Random‐effects meta‐regression models for studying nonlinear dose–response relationship,with an application to alcohol and esophageal squamous cell carcinoma

A fundamental challenge in meta‐analyses of published epidemiological dose–response data is the estimate of the function describing how the risk of disease varies across different levels of a given exposure. Issues in trend estimate include within studies variability, between studies heterogeneity, and nonlinear trend components. We present a method, based on a two‐step process, that addresses simultaneously these issues. First, two‐term fractional polynomial models are fitted within each study included in the meta‐analysis, taking into account the correlation between the reported estimates for different exposure levels. Second, the pooled dose–response relationship is estimated considering the between studies heterogeneity, using a bivariate random‐effects model. This method is illustrated by a meta‐analysis aimed to estimate the shape of the dose–response curve between alcohol consumption and esophageal squamous cell carcinoma (SCC). Overall, 14 case–control studies and one cohort study, including 3000 cases of esophageal SCC, were included. The meta‐analysis provided evidence that ethanol intake was related to esophageal SCC risk in a nonlinear fashion. High levels of alcohol consumption resulted in a substantial risk of esophageal SCC as compared to nondrinkers. However, a statistically significant excess risk for moderate and intermediate doses of alcohol was also observed, with no evidence of a threshold effect. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic prediction in functional concurrent regression with an application to child growth

In many studies, it is of interest to predict the future trajectory of subjects based on their historical data, referred to as dynamic prediction. Mixed effects models have traditionally been used for dynamic prediction. However, the commonly used random intercept and slope model is often not sufficiently flexible for modeling subject‐specific trajectories. In addition, there may be useful exposures/predictors of interest that are measured concurrently with the outcome, complicating dynamic prediction. To address these problems, we propose a dynamic functional concurrent regression model to handle the case where both the functional response and the functional predictors are irregularly measured. Currently, such a model cannot be fit by existing software. We apply the model to dynamically predict children's length conditional on prior length, weight, and baseline covariates. Inference on model parameters and subject‐specific trajectories is conducted using the mixed effects representation of the proposed model. An extensive simulation study shows that the dynamic functional regression model provides more accurate estimation and inference than existing methods. Methods are supported by fast, flexible, open source software that uses heavily tested smoothing techniques.     

Network meta‐analysis models to account for variability in treatment definitions: application to dose effects

For a network meta‐analysis, an interlinked network of nodes representing competing treatments is needed. It is often challenging to define the nodes as these typically refer to similar but rarely identical interventions. The objectives of this paper are as follows: (i) to present a series of network meta‐analysis models that account for variation in the definition of the nodes and (ii) to exemplify the models where variation in the treatment definitions relates to the dose. Starting from the model that assumes each node has a ‘fixed’ definition, we gradually introduce terms to explain variability by assuming that each node has several subnodes that relate to different doses. The effects of subnodes are considered monotonic, linked with a ‘random walk’, random but exchangeable, or have a linear pattern around the treatment mean effect. Each model can be combined with different assumptions for the consistency of effects and might impact on the ranking of the treatments. Goodness of fit, heterogeneity and inconsistency were assessed. The models are illustrated in a star network for the effectiveness of fluoride toothpaste and in a full network comparing agents for multiple sclerosis. The fit and parsimony measures indicate that in the fluoride network the impact of the dose subnodes is important whereas in the multiple sclerosis network the model without subnodes is the most appropriate. The proposed approach can be a useful exploratory tool to explain sources of heterogeneity and inconsistency when there is doubt whether similar interventions should be grouped under the same node. Copyright © 2012 John Wiley & Sons, Ltd.     

Skew‐normal Bayesian nonlinear mixed‐effects models with application to AIDS studies

Studies of HIV dynamics in AIDS research are very important in understanding the pathogenesis of HIV‐1 infection and also in assessing the effectiveness of antiviral therapies. Nonlinear mixed‐effects (NLME) models have been used for modeling between‐subject and within‐subject variations in viral load measurements. Mostly, normality of both within‐subject random error and random‐effects is a routine assumption for NLME models, but it may be unrealistic, obscuring important features of between‐subject and within‐subject variations, particularly, if the data exhibit skewness. In this paper, we develop a Bayesian approach to NLME models and relax the normality assumption by considering both model random errors and random‐effects to have a multivariate skew‐normal distribution. The proposed model provides flexibility in capturing a broad range of non‐normal behavior and includes normality as a special case. We use a real data set from an AIDS study to illustrate the proposed approach by comparing various candidate models. We find that the model with skew‐normality provides better fit to the observed data and the corresponding estimates of parameters are significantly different from those based on the model with normality when skewness is present in the data. These findings suggest that it is very important to assume a model with skew‐normal distribution in order to achieve robust and reliable results, in particular, when the data exhibit skewness. Copyright © 2010 John Wiley & Sons, Ltd.     

Three‐part joint modeling methods for complex functional data mixed with zero‐and‐one–inflated proportions and zero‐inflated continuous outcomes with skewness

We take a functional data approach to longitudinal studies with complex bivariate outcomes. This work is motivated by data from a physical activity study that measured 2 responses over time in 5‐minute intervals. One response is the proportion of time active in each interval, a continuous proportions with excess zeros and ones. The other response, energy expenditure rate in the interval, is a continuous variable with excess zeros and skewness. This outcome is complex because there are 3 possible activity patterns in each interval (inactive, partially active, and completely active), and those patterns, which are observed, induce both nonrandom and random associations between the responses. More specifically, the inactive pattern requires a zero value in both the proportion for active behavior and the energy expenditure rate; a partially active pattern means that the proportion of activity is strictly between zero and one and that the energy expenditure rate is greater than zero and likely to be moderate, and the completely active pattern means that the proportion of activity is exactly one, and the energy expenditure rate is greater than zero and likely to be higher. To address these challenges, we propose a 3‐part functional data joint modeling approach. The first part is a continuation‐ratio model to reorder the ordinal valued 3 activity patterns. The second part models the proportions when they are in interval (0,1). The last component specifies the skewed continuous energy expenditure rate with Box‐Cox transformations when they are greater than zero. In this 3‐part model, the regression structures are specified as smooth curves measured at various time points with random effects that have a correlation structure. The smoothed random curves for each variable are summarized using a few important principal components, and the association of the 3 longitudinal components is modeled through the association of the principal component scores. The difficulties in handling the ordinal and proportional variables are addressed using a quasi‐likelihood type approximation. We develop an efficient algorithm to fit the model that also involves the selection of the number of principal components. The method is applied to physical activity data and is evaluated empirically by a simulation study.     

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.     

Functional linear models for zero‐inflated count data with application to modeling hospitalizations in patients on dialysis

We propose functional linear models for zero‐inflated count data with a focus on the functional hurdle and functional zero‐inflated Poisson (ZIP) models. Although the hurdle model assumes the counts come from a mixture of a degenerate distribution at zero and a zero‐truncated Poisson distribution, the ZIP model considers a mixture of a degenerate distribution at zero and a standard Poisson distribution. We extend the generalized functional linear model framework with a functional predictor and multiple cross‐sectional predictors to model counts generated by a mixture distribution. We propose an estimation procedure for functional hurdle and ZIP models, called penalized reconstruction, geared towards error‐prone and sparsely observed longitudinal functional predictors. The approach relies on dimension reduction and pooling of information across subjects involving basis expansions and penalized maximum likelihood techniques. The developed functional hurdle model is applied to modeling hospitalizations within the first 2 years from initiation of dialysis, with a high percentage of zeros, in the Comprehensive Dialysis Study participants. Hospitalization counts are modeled as a function of sparse longitudinal measurements of serum albumin concentrations, patient demographics, and comorbidities. Simulation studies are used to study finite sample properties of the proposed method and include comparisons with an adaptation of standard principal components regression. Copyright © 2014 John Wiley & Sons, Ltd.     

Estimation of controlled direct effects in time‐varying treatments using structural nested mean models: application to a primary prevention trial for coronary events with pravastatin

For the estimation of controlled direct effects (i.e., direct effects controlling intermediates that are set at a fixed level for all members of the population) without bias, two fundamental assumptions must hold: the absence of unmeasured confounding factors for treatment and outcome and for intermediate variables and outcome. Even if these assumptions hold, one would nonetheless fail to estimate direct effects using standard methods, for example, stratification or regression modeling, when the treatment influences confounding factors. For such situations, the sequential g‐estimation method for structural nested mean models has been developed for estimating controlled direct effects in point‐treatment situations. In this study, we demonstrate that this method can be applied to longitudinal data with time‐varying treatments and repeatedly measured intermediate variables. We sequentially estimate the parameters in two structural nested mean models: one for a repeatedly measured intermediate and the other one for direct effects of a time‐varying treatment. The method was applied to data from a large primary prevention trial for coronary events, in which pravastatin was used to lower the cholesterol levels in patients with moderate hypercholesterolemia. Copyright © 2014 John Wiley & Sons, Ltd.