Modeling data with structural and temporal correlation using lower level and higher level multilevel models

Novel imaging techniques are playing an increasingly important role in drug development, providing insight into the mechanism of action of new chemical entities. The data sets obtained by these methods can be large with complex inter-relationships, but the most appropriate statistical analysis for handling this data is often uncertain - precisely because of the exploratory nature of the way the data are collected. We present an example from a clinical trial using magnetic resonance imaging to assess changes in atherosclerotic plaques following treatment with a tool compound with established clinical benefit. We compared two specific approaches to handle the correlations due to physical location and repeated measurements: two-level and four-level multilevel models. The two methods identified similar structural variables, but higher level multilevel models had the advantage of explaining a greater proportion of variation, and the modeling assumptions appeared to be better satisfied.

Modeling multilevel sleep transitional data via Poisson log-linear multilevel models

This paper proposes Poisson log-linear multilevel models to investigate population variability in sleep state transition rates. We specifically propose a Bayesian Poisson regression model that is more flexible, scalable to larger studies, and easily fit than other attempts in the literature. We further use hierarchical random effects to account for pairings of individuals and repeated measures within those individuals, as comparing diseased to non-diseased subjects while minimizing bias is of epidemiologic importance. We estimate essentially non-parametric piecewise constant hazards and smooth them, and allow for time varying covariates and segment of the night comparisons. The Bayesian Poisson regression is justified through a re-derivation of a classical algebraic likelihood equivalence of Poisson regression with a log(time) offset and survival regression assuming piecewise constant hazards. This relationship allows us to synthesize two methods currently used to analyze sleep transition phenomena: stratified multi-state proportional hazards models and log-linear models with GEE for transition counts. An example data set from the Sleep Heart Health Study is analyzed.

ON MARGINALIZED MULTILEVEL MODELS AND THEIR COMPUTATION

Clustered data analysis is characterized by the need to describe both systematic variation in a mean model and cluster-dependent random variation in an association model. Marginalized multilevel models embrace the robustness and interpretations of a marginal mean model, while retaining the likelihood inference capabilities and flexible dependence structures of a conditional association model. Although there has been increasing recognition of the attractiveness of marginalized multilevel models, there has been a gap in their practical application arising from a lack of readily available estimation procedures. We extend the marginalized multilevel model to allow for nonlinear functions in both the mean and association aspects. We then formulate marginal models through conditional specifications to facilitate estimation with mixed model computational solutions already in place. We illustrate this approach on a cerebrovascular deficiency crossover trial.

Multilevel Latent Class Models with Dirichlet Mixing Distribution

Latent class analysis (LCA) and latent class regression (LCR) are widely used for modeling multivariate categorical outcomes in social sciences and biomedical studies. Standard analyses assume data of different respondents to be mutually independent, excluding application of the methods to familial and other designs in which participants are clustered. In this paper, we develop multilevel latent class model, in which subpopulation mixing probabilities are treated as random effects that vary among clusters according to a common Dirichlet distribution. We apply the Expectation-Maximization (EM) algorithm for model fitting by maximum likelihood (ML). This approach works well, but is computationally intensive when either the number of classes or the cluster size is large. We propose a maximum pairwise likelihood (MPL) approach via a modified EM algorithm for this case. We also show that a simple latent class analysis, combined with robust standard errors, provides another consistent, robust, but less efficient inferential procedure. Simulation studies suggest that the three methods work well in finite samples, and that the MPL estimates often enjoy comparable precision as the ML estimates. We apply our methods to the analysis of comorbid symptoms in the Obsessive Compulsive Disorder study. Our models' random effects structure has more straightforward interpretation than those of competing methods, thus should usefully augment tools available for latent class analysis of multilevel data.

Tooth loss in Brazilian middle-aged adults: multilevel effects

Objective. To examine the link between tooth loss and multilevel factors in a national sample of middle-aged adults in Brazil. Material and methods. Analyses were based on the 2003 cross-sectional national epidemiological survey of the oral health of the Brazilian population, which covered 13 431 individuals (age 35-44 years). Multistage cluster sampling was used. The dependent variable was tooth loss and the independent variables were classified according to the individual or contextual level. A multilevel negative binomial regression model was adopted. Results. The average tooth loss was 14 (standard deviation 9.5) teeth. Half of the individuals had lost 12 teeth. The contextual variables showed independent effects on tooth loss. It was found that having 9 years or more of schooling was associated with protection against tooth loss (means ratio range 0.68-0.76). Not having visited the dentist and not having visited in the last >= 3 years accounted for increases of 33.5% and 21.3%, respectively, in the risk of tooth loss (P < 0.05). The increase in tooth extraction ratio showed a strong contextual effect on increased risk of tooth loss, besides changing the effect of protective variables. Conclusions. Tooth loss in middle-aged adults has important associations with social determinants of health. This study points to the importance of the social context as the main cause of oral health injuries suffered by most middle-aged Brazilian adults.

The effect of patient, provider and financing regulations on the intensity of ambulatory physical therapy episodes : a multilevel analysis based on routinely available data

Background: Many studies have found considerable variations in the resource intensity of physical therapy episodes. Although they have identified several patient-and provider-related factors, few studies have examined their relative explanatory power. We sought to quantify the contribution of patients and providers to these differences and examine how effective Swiss regulations are (nine-session ceiling per prescription and bonus for first treatments). Methods: Our sample consisted of 87,866 first physical therapy episodes performed by 3,365 physiotherapists based on referrals by 6,131 physicians. We modeled the number of visits per episode using a multilevel log linear regression with crossed random effects for physiotherapists and physicians and with fixed effects for cantons. The three-level explanatory variables were patient, physiotherapist and physician characteristics. Results: The median number of sessions was nine (interquartile range 6-13). Physical therapy use increased with age, women, higher health care costs, lower deductibles, surgery and specific conditions. Use rose with the share of nine-session episodes among physiotherapists or physicians, but fell with the share of new treatments. Geographical area had no influence. Most of the variance was explained at the patient level, but the available factors explained only 4% thereof. Physiotherapists and physicians explained only 6% and 5% respectively of the variance, although the available factors explained most of this variance. Regulations were the most powerful factors. Conclusion: Against the backdrop of abundant physical therapy supply, Swiss financial regulations did not restrict utilization. Given that patient-related factors explained most of the variance, this group should be subject to closer scrutiny. Moreover, further research is needed on the determinants of patient demand.

Change of individual BMI in Switzerland and the USA: a multilevel model for growth

Objective The aim is to analyze and compare individual BMI growth patterns of adults from Switzerland and the U.S. Methods The analyses are based on data from two population representative longitudinal household surveys, one from Switzerland, the other from the U.S. Each data set contains up to four data points for each adult individual. We use multilevel models for growth. Results It can be shown that growth patterns are different in different cohorts in the two countries: there are only small growth differences in the youngest and oldest, but large differences in the middle ages. The individual BMI increase of the middle age Swiss amounts to only half of that in the comparable U.S. individuals. Conclusion Given the much higher BMI level especially in the youngest cohort, this points to severe obesity problems in the U.S. middle aged population in the near future. A positive correlation between individual BMI level and growth may aggravate this fact.

Perceived neighborhood problems: multilevel analysis to evaluate psychometric properties in a Southern adult Brazilian population

Abstract Background Physical attributes of the places in which people live, as well as their perceptions of them, may be important health determinants. The perception of place in which people dwell may impact on individual health and may be a more telling indicator for individual health than objective neighborhood characteristics. This paper aims to evaluate psychometric and ecometric properties of a scale on the perceptions of neighborhood problems in adults from Florianopolis, Southern Brazil. Methods Individual, census tract level (per capita monthly familiar income) and neighborhood problems perception (physical and social disorders) variables were investigated. Multilevel models (items nested within persons, persons nested within neighborhoods) were run to assess ecometric properties of variables assessing neighborhood problems. Results The response rate was 85.3%, (1,720 adults). Participants were distributed in 63 census tracts. Two scales were identified using 16 items: Physical Problems and Social Disorder. The ecometric properties of the scales satisfactory: 0.24 to 0.28 for the intra-class correlation and 0.94 to 0.96 for reliability. Higher values on the scales of problems in the physical and social domains were associated with younger age, more length of time residing in the same neighborhood and lower census tract income level. Conclusions The findings support the usefulness of these scales to measure physical and social disorder problems in neighborhoods.

A Multilevel Model with Time Series Components for the Analysis of Tribal Art Prices

In the present work we perform an econometric analysis of the Tribal art market. To this aim, we use a unique and original database that includes information on Tribal art market auctions worldwide from 1998 to 2011. In Literature, art prices are modelled through the hedonic regression model, a classic fixed-effect model. The main drawback of the hedonic approach is the large number of parameters, since, in general, art data include many categorical variables. In this work, we propose a multilevel model for the analysis of Tribal art prices that takes into account the influence of time on artwork prices. In fact, it is natural to assume that time exerts an influence over the price dynamics in various ways. Nevertheless, since the set of objects change at every auction date, we do not have repeated measurements of the same items over time. Hence, the dataset does not constitute a proper panel; rather, it has a two-level structure in that items, level-1 units, are grouped in time points, level-2 units. The main theoretical contribution is the extension of classical multilevel models to cope with the case described above. In particular, we introduce a model with time dependent random effects at the second level. We propose a novel specification of the model, derive the maximum likelihood estimators and implement them through the E-M algorithm. We test the finite sample properties of the estimators and the validity of the own-written R-code by means of a simulation study. Finally, we show that the new model improves considerably the fit of the Tribal art data with respect to both the hedonic regression model and the classic multilevel model.

LIKELIHOOD ESTIMATION OF CONJUGACY RELATIONSHIPS IN LINEAR MODELS WITH APPLICATIONS TO HIGH-THROUGHPUT GENOMICS

In the simultaneous estimation of a large number of related quantities, multilevel models provide a formal mechanism for efficiently making use of the ensemble of information for deriving individual estimates. In this article we investigate the ability of the likelihood to identify the relationship between signal and noise in multilevel linear mixed models. Specifically, we consider the ability of the likelihood to diagnose conjugacy or independence between the signals and noises. Our work was motivated by the analysis of data from high-throughput experiments in genomics. The proposed model leads to a more flexible family. However, we further demonstrate that adequately capitalizing on the benefits of a well fitting fully-specified likelihood in the terms of gene ranking is difficult.

Where is the economics in spatial econometrics?

Spatial econometrics has been criticized by some economists because some model specifications have been driven by data-analytic considerations rather than having a firm foundation in economic theory. In particular this applies to the so-called W matrix, which is integral to the structure of endogenous and exogenous spatial lags, and to spatial error processes, and which are almost the sine qua non of spatial econometrics. Moreover it has been suggested that the significance of a spatially lagged dependent variable involving W may be misleading, since it may be simply picking up the effects of omitted spatially dependent variables, incorrectly suggesting the existence of a spillover mechanism. In this paper we review the theoretical and empirical rationale for network dependence and spatial externalities as embodied in spatially lagged variables, arguing that failing to acknowledge their presence at least leads to biased inference, can be a cause of inconsistent estimation, and leads to an incorrect understanding of true causal processes.

Intermediary and structural determinants of early childhood health in Colombia: exploring the role of communities

This study examines how structural determinants influence intermediary factors of child health inequities and how they operate through the communities where children live. In particular, we explore individual, family and community level characteristics associated with a composite indicator that quantitatively measures intermediary determinants of early childhood health in Colombia. We use data from the 2010 Colombian Demographic and Health Survey (DHS). Adopting the conceptual framework of the Commission on Social Determinants of Health (CSDH), three dimensions related to child health are represented in the index: behavioural factors, psychosocial factors and health system. In order to generate the weight of the variables and take into account the discrete nature of the data, principal component analysis (PCA) using polychoric correlations are employed in the index construction. Weighted multilevel models are used to examine community effects. The results show that the effect of household’s SES is attenuated when community characteristics are included, indicating the importance that the level of community development may have in mediating individual and family characteristics. The findings indicate that there is a significant variance in intermediary determinants of child health between-community, especially for those determinants linked to the health system, even after controlling for individual, family and community characteristics. These results likely reflect that whilst the community context can exert a greater influence on intermediary factors linked directly to health, in the case of psychosocial factors and the parent’s behaviours, the family context can be more important. This underlines the importance of distinguishing between community and family intervention programmes.

Alcohol consumption and social inequality at the individual and country levels--results from an international study.

BACKGROUND: International comparisons of social inequalities in alcohol use have not been extensively investigated. The purpose of this study was to examine the relationship of country-level characteristics and individual socio-economic status (SES) on individual alcohol consumption in 33 countries. METHODS: Data on 101,525 men and women collected by cross-sectional surveys in 33 countries of the GENACIS study were used. Individual SES was measured by highest attained educational level. Alcohol use measures included drinking status and monthly risky single occasion drinking (RSOD). The relationship between individuals' education and drinking indicators was examined by meta-analysis. In a second step the individual level data and country data were combined and tested in multilevel models. As country level indicators we used the Purchasing Power Parity of the gross national income, the Gini coefficient and the Gender Gap Index. RESULTS: For both genders and all countries higher individual SES was positively associated with drinking status. Also higher country level SES was associated with higher proportions of drinkers. Lower SES was associated with RSOD among men. Women of higher SES in low income countries were more often RSO drinkers than women of lower SES. The opposite was true in higher income countries. CONCLUSION: For the most part, findings regarding SES and drinking in higher income countries were as expected. However, women of higher SES in low and middle income countries appear at higher risk of engaging in RSOD. This finding should be kept in mind when developing new policy and prevention initiatives.

Contextual effects on subjective national identity and nationalist vote in Catalonia

The important inflow of foreign population to western countries has boosted the study of acculturation processes among scholars in the last decades. By using the case of Catalonia, a receiver region of international and national migration since the fifties, this paper seeks to intersect a classic acculturation model and a newly reemerging literature in political science on contextual determinants on individual behavior. Does the context matters for understanding individual’s subjective national identity and, therefore, its voting behavior? Multilevel models show that environment matters. Percentage of Spain-born population in the town is statistically significant to account for variance in the subjective national identity and nationalist vote, even after controlling for age, sex, origin, language and left – right orientation and other contextual factors. This conclusion invites researchers not to underestimate the direct effect of the environment on individual outcomes such as feelings of belonging and vote orientation in contexts of rival identities.