation or have specified normal distributions for the attributes. Specifying normal distributions can lead to erroneous interpretation; non-normal distributions may cause problems with convergence to the global maximum of the simulated log-likelihood function. Hierarchical Bayes (HB) of MXL is an alternative estimation approach that may alleviate problems of convergence. We investigated Bayesian and classical approaches to MXL estimation using a DCE that elicited preferences for a genetic technology. The classical approach produced unrealistic results in one of the econometric specifications, which led to an erroneous willingness to pay estimate. The HB procedure produced reasonable results for both specifications and helped ascertain that the classical procedures were converging at a local maximum.