A mixture model for longitudinal data with application to assessment of noncompliance

In clinical trials of a self-administered drug, repeated measures of a laboratory marker, which is affected by study medication and collected in all treatment arms, can provide valuable information on population and individual summaries of compliance. In this paper, we introduce a general finite mixture of nonlinear hierarchical models that allows estimates of component membership probabilities and random effect distributions for longitudinal data arising from multiple subpopulations, such as from noncomplying and complying subgroups in clinical trials. We outline a sampling strategy for fitting these models, which consists of a sequence of Gibbs, Metropolis-Hastings, and reversible jump steps, where the latter is required for switching between component models of different dimensions. Our model is applied to identify noncomplying subjects in the placebo arm of a clinical trial assessing the effectiveness of zidovudine (AZT) in the treatment of patients with HIV, where noncompliance was defined as initiation of AZT during the trial without the investigators' knowledge. We fit a hierarchical nonlinear change-point model for increases in the marker MCV (mean corpuscular volume of erythrocytes) for subjects who noncomply and a constant mean random effects model for those who comply. As part of our fully Bayesian analysis, we assess the sensitivity of conclusions to prior and modeling assumptions and demonstrate how external information and covariates can be incorporated to distinguish subgroups.     

Assessing Toxicities in a Clinical Trial: Bayesian Inference for Ordinal Data Nested within Categories

Summary This article addresses modeling and inference for ordinal outcomes nested within categorical responses. We propose a mixture of normal distributions for latent variables associated with the ordinal data. This mixture model allows us to fix without loss of generality the cutpoint parameters that link the latent variable with the observed ordinal outcome. Moreover, the mixture model is shown to be more flexible in estimating cell probabilities when compared to the traditional Bayesian ordinal probit regression model with random cutpoint parameters. We extend our model to take into account possible dependence among the outcomes in different categories. We apply the model to a randomized phase III study to compare treatments on the basis of toxicities recorded by type of toxicity and grade within type. The data include the different (categorical) toxicity types exhibited in each patient. Each type of toxicity has an (ordinal) grade associated to it. The dependence among the different types of toxicity exhibited by the same patient is modeled by introducing patient‐specific random effects.     

Isolating cost drivers in interstitial lung disease treatment using nonparametric Bayesian methods

Mixture modeling is a popular approach to accommodate overdispersion, skewness, and multimodality features that are very common for health care utilization data. However, mixture modeling tends to rely on subjective judgment regarding the appropriate number of mixture components or some hypothesis about how to cluster the data. In this work, we adopt a nonparametric, variational Bayesian approach to allow the model to select the number of components while estimating their parameters. Our model allows for a probabilistic classification of observations into clusters and simultaneous estimation of a Gaussian regression model within each cluster. When we apply this approach to data on patients with interstitial lung disease, we find distinct subgroups of patients with differences in means and variances of health care costs, health and treatment covariates, and relationships between covariates and costs. The subgroups identified are readily interpretable, suggesting that this nonparametric variational approach to inference can discover valid insights into the factors driving treatment costs. Moreover, the learning algorithm we employed is very fast and scalable, which should make the technique accessible for a broad range of applications.     

Homogenized constrained mixture models for anisotropic volumetric growth and remodeling

Constrained mixture models for soft tissue growth and remodeling have attracted increasing attention over the last decade. They can capture the effects of the simultaneous presence of multiple constituents that are continuously deposited and degraded at in general different rates, which is important to understand essential features of living soft tissues that cannot be captured by simple kinematic growth models. Recently the novel concept of homogenized constrained mixture models was introduced. It was shown that these models produce results which are very similar (and in certain limit cases even identical) to the ones of constrained mixture models based on multi-network theory. At the same time, the computational cost and complexity of homogenized constrained mixture models are much lower. This paper discusses the theory and implementation of homogenized constrained mixture models for anisotropic volumetric growth and remodeling in three dimensions. Previous constrained mixture models of volumetric growth in three dimensions were limited to the special case of isotropic growth. By numerical examples, comparison with experimental data and a theoretical discussion, we demonstrate that there is some evidence raising doubts whether isotropic growth models are appropriate to represent growth and remodeling of soft tissue in the vasculature. Anisotropic constrained mixture models, as introduced in this paper for the first time, may be required to avoid unphysiological results in simulations of vascular growth and remodeling.     

不同运动干预方式对糖尿病前期人群血糖相关指标影响的Meta分析

目的：系统评价有氧运动、抗阻运动、有氧联合抗阻运动三种不同干预方式对糖尿病前期人群血糖的影响。方法：制定文献检索策略,检索PubMed、EMBASE、EBSCO外文数据库以及CNKI、Wanfang中文数据库,以手工查阅检出文献和相关参考文献作为补充,查找符合纳入标准的随机对照试验进行质量评价,运用RevMan5.2统计软件对纳入的数据进行Meta分析,运动干预组和对照组间指标采用均数差（MD）评价。结果：共纳入原始文献8篇,与对照组相比,不同运动干预方式的综合效应对空腹血糖指标无显著性影响,与按不同干预方式进行亚组分析结果一致;有氧运动及有氧联合抗阻运动对餐后2h血糖指标有显著性降低的作用（P < 0.05）;有氧运动对胰岛素抵抗指数有显著降低作用。结论：对糖尿病前期人群,运动干预对餐后2 h血糖、胰岛素抵抗指数的影响与运动方式有关,但对空腹血糖的作用尚不能确定。     

Reparameterizing the pattern mixture model for sensitivity analyses under informative dropout

Pattern mixture models are frequently used to analyze longitudinal data where missingness is induced by dropout. For measured responses, it is typical to model the complete data as a mixture of multivariate normal distributions, where mixing is done over the dropout distribution. Fully parameterized pattern mixture models are not identified by incomplete data; Little (1993, Journal of the American Statistical Association 88, 125-134) has characterized several identifying restrictions that can be used for model fitting. We propose a reparameterization of the pattern mixture model that allows investigation of sensitivity to assumptions about nonidentified parameters in both the mean and variance, allows consideration of a wide range of nonignorable missing-data mechanisms, and has intuitive appeal for eliciting plausible missing-data mechanisms. The parameterization makes clear an advantage of pattern mixture models over parametric selection models, namely that the missing-data mechanism can be varied without affecting the marginal distribution of the observed data. To illustrate the utility of the new parameterization, we analyze data from a recent clinical trial of growth hormone for maintaining muscle strength in the elderly. Dropout occurs at a high rate and is potentially informative. We undertake a detailed sensitivity analysis to understand the impact of missing-data assumptions on the inference about the effects of growth hormone on muscle strength.     

Modeling tumor growth with random onset

The longitudinal assessment of tumor volume is commonly used as an endpoint in small animal studies in cancer research. Groups of genetically identical mice are injected with mutant cells from clones developed with different mutations. The interest is on comparing tumor onset (i.e., the time of tumor detection) and tumor growth after onset, between mutation groups. This article proposes a class of linear and nonlinear growth models for jointly modeling tumor onset and growth in this situation. Our approach allows for interval-censored time of onset and missing-at-random dropout due to early sacrifice, which are common situations in animal research. We show that our approach has good small-sample properties for testing and is robust to some key unverifiable modeling assumptions. We illustrate this methodology with an application examining the effect of different mutations on tumorigenesis.     

Finite mixture modeling with mixture outcomes using the EM algorithm

This paper discusses the analysis of an extended finite mixture model where the latent classes corresponding to the mixture components for one set of observed variables influence a second set of observed variables. The research is motivated by a repeated measurement study using a random coefficient model to assess the influence of latent growth trajectory class membership on the probability of a binary disease outcome. More generally, this model can be seen as a combination of latent class modeling and conventional mixture modeling. The EM algorithm is used for estimation. As an illustration, a random-coefficient growth model for the prediction of alcohol dependence from three latent classes of heavy alcohol use trajectories among young adults is analyzed.     

Effects of dietary crude protein on fertility: Meta-analysis and meta-regression

Studies used to evaluate effects of dietary intervention on fertility may be subject to confounding because modification of one nutritional input requires a change in at least one other input. Meta-analytical modeling allows examination of a main intervention for a series of studies, but also an examination of a series of related effects through use of meta-regression. Effects of dietary crude protein (CP) on fertility were examined using this approach. We obtained 21 studies containing 32 comparisons that had pregnancy or conception data and met the eligibility criteria for meta-analysis of randomized controlled experiments providing information on diets used. Publications that contained data on prospective, randomized controlled experiments examining effects of dietary CP, either concentrations or degradability, or effects of a specific feed ingredient intervention on fertility were identified. Details on dietary formulation and diet intake were extracted from the publications, as were measures of urea in blood or plasma. Estimated fixed and random effects relative risks showed that risk of conception was lower in cows fed higher CP or more degradable CP diets (fixed effect (Mantel-Haenszel Relative Risk) = 0.91 (95% CI 0.84-0.98); P=0.019). This effect was homogenous (I² = 0) and not influenced by difference in blood urea N, duration of intervention, breed, parity, milk production or type of diet delivery. Significant associations among CP components of the diet and carbohydrate fractions supported the hypothesized potential for confounding, but only the amount of soluble CP eaten was a significant meta-regression covariate that reduced risk of conception. There was no evidence that the significant reduction in fiber or non-fiber carbohydrate (NFC) fractions of the diets associated with increased concentration of CP, soluble CP or rumen degradable fractions or soyabean products content of the diet influenced conception rates. Results support findings of experiments showing that increased intake of soluble CP reduced conception rates, and provides strong evidence that increased concentrations of CP or increased degradability of CP, within the ranges evaluated in the studies contributing to this meta-analysis, reduce the risk of conception in lactating dairy cattle.     

Outcomes and moderators of a preventive school-based mental health intervention for children affected by war in Sri Lanka: a cluster randomized trial

We aimed to examine outcomes, moderators and mediators of a preventive school-based mental health intervention implemented by paraprofessionals in a war-affected setting in northern Sri Lanka. A cluster randomized trial was employed. Subsequent to screening 1,370 children in randomly selected schools, 399 children were assigned to an intervention (n=199) or waitlist control condition (n=200). The intervention consisted of 15 manualized sessions over 5 weeks of cognitive behavioral techniques and creative expressive elements. Assessments took place before, 1 week after, and 3 months after the intervention. Primary outcomes included post-traumatic stress disorder (PTSD), depressive, and anxiety symptoms. No main effects on primary outcomes were identified. A main effect in favor of intervention for conduct problems was observed. This effect was stronger for younger children. Furthermore, we found intervention benefits for specific subgroups. Stronger effects were found for boys with regard to PTSD and anxiety symptoms, and for younger children on pro-social behavior. Moreover, we found stronger intervention effects on PTSD, anxiety, and function impairment for children experiencing lower levels of current war-related stressors. Girls in the intervention condition showed smaller reductions on PTSD symptoms than waitlisted girls. We conclude that preventive school-based psychosocial interventions in volatile areas characterized by ongoing war-related stressors may effectively improve indicators of psychological wellbeing and posttraumatic stress-related symptoms in some children. However, they may undermine natural recovery for others. Further research is necessary to examine how gender, age and current war-related experiences contribute to differential intervention effects.     

Effects of a Brief Intervention on Retention of Patients in a Cardiac Rehabilitation Program

This intervention assessed the effects of a brief intervention on dropout rate in a cardiac rehabilitation program. One hundred thirty five patients were recruited from a cardiac rehabilitation program and randomized to either a control or intervention group. The intervention group participated in four sessions of motivational interviewing and stress management-relaxation in addition to standard cardiac rehabilitation. The control group underwent cardiac rehabilitation alone. Patients who completed the intervention completed an average of 30 sessions while those who dropped out of the intervention completed about six (p < 0.001). Anxiety and depression measured at baseline were the primary predictors of dropout. Patients in both the intervention and controls groups who completed cardiac rehabilitation improved the distance walked, quality of life and decreased anxiety.     

Designing optimal allocations for cancer screening using queuing network models

Cancer is one of the leading causes of death, but mortality can be reduced by detecting tumors earlier so that treatment is initiated at a less aggressive stage. The tradeoff between costs associated with screening and its benefit makes the decision of whom to screen and when a challenge. To enable comparisons across screening strategies for any cancer type, we demonstrate a mathematical modeling platform based on the theory of queuing networks designed for quantifying the benefits of screening strategies. Our methodology can be used to design optimal screening protocols and to estimate their benefits for specific patient populations. Our method is amenable to exact analysis, thus circumventing the need for simulations, and is capable of exactly quantifying outcomes given variability in the age of diagnosis, rate of progression, and screening sensitivity and intervention outcomes. We demonstrate the power of this methodology by applying it to data from the Surveillance, Epidemiology and End Results (SEER) program. Our approach estimates the benefits that various novel screening programs would confer to different patient populations, thus enabling us to formulate an optimal screening allocation and quantify its potential effects for any cancer type and intervention.     

Editors' Introduction: Pathways to Identity and Positive Development Among Muslim Youth in the West

The present study used a person-centered approach to examine patterns of conflict experience among 198 3rd–6th grade children. Peer reports of aggressive behavior, sociability, victimization, and an assessment of psychological mindedness in narrative accounts of conflict experiences were used. Three patterns were identified using mixture modeling: Managers, Avoiders, and Sustainers. Patterns differed with respect to narrative skills and social adjustment. Findings demonstrate the benefit of examining children's ability to tell their own stories in combination with peer perceptions of children's behavior. Discussion focuses on how children may rely on behavioral and narrative skills to develop different ways of responding to peer conflict in context, as well as on the application of findings in school settings.     

Dose-structured population dynamics

Applied population dynamics modeling is relied upon with increasing frequency to quantify how human activities affect human and non-human populations. Current techniques include variously the population's spatial transport, age, size, and physiology, but typically not the life-histories of exposure to other important things occurring in the ambient environment, such as chemicals, heat, or radiation. Consequently, the effects of such 'abiotic' aspects of an ecosystem on populations are only currently addressed through individual-based modeling approaches that despite broad utility are limited in their applicability to realistic ecosystems [V. Grimm, Ten years of individual-based modeling in ecology: what have we learned and what could we learn in the future? Ecol. Model. 115 (1999) 129-148][1]. We describe a new category of population dynamics modeling, wherein population dynamical states of the biotic phases are structured on dose, and apply this framework to demonstrate how chemical species or other ambient aspects can be included in population dynamics in three separate examples involving growth suppression in fish, inactivation of microorganisms with ultraviolet irradiation, and metabolic lag in population growth. Dose-structuring is based on a kinematic approach that is a simple generalization of age-structuring, views the ecosystem as a multi-component mixture with reacting biotic/abiotic components. The resulting model framework accommodates (a) different memories of exposure as in recovery from toxic ambient conditions, (b) differentiation between exogenous and endogenous sources of variation in population response, and (c) quantification of acute or sub-acute effects on populations arising from life-history exposures to abiotic species. Classical models do not easily address the very important fact that organisms differ and have different experiences over their life cycle. The dose structuring is one approach to incorporate some of these elements into the existing structures of the classical models, while retaining many of the features (and other limitations) of classical models.     

Interval mapping of quantitative trait loci for time-to-event data with the proportional hazards mixture cure model

Interval mapping using normal mixture models has been an important tool for analyzing quantitative traits in experimental organisms. When the primary phenotype is time-to-event, it is natural to use survival models such as Cox's proportional hazards model instead of normal mixtures to model the phenotype distribution. An extra challenge for modeling time-to-event data is that the underlying population may consist of susceptible and nonsusceptible subjects. In this article, we propose a semiparametric proportional hazards mixture cure model which allows missing covariates. We discuss applications to quantitative trait loci (QTL) mapping when the primary trait is time-to-event from a population of mixed susceptibility. This model can be used to characterize QTL effects on both susceptibility and time-to-event distribution, and to estimate QTL location. The model can naturally incorporate covariate effects of other risk factors. Maximum likelihood estimates for the parameters in the model as well as their corresponding variance estimates can be obtained numerically using an EM-type algorithm. The proposed methods are assessed by simulations under practical settings and illustrated using a real data set containing survival times of mice after infection with Listeria monocytogenes. An extension to multiple intervals is also discussed.     

A biomechanical analysis on the impact of episiotomy during childbirth

Episiotomy is still a controversy issue among physicians, despite the enormous growth of clinical research. Therefore, the potential of numerical modeling of anatomical structures to simulate biomechanical processes was exploited to realize quantitatively the real effects of the episiotomy and its consequences on the pelvic floor muscle. As such, a numerical model was used composed of pelvic floor muscles, a surface delimiting the anterior region, and a fetus body. A normal vaginal delivery without and with different episiotomies was simulated with the fetus in vertex presentation and occipitoanterior position. According to our numerical results, a mediolateral episiotomy has a protective effect, reducing the stress on the muscles, and the force required to delivery successfully up to 52.2 %. The intervention also has benefits on muscle injury, reducing the damage to a small zone. This study demonstrates the feasibility of using a computational modeling approach to study parturition, namely the capability to isolate and evaluate the mechanical significance of a single feature. It must, however, be taken into account that the numerical model does not assess problems that may occur as blood loss, infections and others, so it is necessary to examine whether the benefits of an intervention outweigh the risks.     

Oscillatory behaviour control in a continuous culture under double-substrate limitation

The paper discusses the possibility of using a mixture of two growth limiting substrates to induce or eliminate self-sustained oscillations in a continuous culture process. The proportion of both substrates in the mixture is treated as a new control variable. The presented approach is based on the assumption that the oscillatory behaviour occurs for selected substrates in some range of dilution rates. Because a double-substrate limitation may occur, the analysis is performed for two fundamental substrate utilization patterns: simultaneous consumption and diauxic growth. By using model simulations and bifurcation analysis, we show that an appropriate proportion of two substrates in the mixture allows for the control of the oscillatory behaviour.     

The use of PSA as biomarker in nutritional intervention studies of prostate cancer

Epidemiological evidence suggests that environmental factors, such as diet, play a role in the development and progression of prostate cancer (PC). The number of potential protective dietary compounds or whole dietary products that are indicated to have preventive effects is piling up and demands further evaluation. The number of options urges for a reliable high-throughput screening system. To face this growing field, we suggest a strategy that combines prostate-specific antigen (PSA)-based clinical trials with experimental human xenograft studies to evaluate potential chemopreventive agents for PC. This review describes the first results that have come available using this method. In Rotterdam, two nutrition-based tertiary chemoprevention trials were conducted in patients aiming to delay progression of minimal PC. In these studies two different supplements were used both consisting of a (different) mixture of components reported to be related to cancer prevention. PC patients that were locally treated but had rising levels of circulating PSA of unknown origin were randomised into a double-blind, placebo-controlled study with a crossover design. PSA kinetics was followed during the two intervention periods. The time frame of the study design was 6 months. Results of these intervention studies showed increased PSA doubling times after dietary supplementation as compared to placebo. The lack of information on tumor burden in these patients requires the need for additional xenograft studies that can provide supplement-induced PSA and tumor responses. Such parallel experimental studies will enable to validate PSA as a biomarker for tumor volume response and may link clinical PSA kinetics to actual tumor response. For one of the clinical study, such an experimental confirmation study was performed. The dietary supplement similar to what was used in the clinical study was administered to animals that were injected intraprostatically with human PC-346C cells. Responses on tumor growth and PSA were recorded over time and allowed to monitor a potential differential effect on PSA or tumor growth. This animal study revealed no difference in response as determined by tumor volume or PSA release between supplemented and placebo mice, and confirmed that PSA levels reflected tumor response under this specific dietary intervention. We propose that the strategy of PSA-based early phase II clinical trials accompanied by experimental human xenograft studies, to assess the reliability of PSA response to reflect tumor response, allows for a concise, relatively fast test system that is able to screen the various treatment options for chemoprevention in a relatively short period of time.