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 competing risk models to evaluate the risk of nosocomial infection

Introduction Risk factor analyses for nosocomial infections (NIs) are complex. First, due to competing events for NI, the association between risk factors of NI as measured using hazard rates may not coincide with the association using cumulative probability (risk). Second, patients from the same intensive care unit (ICU) who share the same environmental exposure are likely to be more similar with regard to risk factors predisposing to a NI than patients from different ICUs. We aimed to develop an analytical approach to account for both features and to use it to evaluate associations between patient- and ICU-level characteristics with both rates of NI and competing risks and with the cumulative probability of infection. Methods We considered a multicenter database of 159 intensive care units containing 109,216 admissions (813,739 admission-days) from the Spanish HELICS-ENVIN ICU network. We analyzed the data using two models: an etiologic model (rate based) and a predictive model (risk based). In both models, random effects (shared frailties) were introduced to assess heterogeneity. Death and discharge without NI are treated as competing events for NI. Results There was a large heterogeneity across ICUs in NI hazard rates, which remained after accounting for multilevel risk factors, meaning that there are remaining unobserved ICU-specific factors that influence NI occurrence. Heterogeneity across ICUs in terms of cumulative probability of NI was even more pronounced. Several risk factors had markedly different associations in the rate-based and risk-based models. For some, the associations differed in magnitude. For example, high Acute Physiology and Chronic Health Evaluation II (APACHE II) scores were associated with modest increases in the rate of nosocomial bacteremia, but large increases in the risk. Others differed in sign, for example respiratory vs cardiovascular diagnostic categories were associated with a reduced rate of nosocomial bacteremia, but an increased risk. Conclusions A combination of competing risks and multilevel models is required to understand direct and indirect risk factors for NI and distinguish patient-level from ICU-level factors.

Comparing multilevel and Bayesian spatial random effects survival models to assess geographical inequalities in colorectal cancer survival: a case study

Background Multilevel and spatial models are being increasingly used to obtain substantive information on area-level inequalities in cancer survival. Multilevel models assume independent geographical areas, whereas spatial models explicitly incorporate geographical correlation, often via a conditional autoregressive prior. However the relative merits of these methods for large population-based studies have not been explored. Using a case-study approach, we report on the implications of using multilevel and spatial survival models to study geographical inequalities in all-cause survival. Methods Multilevel discrete-time and Bayesian spatial survival models were used to study geographical inequalities in all-cause survival for a population-based colorectal cancer cohort of 22,727 cases aged 20–84 years diagnosed during 1997–2007 from Queensland, Australia. Results Both approaches were viable on this large dataset, and produced similar estimates of the fixed effects. After adding area-level covariates, the between-area variability in survival using multilevel discrete-time models was no longer significant. Spatial inequalities in survival were also markedly reduced after adjusting for aggregated area-level covariates. Only the multilevel approach however, provided an estimation of the contribution of geographical variation to the total variation in survival between individual patients. Conclusions With little difference observed between the two approaches in the estimation of fixed effects, multilevel models should be favored if there is a clear hierarchical data structure and measuring the independent impact of individual- and area-level effects on survival differences is of primary interest. Bayesian spatial analyses may be preferred if spatial correlation between areas is important and if the priority is to assess small-area variations in survival and map spatial patterns. Both approaches can be readily fitted to geographically enabled survival data from international settings

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.

Modeling crash outcome probabilities at rural intersections: Application of hierarchical binomial logistic models

It is important to examine the nature of the relationships between roadway, environmental, and traffic factors and motor vehicle crashes, with the aim to improve the collective understanding of causal mechanisms involved in crashes and to better predict their occurrence. Statistical models of motor vehicle crashes are one path of inquiry often used to gain these initial insights. Recent efforts have focused on the estimation of negative binomial and Poisson regression models (and related deviants) due to their relatively good fit to crash data. Of course analysts constantly seek methods that offer greater consistency with the data generating mechanism (motor vehicle crashes in this case), provide better statistical fit, and provide insight into data structure that was previously unavailable. One such opportunity exists with some types of crash data, in particular crash-level data that are collected across roadway segments, intersections, etc. It is argued in this paper that some crash data possess hierarchical structure that has not routinely been exploited. This paper describes the application of binomial multilevel models of crash types using 548 motor vehicle crashes collected from 91 two-lane rural intersections in the state of Georgia. Crash prediction models are estimated for angle, rear-end, and sideswipe (both same direction and opposite direction) crashes. The contributions of the paper are the realization of hierarchical data structure and the application of a theoretically appealing and suitable analysis approach for multilevel data, yielding insights into intersection-related crashes by crash type.

The Coxian phase-type distribution as a contribution to the multilevel model of in-hospital mortality

This paper presents multilevel models that utilize the Coxian phase-type distribution in order to be able to include a survival component in the model. The approach is demonstrated by modeling patient length of stay and in-hospital mortality in geriatric wards in Italy. The multilevel model is used to provide a means of controlling for the existence of possible intra-ward correlations, which may make patients within a hospital more alike in terms of experienced outcome than patients coming from different hospitals, everything else being equal. Within this multilevel model we introduce the use of the Coxian phase-type distribution to create a covariate that represents patient length of stay or stage (of hospital care). Results demonstrate that the use of the multilevel model for representing the in-patient mortality is successful and further enhanced by the inclusion of the Coxian phase-type distribution variable (stage covariate).

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.

Psychological determinants of safety culture

- Safety psychology and workplace safety - Motivational and attitudinal components of safety - Psychological determinants of safety - Addressing risk-behaviour in safety - Case Study from Construction - Discussion and Questions

Estresse e acidentes de trabalho: Estudo Pró-Saúde

Esta tese tem o objetivo geral de investigar a associação entre estresse e acidentes no trabalho em funcionários técnico-administrativos efetivos de uma universidade pública no Rio de Janeiro por meio de modelos multiníveis. Para alcançar tal objetivo, a tese foi distribuída em dois artigos. O primeiro artigo investiga a associação entre estresse e acidentes no trabalho considerando componentes hierárquicos da estrutura dos dados por meio de modelos multiníveis com funcionários no primeiro nível agrupados em setores de trabalho no segundo nível. O segundo artigo investiga o comportamento dos coeficientes fixos e aleatórios dos modelos multiníveis com classificação cruzada entre setores de trabalho e grupos ocupacionais em relação aos modelos multiníveis que consideram apenas componentes hierárquicos dos setores de trabalho, ignorando o ajuste dos grupos ocupacionais. O estresse psicossocial no trabalho foi abordado a partir das relações entre alta demanda psicológica e baixo controle do processo laboral, Estas dimensões foram captadas por meio da versão resumida da escala Karasek, que também contém informações sobre o apoio social no trabalho. Dimensões isoladas do estresse no trabalho (demanda e controle), razão entre demanda psicológica e controle do trabalho (Razão D/C) e o apoio social no trabalho foram mensurados no nível individual e nos setores de trabalho. De modo geral, os resultados destacam a demanda psicológica mensurada no nível individual como um importante fator associado à ocorrência de acidentes de trabalho. O apoio social no trabalho, mensurado no nível individual e no setor de trabalho, apresentou associação inversa à prevalência de acidentes de trabalho, sendo, no setor, acentuada entre as mulheres. Os resultados também mostram que os parâmetros fixos dos modelos com e sem classificação cruzada foram semelhantes e que, de modo geral, os erros padrões (EP) foram um pouco maiores nos modelos com classificação cruzada, apesar deste comportamento do EP não ter sido observado quando relacionado aos coeficientes fixos das variáveis agregadas no setor de trabalho. A maior distinção entre as duas abordagens foi observada em relação aos coeficientes aleatórios relacionados aos setores de trabalho, que alteraram substancialmente após ajustar o efeito da ocupação por meio dos modelos com classificação cruzada. Este estudo reforça a importância de características psicossociais na ocorrência de acidentes de trabalho e contribui para o conhecimento dessas relações a partir de abordagens analíticas que refinam a captação da estrutura de dependência dos indivíduos em seu ambiente de trabalho. Sugere-se a realização de outros estudos com metodologia similar, que permitam aprofundar o conhecimento sobre estresse e acidentes no trabalho.