Cluster-specific Random Effects Research Articles

Application of longitudinal multilevel zero inflated Poisson regression in modeling of infectious diseases among infants in Ethiopia

BackgroundIn sub-Saharan African countries, preventable and manageable diseases such as diarrhea and acute respiratory infections still claim the lives of children. Hence, this study aims to estimate the rate of change in the log expected number of days a child suffers from Diarrhea (NOD) and flu/common cold (NOF) among children aged 6 to 11 months at the baseline of the study.MethodologyThis study used secondary data which exhibit a longitudinal and multilevel structure. Based on the results of exploratory analysis, a multilevel zero-inflated Poisson regression model with a rate of change in the log expected NOD and NOF described by a quadratic trend was proposed to efficiently analyze both outcomes accounting for correlation between observations and individuals through random effects. Furthermore, residual plots were used to assess the goodness of fit of the model.ResultsConsidering subject and cluster-specific random effects, the results revealed a quadratic trend in the rate of change of the log expected NOD. Initially, low dose iron Micronutrient Powder (MNP) users exhibited a higher rate of change compared to non-users, but this trend reversed over time. Similarly, the log expected NOF decreased for children who used MNP and exclusively breastfed for six months, in comparison to their counterparts. In addition, the odds of not having flu decreased with each two-week increment for MNP users, as compared to non-MNP users. Furthermore, an increase in NOD resulted in an increase in the log expected NOF. Region and exclusive breastfeeding also have a significant relationships with both NOD and NOF.ConclusionThe findings of this study underscore the importance of commencing analysis of data generated from a study with exploratory analysis. The study highlights the critical role of promoting EBF for the first six months and supporting children with additional food after six months to reduce the burden of infectious diseases.

Abstract PO1-09-10: County-level Social Vulnerability and Survival among Women with Inflammatory Breast Cancer

Abstract Purpose: Inflammatory breast cancer (IBC) is an aggressive form of breast cancer with a poor overall prognosis compared to other forms of breast cancer. Advances in treatment have contributed to improvement in IBC survival rates in recent years, yet disparities in outcomes persist. It is unclear whether social determinants of health impact IBC prognosis independent of access to quality cancer care. Thus, the aim of this study was to examine whether the US county-level social vulnerability index (SVI) was associated with IBC stage at diagnosis and overall survival (OS) among women with IBC treated at a single institution. Methods: Patients enrolled in the IBC registry at Dana-Farber Cancer Institute (DFCI) were included in this study. We linked participant’s residential zip codes to the 2020 CDC’s county-level SVI, which is calculated from 15 social determinants of health attributes from the American Community Survey including socioeconomic status, household composition, language and minority status, and housing and transportation factors. The SVI value reflects the percentile of counties in the nation that are less vulnerable than the county of interest. We assessed associations between SVI and stage at diagnosis using t-tests. Kaplan-Meier curves and log-rank tests were used to assess survival across SVI quartiles based on distribution (1st [least vulnerable] and 4th [most vulnerable]). Using hierarchical logistic regression models and Cox proportional hazards models with mixed effects incorporating cluster-specific random effects that modify the baseline hazard function, we assessed whether SVI is associated with the presence of de novo metastatic disease and OS in IBC. Results: A total of 586 women (86% White) enrolled in the IBC registry at DFCI between 1986 and 2021 were included in this study. Of these, 69.1% had stage III and 30.9% had de novo metastatic disease. 280 deaths occurred in the study population over a mean follow-up of 4.1 years. SVI for the counties where study participants resided ranged from 2.6% to 95.8% (median=34.2%). The mean SVI did not significantly differ according to stage at diagnosis (41.6% in non-metastatic and 40.8% in metastatic at presentation; p=0.70). OS did not significantly differ across SVI quartiles (p-value=0.63). In the age-adjusted models, the SVI was not associated with the presence of de novo metastatic disease (odds ratio (OR (95% CI)=0.99 (0.84, 1.16)) or OS (HR (95% CI)=0.79 (0.46, 1.33). Conclusions: Our findings that residing in socially vulnerable US counties is not associated with the presence of de novo metastatic disease or IBC survival among a subset of women accessing high-quality cancer care suggest that improving access to quality cancer care may overcome underlying socioeconomic factors that contribute to disparities in IBC outcomes. Future studies are needed to confirm these findings in other settings. Citation Format: Kelly Hirko, Elizabeth Troll, Sean Ryan, Faina Nakhlis, Jennifer Bellon, Olga Kantor, Christina Minami, Eren Yeh, Ilana Schlam, Laura Warren, Caroline Block, Susan Schumer, Filipa Lynce. County-level Social Vulnerability and Survival among Women with Inflammatory Breast Cancer [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO1-09-10.

R-VGAL: a sequential variational Bayes algorithm for generalised linear mixed models

Models with random effects, such as generalised linear mixed models (GLMMs), are often used for analysing clustered data. Parameter inference with these models is difficult because of the presence of cluster-specific random effects, which must be integrated out when evaluating the likelihood function. Here, we propose a sequential variational Bayes algorithm, called Recursive Variational Gaussian Approximation for Latent variable models (R-VGAL), for estimating parameters in GLMMs. The R-VGAL algorithm operates on the data sequentially, requires only a single pass through the data, and can provide parameter updates as new data are collected without the need of re-processing the previous data. At each update, the R-VGAL algorithm requires the gradient and Hessian of a “partial” log-likelihood function evaluated at the new observation, which are generally not available in closed form for GLMMs. To circumvent this issue, we propose using an importance-sampling-based approach for estimating the gradient and Hessian via Fisher’s and Louis’ identities. We find that R-VGAL can be unstable when traversing the first few data points, but that this issue can be mitigated by introducing a damping factor in the initial steps of the algorithm. Through illustrations on both simulated and real datasets, we show that R-VGAL provides good approximations to posterior distributions, that it can be made robust through damping, and that it is computationally efficient.

Correlations among the maternal healthcare services in Bangladesh: An application of joint modelling technique

BackgroundCaesarean section (C-section) in Bangladesh have received great attention as the number has been amplified during the last two decades. The question arises whether this rise has a correlation with other maternal healthcare services and/or has been influenced by their predictors. ObjectiveThe main objectives of this study are to assess correlations among the maternal healthcare indicators—antenatal care use, childbirth in private facilities, and childbirth through C-section—and identify their associated predictors in Bangladesh through the development of an appropriate cluster-adjusted joint model that accounts for inter-correlation among the indicators in the same cluster. DesignThe 2019 Bangladesh Multiple Indicator Cluster Survey data have been utilized in this study. Separate generalized linear mixed models developed for the three outcome variables are combined into a joint model by letting cluster-specific random effects be in association. FindingsThe joint model shows that the number of antenatal cares is fairly positively correlated with delivery in private facilities and C-section, while the latter two are strongly positively correlated. Household socio-economic condition, women and their partners' education, women's exposure to mass media, place of residence, religion, and regional settings have significant influence on the joint likelihood of receiving antenatal care, choosing a private health facility for birth, and opting for C-section birth. Key conclusions and implicationsThe rising rate of C-section delivery over time is alarming for Bangladesh to achieve the World Health Organization target of 10–15 %. The joint model reveals that the rising rate of C-sections may be correlated with the choice of a private health facility as the delivery place. The study findings also suggest that maternal childbirth care is private-dominant and predominantly utilized by urban women with better education and higher socio-economic status. The policy should focus on strengthening the public health sector while also keeping importance in increasing coverage of maternal care services among the less well-off.

Adversarially-Regularized Mixed Effects Deep Learning (ARMED) Models Improve Interpretability, Performance, and Generalization on Clustered (non-iid) Data.

Natural science datasets frequently violate assumptions of independence. Samples may be clustered (e.g., by study site, subject, or experimental batch), leading to spurious associations, poor model fitting, and confounded analyses. While largely unaddressed in deep learning, this problem has been handled in the statistics community through mixed effects models, which separate cluster-invariant fixed effects from cluster-specific random effects. We propose a general-purpose framework for Adversarially-Regularized Mixed Effects Deep learning (ARMED) models through non-intrusive additions to existing neural networks: 1) an adversarial classifier constraining the original model to learn only cluster-invariant features, 2) a random effects subnetwork capturing cluster-specific features, and 3) an approach to apply random effects to clusters unseen during training. We apply ARMED to dense, convolutional, and autoencoder neural networks on 4 datasets including simulated nonlinear data, dementia prognosis and diagnosis, and live-cell image analysis. Compared to prior techniques, ARMED models better distinguish confounded from true associations in simulations and learn more biologically plausible features in clinical applications. They can also quantify inter-cluster variance and visualize cluster effects in data. Finally, ARMED matches or improves performance on data from clusters seen during training (5-28% relative improvement) and generalization to unseen clusters (2-9% relative improvement) versus conventional models.

Tweedie Compound Poisson Models with Covariate-Dependent Random Effects for Multilevel Semicontinuous Data.

Multilevel semicontinuous data occur frequently in medical, environmental, insurance and financial studies. Such data are often measured with covariates at different levels; however, these data have traditionally been modelled with covariate-independent random effects. Ignoring dependence of cluster-specific random effects and cluster-specific covariates in these traditional approaches may lead to ecological fallacy and result in misleading results. In this paper, we propose Tweedie compound Poisson model with covariate-dependent random effects to analyze multilevel semicontinuous data where covariates at different levels are incorporated at relevant levels. The estimation of our models has been developed based on the orthodox best linear unbiased predictor of random effect. Explicit expressions of random effects predictors facilitate computation and interpretation of our models. Our approach is illustrated through the analysis of the basic symptoms inventory study data where 409 adolescents from 269 families were observed at varying number of times from 1 to 17 times. The performance of the proposed methodology was also examined through the simulation studies.

Respiratory symptoms and cardiovascular causes of deaths: A population-based study with 45 years of follow-up.

This study determined the association between respiratory symptoms and death from cardiovascular (CV) diseases during 45 years in a pooled sample of four cohorts of random samples of the Norwegian population with 95,704 participants. Respiratory symptoms were assessed using a modification of the MRC questionnaire on chronic bronchitis. We analyzed the association between respiratory symptoms and specific cardiovascular deaths by using Cox regression analysis with age as the time variable, accounting for cluster-specific random effects using shared frailty for study cohort. Hazard ratios (HR) for death were adjusted for sex, highest attained education, smoking habits, occupational air pollution, and birth cohort. Overall, 12,491 (13%) of participants died from CV diseases: 4,123 (33%) acute myocardial infarction, 2,326 (18%) other ischemic heart disease, 2,246 (18%) other heart diseases, 2,553 (20%) cerebrovascular diseases, and 1,120 (9%) other vascular diseases. The adjusted HR (95% confidence interval) for CV deaths was 1.9 (1.7-2.1) in men and 1.5 (1.2-1.9) in women for "yes" to the question "Are you breathless when you walk on level ground at an ordinary pace?". The same item response showed an adjusted HR for death from acute myocardial infarction of 1.8 (1.5-2.1), other ischemic heart disease 2.2 (1.8-2.7), other heart diseases 1.5 (1.1-1.9), cerebrovascular disease 1.8 (1.5-2.3), and other circulatory diseases 1.7 (1.2-2.4). The adjusted HR for CV death was 1.3 (1.2-1.4) when answering positive to the question" Are you more breathless than people of your own age when walking uphill?". However, positive answers to questions on cough, phlegm, wheezing and attacks of breathlessness were after adjustments not associated with early CV deaths. The associations between CV deaths and breathlessness were also present in never smokers. Self-reported breathlessness was associated with CV deaths and could be an early marker of CV deaths.

A doubly robust method to handle missing multilevel outcome data with application to the China Health and Nutrition Survey.

Missing data are common in longitudinal cohort studies and can lead to bias, particularly in studies with informative missingness. Many common methods for handling informatively missing data in survey samples require correctly specifying a model for missingness. Although doubly robust methods exist to provide unbiased regression coefficients in the presence of missing outcome data, these methods do not account for correlation due to clustering inherent in longitudinal or cluster-sampled studies. In this work, we developed a doubly robust method to estimate the regression of an outcome on a predictor in the presence of missing multilevel data on the outcome, which results in consistent estimation of regression coefficients assuming correct specification of either (1) the probability of missingness or (2) the outcome model. This method involves specification of separate hierarchical models for missingness and for the outcome, conditional on observed auxiliary variables and cluster-specific random effects, to account for correlation among observations. We showed this proposed estimator is doubly robust and derived its asymptotic distribution, conducted simulation studies to compare the method to an existing doubly robust method developed for independent data, and applied the method to data from the China Health and Nutrition Survey, an ongoing multilevel longitudinal cohort study.

An Emerging Problem of Shisha Smoking among High School Students in Ethiopia.

Shisha smoking is also known as hookah, water pipe, goza, and nargile. Shisha use among the young is increasing globally. Shisha smoke results in a high concentration of carbon monoxide, tar, nicotine, and heavy metals which can be toxic to humans, especially with chronic exposure. This study aims to determine the prevalence and risk factors of shisha smoking among in-school adolescents in Ethiopia. Four regional states in Ethiopia (Oromia, Amhara, Southern Nations, Nationalities, and Peoples’ Region, Tigray) and the capital city (Addis Ababa) were the study areas. A two-stage cluster sampling approach was employed to produce a representative sample. From the sampling frames in the study areas, 36 high schools were selected randomly. A multi-level logistic regression analysis was used to account for cluster-specific random effects, the effect of individuals’, and school-level variables for ever-use of shisha. A total of 3355 secondary school grade 9 and 10 students aged between 13 and 22 years took part in this study. A total of 86 (2.6%) and 20 (0.6%) of the study participants, reported that they had ever smoked or were current smokers of shisha, respectively. Of all study participants, 38.6% perceived shisha as less harmful than cigarettes and 48.5% reported that they do not know which was more harmful to health. Students were more likely to ever use shisha if they had friend/s who smoke shisha (AOR = 16.8, 95% CI: 6.4–44.3), ever smoked cigarettes (AOR = 8.2, 95% CI: 3.4–19.8), ever used khat (AOR = 4.2, 95% CI: 1.9–10.4), ever used marijuana (AOR = 3.9, 95% CI: 1.4–11.1), ever used smokeless tobacco (AOR = 3.1 95% CI: 1.1–8.4), and students had received income from their parents (AOR = 3.1 CI: 1.1–8.8). Prevalence of ever and current use of shisha among high school students is low in Ethiopia compared to many countries in Africa. The majority of adolescents perceived shisha as less harmful to health than cigarette smoking. Health education about the harmful effects of shisha should be delivered to adolescents, along with information on other substances like khat, cigarettes, marijuana, and smokeless tobacco to prevent initiation of substance use.

A three-step methodology to complement underreporting maritime accident records

The underreporting issue on shipping accident data has plagued the researchers focused on maritime safety analysis for many years. For improving the quality of shipping accident records, this study proposes a novel methodology comprising three steps to complement the underreported maritime accident records. The first step is to investigate the underreporting rates under various conditions through questionnaire survey. Based on the survey results, the second step is to build a Cluster-Specific Random Effects (CSRE) model to estimate the underreporting rates under various scenarios. Then, the third step is to replicate the underreported accident records using the Monte Carlo simulation technique. Model results show that the occurrence probability of missing accident records involving liquid cargo ships is lower than other ship categories while fishing ships are more likely to have a higher underreporting rate. Non-serious accidents are more likely to be underreported than serious accidents. The case study confirms the effectiveness of the proposed three-step method for complementing the maritime accident databases suffering underreporting problems.

Bootstrapped inference for variance parameters, measures of heterogeneity and random effects in multilevel logistic regression models

We used Monte Carlo simulations to assess the performance of three bootstrap procedures for use with multilevel data (the parametric bootstrap, the residuals bootstrap, and the nonparametric bootstrap) for estimating the sampling variation of three measures of cluster variation and heterogeneity when using a multilevel logistic regression model: the variance of the distribution of the random effects, the variance partition coefficient (equivalent here to the intraclass correlation coefficient), and the median odds ratio. We also described a novel parametric bootstrap procedure to estimate the standard errors of the predicted cluster-specific random effects. Our results suggest that the parametric and residuals bootstrap should, in general, be used to estimate the sampling variation of key measures of cluster variation and heterogeneity. The performance of the novel parametric bootstrap procedure for estimating the standard errors of predicted cluster-specific random effects tended to exceed that of the model-based estimates.

Associations and contribution of childhood diseases to fever risk among children less than five years in Uganda

Background Despite massive investment in diseases responsible for fever among children less than five years in Uganda, the burden of the fever symptom remains high and disproportionately distributed across regions. In Uganda, studies assessing the relationship between fever prevalence and multiple childhood diseases, especially at a local scale are scanty. We analyse the 2016 Demographic and Health Survey (DHS) data to quantify the associations and contribution of childhood diseases to fever prevalence among children less than five years in Uganda at the national and regional level. Findings can lead to the development and implementation of preventive and treatment measures especially at a local scale to minimize fever-related diseases among the under-fives in Uganda. Methods Bayesian geostatistical logistic regression models with spatially varying coefficients were fitted to determine the associations and contribution of childhood diseases on fever prevalence at the national and regional levels. Region-specific spatially varying coefficients were modeled by a conditional autoregressive distribution. Cluster-specific random effects were introduced into the model to take into account spatial dependence in fever prevalence. Bayesian geostatistical stochastic search variable selection was applied to determine the most important predictors in explaining variation in fever prevalence. The contribution of childhood diseases to fever prevalence was estimated using population attributable fractions. Results The prevalence of fever was highest in Busoga and Teso regions and lowest in Bunyoro region. At the national level, the population attribution fraction of diarrhoea, acute respiratory infections (ARI) and malaria to the prevalence of fever in the under-five was 38.12 (95% Bayesian credible intervals, BCI=25.15-41.59), 30.99 (95% BCI=9.82-34.26) and 9.50 (95% BCI=2.34-25.15), respectively. The attribution of diarrhoea was common in all regions except Bunyoro, while ARI was more common in Bugisu, Karamoja and West Nile, and malaria was commonest in Bunyoro. In Lango, the attribution of diarrhoea and ARI was similar. Conclusions Majority of fevers among the under-five are due to diarrhoea, followed by ARI. Hand washing with soap and water/detergent should be strengthened in all regions. Vaccination against ARI should be encouraged, in the regions of Central 2, Bugisu, Teso, Karamoja, Lango, West-Nile and Tooro. The health system should be reinforced to treat diarrhoea and ARI.

Contemporary patterns in kidney graft survival from donors after circulatory death in the United States.

Kidney transplants from donors after circulatory death (DCD) make up an increasing proportion of all deceased donor kidney transplants in the United States (US). However, DCD grafts are considered to be of lower quality than kidneys from donors after brain death (DBD). It is unclear whether graft survival is different for these two types of donor kidneys. We conducted a retrospective cohort study of US deceased donor kidney recipients using data from the United Network of Organ Sharing from 12/4/2014 to 6/30/2018. We employed a Cox proportional hazard model with mixed effects to compare all-cause graft loss and death-censored graft loss for DCD versus DBD deceased donor kidney transplant recipients. We used transplant center as the random effects term to account for cluster-specific random effects. In the multivariable analysis, we adjusted for recipient characteristics, donor factors, and transplant logistics. Our cohort included 27,494 DBD and 7,770 DCD graft recipients transplanted from 2014 to 2018 who were followed over a median of 1.92 years (IQR 1.08-2.83). For DCD compared with DBD recipients, we did not find a significant difference in all-cause graft loss (hazard ratio [HR] 0.96, 95% confidence interval [CI] 0.87-1.05 in univariable and HR 1.03 [95% CI 0.95-1.13] in multivariable analysis) or for death-censored graft loss (HR 0.97 (95% CI 0.91-1.06) in univariable and 1.05 (95% CI 0.99-1.11) in multivariable analysis). For a contemporary cohort of deceased donor kidney transplant recipients, we did not find a difference in the likelihood of graft loss for DCD compared with DBD grafts. These findings signal a need for additional investigation into whether DCD status independently contributes to other important outcomes for current kidney transplant recipients and indices of graft quality.

Modelling the number of antenatal care visits in Bangladesh to determine the risk factors for reduced antenatal care attendance.

The existence of excess zeros in the distribution of antenatal care (ANC) visits in Bangladesh raises the research question of whether there are two separate generating processes in taking ANC and the frequency of ANC. Thus the main objective of this study is to identify a proper count regression model for the number of ANC visits by pregnant women in Bangladesh covering the issues of overdispersion, zero-inflation, and intra-cluster correlation with an additional objective of determining risk factors for ANC use and its frequency. The data have been extracted from the nationally representative 2014 Bangladesh Demographic and Health Survey, where 22% of the total 4493 women did not take any ANC during pregnancy. Since these zero ANC visits can be either structural or sampling zeros, two-part zero-inflated and hurdle regression models are investigated along with the standard one-part count regression models. Correlation among response values has been accounted for by incorporating cluster-specific random effects in the models. The hurdle negative binomial regression model with cluster-specific random intercepts in both the zero and the count part is found to be the best model according to various diagnostic tools including likelihood ratio and uniformity tests. The results show that women who have poor education, live in poor households, have less access to mass media, or belong to the Sylhet and Chittagong regions are less likely to use ANC and also have fewer ANC visits. Additionally, women who live in rural areas, depend on family members' decisions to take health care, and have unintended pregnancies had fewer ANC visits. The findings recommend taking both cluster-specific random effects and overdispersion and zero-inflation into account in modelling the ANC data of Bangladesh. Moreover, safe motherhood programmes still need to pay particular attention to disadvantaged and vulnerable subgroups of women.

Nonproportional hazards and unobserved heterogeneity in clustered survival data: When can we tell the difference?

Multivariate survival data are frequently encountered in biomedical applications in the form of clustered failures (or recurrent events data). A popular way of analyzing such data is by using shared frailty models, which assume that the proportional hazards assumption holds conditional on an unobserved cluster‐specific random effect. Such models are often incorporated in more complicated joint models in survival analysis.If the random effect distribution has finite expectation, then the conditional proportional hazards assumption does not carry over to the marginal models. It has been shown that, for univariate data, this makes it impossible to distinguish between the presence of unobserved heterogeneity (eg, due to missing covariates) and marginal nonproportional hazards. We show that time‐dependent covariate effects may falsely appear as evidence in favor of a frailty model also in the case of clustered failures or recurrent events data, when the cluster size or number of recurrent events is small. When true unobserved heterogeneity is present, the presence of nonproportional hazards leads to overestimating the frailty effect. We show that this phenomenon is somewhat mitigated as the cluster size grows.We carry out a simulation study to assess the behavior of test statistics and estimators for frailty models in such contexts. The gamma, inverse Gaussian, and positive stable shared frailty models are contrasted using a novel software implementation for estimating semiparametric shared frailty models. Two main questions are addressed in the contexts of clustered failures and recurrent events: whether covariates with a time‐dependent effect may appear as indication of unobserved heterogeneity and whether the additional presence of unobserved heterogeneity can be detected in this case. Finally, the practical implications are illustrated in a real‐world data analysis example.

Marginalized models for right-truncated and interval-censored time-to-event data

ABSTRACTAnalysis of clustered data is often performed using random effects regression models. In such conditional models, a cluster-specific random effect is often introduced into the linear predictor function. Parameter interpretation of the covariate effects is then conditioned on the random effects, leading to a subject-specific interpretation of the regression parameters. Recently, Marginalized Multilevel Models (MMM) and the Bridge distribution models have been proposed as a unified approach, which allows one to capture the within-cluster correlations by specifying random effects while still allowing for marginal parameter interpretation. In this paper, we investigate these two approaches, and the conditional Generalized Linear Mixed Model (GLMM), in the context of right-truncated, interval-censored time-to-event data, further characterized by clustering and additional overdispersion. While these models have been applied in literature to model the mean, here we extend their application to modeling the hazard function for the survival endpoints. The models are applied to analyze data from the HET-CAMVT experiment which was designed to assess the potential of a compound to cause injection site reaction. Results show that the MMM and Bridge distribution approaches are useful when interest is in the marginal interpretation of the covariate effects.

Random scaling factors in Bayesian distributional regression models with an application to real estate data

Distributional structured additive regression provides a flexible framework for modelling each parameter of a potentially complex response distribution in dependence of covariates. Structured additive predictors allow for an additive decomposition of covariate effects with non-linear effects and time trends, unit- or cluster-specific heterogeneity, spatial heterogeneity and complex interactions between covariates of different type. Within this framework, we present a simultaneous estimation approach for multiplicative random effects that allow for cluster-specific heterogeneity with respect to the scaling of a covariate′s effect. More specifically, a possibly non-linear function f( z) of a covariate z may be scaled by a multiplicative and possibly spatially correlated cluster-specific random effect (1+αc). Inference is fully Bayesian and is based on highly efficient Markov Chain Monte Carlo (MCMC) algorithms. We investigate the statistical properties of our approach within extensive simulation experiments for different response distributions. Furthermore, we apply the methodology to German real estate data where we identify significant district-specific scaling factors. According to the deviance information criterion, the models incorporating these factors perform significantly better than standard models without (spatially correlated) random scaling factors.

The effect of number of clusters and cluster size on statistical power and Type I error rates when testing random effects variance components in multilevel linear and logistic regression models

When using multilevel regression models that incorporate cluster-specific random effects, the Wald and the likelihood ratio (LR) tests are used for testing the null hypothesis that the variance of the random effects distribution is equal to zero. We conducted a series of Monte Carlo simulations to examine the effect of the number of clusters and the number of subjects per cluster on the statistical power to detect a non-null random effects variance and to compare the empirical type I error rates of the Wald and LR tests. Statistical power increased with increasing number of clusters and number of subjects per cluster. Statistical power was greater for the LR test than for the Wald test. These results applied to both the linear and logistic regressions, but were more pronounced for the latter. The use of the LR test is preferable to the use of the Wald test.

Describing the association between socioeconomic inequalities and cancer survival: methodological guidelines and illustration with population-based data.

BackgroundDescribing the relationship between socioeconomic inequalities and cancer survival is important but methodologically challenging. We propose guidelines for addressing these challenges and illustrate their implementation on French population-based data.MethodsWe analyzed 17 cancers. Socioeconomic deprivation was measured by an ecological measure, the European Deprivation Index (EDI). The Excess Mortality Hazard (EMH), ie, the mortality hazard among cancer patients after accounting for other causes of death, was modeled using a flexible parametric model, allowing for nonlinear and/or time-dependent association between the EDI and the EMH. The model included a cluster-specific random effect to deal with the hierarchical structure of the data.ResultsWe reported the conventional age-standardized net survival (ASNS) and described the changes of the EMH over the time since diagnosis at different levels of deprivation. We illustrated nonlinear and/or time-dependent associations between the EDI and the EMH by plotting the excess hazard ratio according to EDI values at different times after diagnosis. The median excess hazard ratio quantified the general contextual effect. Lip–oral cavity–pharynx cancer in men showed the widest deprivation gap, with 5-year ASNS at 41% and 29% for deprivation quintiles 1 and 5, respectively, and we found a nonlinear association between the EDI and the EMH. The EDI accounted for a substantial part of the general contextual effect on the EMH. The association between the EDI and the EMH was time dependent in stomach and pancreas cancers in men and in cervix cancer.ConclusionThe methodological guidelines proved efficient in describing the way socioeconomic inequalities influence cancer survival. Their use would allow comparisons between different health care systems.

Informatively clustering longitudinal microarrays using binary or survival outcome data

ABSTRACTThe goal of this research is to discover what groups of genes are associated with the disease process. We use binary and failure time outcomes to inform the clustering of longitudinally-collected microarray data. We propose a linear model with normally distributed cluster-specific random effects for the longitudinal gene expression trajectory. The random effects are linearly related to a latent continuous representation of the outcome, where the probability or hazard of the outcome depends on these latent variables. We apply our method to microarray data collected from trauma patients in the inflammation and host response to Injury project.