Disease mapping of zero-excessive mesothelioma data in Flanders

PurposeTo investigate the distribution of mesothelioma in Flanders using Bayesian disease mapping models that account for both an excess of zeros and overdispersion.MethodsThe numbers of newly diagnosed mesothelioma cases within all Flemish municipalities between 1999 and 2008 were obtained from the Belgian Cancer Registry. To deal with overdispersion, zero inflation, and geographical association, the hurdle combined model was proposed, which has three components: a Bernoulli zero-inflation mixture component to account for excess zeros, a gamma random effect to adjust for overdispersion, and a normal conditional autoregressive random effect to attribute spatial association. This model was compared with other existing methods in literature.ResultsThe results indicate that hurdle models with a random effects term accounting for extra variance in the Bernoulli zero-inflation component fit the data better than hurdle models that do not take overdispersion in the occurrence of zeros into account. Furthermore, traditional models that do not take into account excessive zeros but contain at least one random effects term that models extra variance in the counts have better fits compared to their hurdle counterparts. In other words, the extra variability, due to an excess of zeros, can be accommodated by spatially structured and/or unstructured random effects in a Poisson model such that the hurdle mixture model is not necessary.ConclusionsModels taking into account zero inflation do not always provide better fits to data with excessive zeros than less complex models. In this study, a simple conditional autoregressive model identified a cluster in mesothelioma cases near a former asbestos processing plant (Kapelle-op-den-Bos). This observation is likely linked with historical local asbestos exposures. Future research will clarify this.     

Epidemiological characteristics of reported sporadic and outbreak cases of E. coli O157 in people from Alberta, Canada (2000-2002): methodological challenges of comparing clustered to unclustered data

Using multivariable models, we compared whether there were significant differences between reported outbreak and sporadic cases in terms of their sex, age, and mode and site of disease transmission. We also determined the potential role of administrative, temporal, and spatial factors within these models. We compared a variety of approaches to account for clustering of cases in outbreaks including weighted logistic regression, random effects models, general estimating equations, robust variance estimates, and the random selection of one case from each outbreak. Age and mode of transmission were the only epidemiologically and statistically significant covariates in our final models using the above approaches. Weighing observations in a logistic regression model by the inverse of their outbreak size appeared to be a relatively robust and valid means for modelling these data. Some analytical techniques, designed to account for clustering, had difficulty converging or producing realistic measures of association.     

Joint analysis of multi-level repeated measures data and survival: an application to the end stage renal disease (ESRD) data

Shared random effects models have been increasingly common in the joint analyses of repeated measures (e.g. CD4 counts, hemoglobin levels) and a correlated failure time such as death. In this paper we study several shared random effects models in the multi-level repeated measures data setting with dependent failure times. Distinct random effects are used to characterize heterogeneity in repeated measures at different levels. The hazard of death may be dependent on random effects from various levels. To simplify the estimation procedure, we adopt the Gaussian quadrature technique with a piecewise log-linear baseline hazard for the death process, which can be conveniently implemented in the freely available software aML. As an example, we analyze repeated measures of hematocrit level and survival for end stage renal disease patients clustered within a randomly selected 126 dialysis centers in the U.S. renal data system data set. Our model is very comprehensive yet easy to implement, making it appealing to general statistical practitioners.     

Hierarchical Bayesian spatial modelling of small-area rates of non-rare disease

We present Bayesian hierarchical spatial models for the analysis of the geographical distribution of a non-rare disease or event. The work is motivated by the need for ascertaining regional variations in health services outcomes and resource use and for assessing the potential sources of these variations. The models discussed herein readily accommodate random spatial effects and covariate effects. We discuss Bayesian inferential framework and implementation of a hybrid Markov chain Monte Carlo method for full Bayesian model inference. The methods are illustrated through an analysis of regional variation in chronic lung disease (CLD) rates among neonatal intensive care unit (NICU) patients across Canada. Specifically, we first present a random effects binomial model for spatially correlated CLD rates, with random spatial effects accounting for latent or covariate effects. These random spatial effects depict regional or spatial variation in chronic lung disease occurrence. We then extend this model to include covariates. With this extension, we assess residual spatial effects and the extent to which risk factors such as illness severity at NICU admission, low birth weight, and very low birth weight influence the CLD rate variation.     

Proportional hazards models with frailties and random effects

We discuss some of the fundamental concepts underlying the development of frailty and random effects models in survival. One of these fundamental concepts was the idea of a frailty model where each subject has his or her own disposition to failure, their so-called frailty, additional to any effects we wish to quantify via regression. Although the concept of individual frailty can be of value when thinking about how data arise or when interpreting parameter estimates in the context of a fitted model, we argue that the concept is of limited practical value. Individual random effects (frailties), whenever detected, can be made to disappear by elementary model transformation. In consequence, unless we are to take some model form as unassailable, beyond challenge and carved in stone, and if we are to understand the term 'frailty' as referring to individual random effects, then frailty models have no value. Random effects models on the other hand, in which groups of individuals share some common effect, can be used to advantage. Even in this case however, if we are prepared to sacrifice some efficiency, we can avoid complex modelling by using the considerable power already provided by the stratified proportional hazards model. Stratified models and random effects models can both be seen to be particular cases of partially proportional hazards models, a view that gives further insight. The added structure of a random effects model, viewed as a stratified proportional hazards model with some added distributional constraints, will, for group sizes of five or more, provide no more than modest efficiency gains, even when the additional assumptions are exactly true. On the other hand, for moderate to large numbers of very small groups, of sizes two or three, the study of twins being a well known example, the efficiency gains of the random effects model can be far from negligible. For such applications, the case for using random effects models rather than the stratified model is strong. This is especially so in view of the good robustness properties of random effects models. Nonetheless, the simpler analysis, based upon the stratified model, remains valid, albeit making a less efficient use of resources.     

Robustness of a parametric model for informatively censored bivariate longitudinal data under misspecification of its distributional assumptions: A simulation study

Repeated measurements of surrogate markers are frequently used to track disease progression, but these series are often prematurely terminated due to disease progression or death. Analysing such data through standard likelihood-based approaches can yield severely biased estimates if the censoring mechanism is non-ignorable. Motivated by this problem, we have proposed the bivariate joint multivariate random effects (JMRE) model, which has shown that when correctly specified it performs well in terms of bias reduction and precision.The bivariate JMRE model is fully parametric and belongs to the class of shared parameters joint models where a survival model for the dropouts and a mixed model for the markers' evolution are linked through a multivariate normal distribution of random effects. As in every parametric model, robustness under violations of its distributional assumptions is of great importance. In this study we generated 500 simulated data sets assuming that random effects jointly follow a heavy-tailed distribution, two skewed distributions or a mixture of two normal distributions. Moreover, we generated data where level-1 errors or residuals in the survival part of the model follow a skewed distribution. Further sensitivity analysis on the effects of reduced sample size, increased level-1 variances and altered fixed effects values was also performed.We found that fixed effects estimates are almost unaffected, but their standard errors (SEs) may be underestimated especially under heavily skewed distributions. The proposed model seems robust enough, but its performance on smaller data sets or under more extreme departures of its assumptions needs further investigation.     

Logistic regression of family data from retrospective study designs

We wish to study the effects of genetic and environmental factors on disease risk, using data from families ascertained because they contain multiple cases of the disease. To do so, we must account for the way participants were ascertained, and for within-family correlations in both disease occurrences and covariates. We model the joint probability distribution of the covariates of ascertained family members, given family disease occurrence and pedigree structure. We describe two such covariate models: the random effects model and the marginal model. Both models assume a logistic form for the distribution of one person's covariates that involves a vector beta of regression parameters. The components of beta in the two models have different interpretations, and they differ in magnitude when the covariates are correlated within families. We describe ascertainment assumptions needed to estimate consistently the parameters beta(RE) in the random effects model and the parameters beta(M) in the marginal model. Under the ascertainment assumptions for the random effects model, we show that conditional logistic regression (CLR) of matched family data gives a consistent estimate beta(RE) for beta(RE) and a consistent estimate for the covariance matrix of beta(RE). Under the ascertainment assumptions for the marginal model, we show that unconditional logistic regression (ULR) gives a consistent estimate for beta(M), and we give a consistent estimator for its covariance matrix. The random effects/CLR approach is simple to use and to interpret, but it can use data only from families containing both affected and unaffected members. The marginal/ULR approach uses data from all individuals, but its variance estimates require special computations. A C program to compute these variance estimates is available at http://www.stanford.edu/dept/HRP/epidemiology. We illustrate these pros and cons by application to data on the effects of parity on ovarian cancer risk in mother/daughter pairs, and use simulations to study the performance of the estimates.     

Meta‐analysis of diagnostic accuracy studies accounting for disease prevalence: Alternative parameterizations and model selection

In a meta‐analysis of diagnostic accuracy studies, the sensitivities and specificities of a diagnostic test may depend on the disease prevalence since the severity and definition of disease may differ from study to study due to the design and the population considered. In this paper, we extend the bivariate nonlinear random effects model on sensitivities and specificities to jointly model the disease prevalence, sensitivities and specificities using trivariate nonlinear random‐effects models. Furthermore, as an alternative parameterization, we also propose jointly modeling the test prevalence and the predictive values, which reflect the clinical utility of a diagnostic test. These models allow investigators to study the complex relationship among the disease prevalence, sensitivities and specificities; or among test prevalence and the predictive values, which can reveal hidden information about test performance. We illustrate the proposed two approaches by reanalyzing the data from a meta‐analysis of radiological evaluation of lymph node metastases in patients with cervical cancer and a simulation study. The latter illustrates the importance of carefully choosing an appropriate normality assumption for the disease prevalence, sensitivities and specificities, or the test prevalence and the predictive values. In practice, it is recommended to use model selection techniques to identify a best‐fitting model for making statistical inference. In summary, the proposed trivariate random effects models are novel and can be very useful in practice for meta‐analysis of diagnostic accuracy studies. Copyright © 2009 John Wiley & Sons, Ltd.     

A semi-parametric Bayesian approach to generalized linear mixed models

The linear mixed effects model with normal errors is a popular model for the analysis of repeated measures and longitudinal data. The generalized linear model is useful for data that have non-normal errors but where the errors are uncorrelated. A descendant of these two models generates a model for correlated data with non-normal errors, called the generalized linear mixed model (GLMM). Frequentist attempts to fit these models generally rely on approximate results and inference relies on asymptotic assumptions. Recent advances in computing technology have made Bayesian approaches to this class of models computationally feasible. Markov chain Monte Carlo methods can be used to obtain ‘exact’ inference for these models, as demonstrated by Zeger and Karim. In the linear or generalized linear mixed model, the random effects are typically taken to have a fully parametric distribution, such as the normal distribution. In this paper, we extend the GLMM by allowing the random effects to have a non-parametric prior distribution. We do this using a Dirichlet process prior for the general distribution of the random effects. The approach easily extends to more general population models. We perform computations for the models using the Gibbs sampler. © 1998 John Wiley & Sons, Ltd.     

Regression B-spline smoothing in Bayesian disease mapping: with an application to patient safety surveillance

In the context of Bayesian disease mapping, recent literature presents generalized linear mixed models that engender spatial smoothing. The methods assume spatially varying random effects as a route to partially pooling data and 'borrowing strength' in small-area estimation. When spatiotemporal disease rates are available for sequential risk mapping of several time periods, the 'smoothing' issue may be explored by considering spatial smoothing, temporal smoothing and spatiotemporal interaction. In this paper, these considerations are motivated and explored through development of a Bayesian semiparametric disease mapping model framework which facilitates temporal smoothing of rates and relative risks via regression B-splines with mixed-effect representation of coefficients. Specifically, we develop spatial priors such as multivariate Gaussian Markov random fields and non-spatial priors such as unstructured multivariate Gaussian distributions and illustrate how time trends in small-area relative risks may be explored by splines which vary in either a spatially structured or unstructured manner. In particular, we show that with suitable prior specifications for the random effects ensemble, small-area relative risk trends may be fit by 'spatially varying' or randomly varying B-splines. A recently developed Bayesian hierarchical model selection criterion, the deviance information criterion, is used to assess the trade-off between goodness-of-fit and smoothness and to select the number of knots. The methodological development aims to provide reliable information about the patterns (both over space and time) of disease risks and to quantify uncertainty. The study offers a disease and health outcome surveillance methodology for flexible and efficient exploration and assessment of emerging risk trends and clustering. The methods are motivated and illustrated through a Bayesian analysis of adverse medical events (also known as iatrogenic injuries) among hospitalized elderly patients in British Columbia, Canada.     

Nested frailty models using maximum penalized likelihood estimation

The frailty model is a random effect survival model, which allows for unobserved heterogeneity or for statistical dependence between observed survival data. The nested frailty model accounts for the hierarchical clustering of the data by including two nested random effects. Nested frailty models are particularly appropriate when data are clustered at several hierarchical levels naturally or by design. In such cases it is important to estimate the parameters of interest as accurately as possible by taking into account the hierarchical structure of the data. We present a maximum penalized likelihood estimation (MPnLE) to estimate non-parametrically a continuous hazard function in a nested gamma-frailty model with right-censored and left-truncated data. The estimators for the regression coefficients and the variance components of the random effects are obtained simultaneously. The simulation study demonstrates that this semi-parametric approach yields satisfactory results in this complex setting. In order to illustrate the MPnLE method and the nested frailty model, we present two applications. One is for modelling the effect of particulate air pollution on mortality in different areas with two levels of geographical regrouping. The other application is based on recurrent infection times of patients from different hospitals. We illustrate that using a shared frailty model instead of a nested frailty model with two levels of regrouping leads to inaccurate estimates, with an overestimation of the variance of the random effects. We show that even when the frailty effects are fairly small in magnitude, they are important since they alter the results in a systematic pattern.     

A comparison of conditional autoregressive models used in Bayesian disease mapping

Disease mapping is the area of epidemiology that estimates the spatial pattern in disease risk over an extended geographical region, so that areas with elevated risk levels can be identified. Bayesian hierarchical models are typically used in this context, which represent the risk surface using a combination of available covariate data and a set of spatial random effects. These random effects are included to model any overdispersion or spatial correlation in the disease data, that has not been accounted for by the available covariate information. The random effects are typically modelled by a conditional autoregressive (CAR) prior distribution, and a number of alternative specifications have been proposed. This paper critiques four of the most common models within the CAR class, and assesses their appropriateness via a simulation study. The four models are then applied to a new study mapping cancer incidence in Greater Glasgow, Scotland, between 2001 and 2005.     

Conditional mixed models adjusting for non-ignorable drop-out with administrative censoring in longitudinal studies

In this paper, a class of conditional mixed models is proposed to adjust for non-ignorable drop-out, while also accommodating unequal follow-up due to staggered entry and administrative censoring in longitudinal studies. Conditional linear and quadratic models which model subject-specific slopes as linear or quadratic functions of the time-to-drop-out, as well as pattern mixture models are both special cases of this approach. We illustrate these models and compare them with the usual maximum likelihood approach assuming ignorable drop-out using data from a multi-centre randomized clinical trial of renal disease. Simulations under various scenarios where the drop-out mechanism is ignorable and non-ignorable are employed to evaluate the performance of these models.     

A latent‐variable marginal method for multi‐level incomplete binary data

Incomplete multi‐level data arise commonly in many clinical trials and observational studies. Because of multi‐level variations in this type of data, appropriate data analysis should take these variations into account. A random effects model can allow for the multi‐level variations by assuming random effects at each level, but the computation is intensive because high‐dimensional integrations are often involved in fitting models. Marginal methods such as the inverse probability weighted generalized estimating equations can involve simple estimation computation, but it is hard to specify the working correlation matrix for multi‐level data. In this paper, we introduce a latent variable method to deal with incomplete multi‐level data when the missing mechanism is missing at random, which fills the gap between the random effects model and marginal models. Latent variable models are built for both the response and missing data processes to incorporate the variations that arise at each level. Simulation studies demonstrate that this method performs well in various situations. We apply the proposed method to an Alzheimer's disease study. Copyright © 2012 John Wiley & Sons, Ltd.     

Misspecifying the covariance structure in a linear mixed model under MAR drop-out

Misspecification of the covariance structure in a linear mixed model (LMM) can lead to biased population parameters' estimates under MAR drop-out. In our motivating example of modeling CD4 cell counts during untreated HIV infection, random intercept and slope LMMs are frequently used. In this article, we evaluate the performance of LMMs with specific covariance structures, in terms of bias in the fixed effects estimates, under specific MAR drop-out mechanisms, and adopt a Bayesian model comparison criterion to discriminate between the examined approaches in real-data applications. We analytically show that using a random intercept and slope structure when the true one is more complex can lead to seriously biased estimates, with the degree of bias depending on the magnitude of the MAR drop-out. Under misspecified covariance structure, we compare in terms of induced bias the approach of adding a fractional Brownian motion (BM) process on top of random intercepts and slopes with the approach of using splines for the random effects. In general, the performance of both approaches was satisfactory, with the BM model leading to smaller bias in most cases. A simulation study is carried out to evaluate the performance of the proposed Bayesian criterion in identifying the model with the correct covariance structure. Overall, the proposed method performs better than the AIC and BIC criteria under our specific simulation setting. The models under consideration are applied to real data from the CASCADE study; the most plausible model is identified by all examined criteria.     

The use of mixture models for identifying high risks in disease mapping.

Conventional approaches for estimating risks in disease mapping or mortality studies are based on Poisson inference. Frequently, overdispersion is present and this extra variability is modelled by introducing random effects. In this paper we compare two computationally simple approaches for incorporating random effects: one based on a non-parametric mixture model assuming that the population arises from a discrete mixture of Poisson distributions, and the second using a Poisson-normal mixture model which allows for spatial autocorrelation. The comparison is focused on how well each of these methods identify the regions which have high risks. Such identification is important because policy makers may wish to target regions associated with such extreme risks for financial assistance while epidemiologists may wish to target such regions for further study. The Poisson-normal mixture model is presented from both a frequentist, or empirical Bayes, and a fully Bayesian point of view. We compare results obtained with the parametric and non-parametric models specifically in terms of detecting extreme mortality risks, using infant mortality data of British Columbia, Canada, for the period 1981-1985, breast cancer data from Sardinia, for the period 1983-1987, and Scottish lip cancer data for 1975-1980. However, we also investigate the performance of these models in a simulation study. The key finding is that discrete mixture models seem to be able to locate regions which experience high risks; normal mixture models also work well in this regard, and perform substantially better when spatial autocorrelation is present.     

A Bayesian approach to joint analysis of multivariate longitudinal data and parametric accelerated failure time

Impairment caused by Parkinson's disease (PD) is multidimensional (e.g., sensoria, functions, and cognition) and progressive. Its multidimensional nature precludes a single outcome to measure disease progression. Clinical trials of PD use multiple categorical and continuous longitudinal outcomes to assess the treatment effects on overall improvement. A terminal event such as death or dropout can stop the follow‐up process. Moreover, the time to the terminal event may be dependent on the multivariate longitudinal measurements. In this article, we consider a joint random‐effects model for the correlated outcomes. A multilevel item response theory model is used for the multivariate longitudinal outcomes and a parametric accelerated failure time model is used for the failure time because of the violation of proportional hazard assumption. These two models are linked via random effects. The Bayesian inference via MCMC is implemented in ‘BUGS ’ language. Our proposed method is evaluated by a simulation study and is applied to DATATOP study, a motivating clinical trial to determine if deprenyl slows the progression of PD. © 2013 The authors. Statistics in Medicine published by John Wiley & Sons, Ltd.     

Multilevel mixed effects parametric survival models using adaptive Gauss–Hermite quadrature with application to recurrent events and individual participant data meta‐analysis

Multilevel mixed effects survival models are used in the analysis of clustered survival data, such as repeated events, multicenter clinical trials, and individual participant data (IPD) meta‐analyses, to investigate heterogeneity in baseline risk and covariate effects. In this paper, we extend parametric frailty models including the exponential, Weibull and Gompertz proportional hazards (PH) models and the log logistic, log normal, and generalized gamma accelerated failure time models to allow any number of normally distributed random effects. Furthermore, we extend the flexible parametric survival model of Royston and Parmar, modeled on the log‐cumulative hazard scale using restricted cubic splines, to include random effects while also allowing for non‐PH (time‐dependent effects). Maximum likelihood is used to estimate the models utilizing adaptive or nonadaptive Gauss–Hermite quadrature. The methods are evaluated through simulation studies representing clinically plausible scenarios of a multicenter trial and IPD meta‐analysis, showing good performance of the estimation method. The flexible parametric mixed effects model is illustrated using a dataset of patients with kidney disease and repeated times to infection and an IPD meta‐analysis of prognostic factor studies in patients with breast cancer. User‐friendly Stata software is provided to implement the methods. Copyright © 2014 John Wiley & Sons, Ltd.     

A semi-parametric regression analysis of CD4 cell counts.

This paper considers the regression analysis of CD4 cell counts, a commonly used indicator and prognostic factor of AIDS progression. For this purpose, a number of methods have been proposed and most of them are based on random effects models. We present an alternative that is based on a mean function regression model. The new method is more natural and particularly appropriate if population parameters such as treatment comparison are mainly of interest. To estimate regression parameters, we present an estimating equation-based approach, which does not require estimation of the baseline mean function. This makes the implementation of the approach and the study of the properties of the estimated regression parameters much easier than those based on random effects models. The method is illustrated with a set of CD4 cell count data arising from an AIDS clinical trial and simulated data.     

You sneeze,you lose:: The impact of pollen exposure on cognitive performance during high-stakes high school exams

Pollen is known to cause allergic reactions and affect cognitive performance in around 20% of the population. Although pollen season peaks when students take high-stakes exams, the effect of pollen allergies on school performance has received nearly no attention from economists. Using a student fixed effects model and administrative Norwegian data, this paper finds that increasing the ambient pollen levels by one standard deviation at the mean leads to a 2.5% standard deviation decrease in test scores, with potentially larger effects for allergic students. There also appear to be longer-run effects. The findings imply that random increases in pollen counts reduce test scores for allergic students relative to their peers, who consequently will be at a disadvantage when competing for jobs or higher education. This paper contributes to the literature by illuminating the interplay between individual health and human capital accumulation, which in turn can impact long-run economic growth.