Fixed effects and variance components estimation in three-level meta-analysis

Meta-analytic methods have been widely applied to education, medicine, and the social sciences. Much of meta-analytic data are hierarchically structured because effect size estimates are nested within studies, and in turn, studies can be nested within level-3 units such as laboratories or investigators, and so forth. Thus, multilevel models are a natural framework for analyzing meta-analytic data. This paper discusses the application of a Fisher scoring method in two-level and three-level meta-analysis that takes into account random variation at the second and third levels. The usefulness of the model is demonstrated using data that provide information about school calendar types. sas proc mixed and hlm can be used to compute the estimates of fixed effects and variance components. Copyright © 2011 John Wiley & Sons, Ltd.

Evaluating regional differences in breast-feeding in French maternity units: a multi-level approach

OBJECTIVES

To study how individual and regional characteristics might explain regional variations in breast-feeding rates in maternity units and to identify outlier regions with very low or high breast-feeding rates.

DESIGN

Individual characteristics (mother and infant) were collected during hospital stay. All newborns fed entirely or partly on breast milk were considered breast-fed. Regional characteristics were extracted from census data. Statistical analysis included multi-level models and estimation of empirical Bayes residuals to identify outlier regions.

SETTING

All births in all administrative regions in France in 2003.

SUBJECTS

A national representative sample of 13 186 live births.

RESULTS

Breast-feeding rates in maternity units varied from 43 % to 80 % across regions. Differences in the distribution of individual characteristics accounted for 55 % of these variations. We identified two groups of regions with the lowest and highest breast-feeding rates, after adjusting for individual-level characteristics. In addition to maternal occupation and nationality, the social characteristics of regions, particularly the population's educational level and the percentage of non-French residents, were significantly associated with breast-feeding rates.

CONCLUSIONS

Social characteristics at both the individual and regional levels influence breast-feeding rates in maternity units. Promotion policies should be directed at specific regions, groups within the community and categories of mothers to reduce the gaps and increase the overall breast-feeding rate.

It Takes a Village (Perhaps a Nation): Families, States, and Educational Achievement

Research in the United States has shown that children growing up in 2-parent households do better in school than children from single-parent households. We used the Trends in International Mathematics and Science Study (TIMSS) data to test whether this finding applied to other countries as well (N = 100,307). We found that it did, but that the educational gap was greater in the United States than in the other 13 countries considered. Results from 2-level hierarchical linear models demonstrated that international differences in the educational gap were associated with several indicators of national policy and demographic contexts. No single policy appeared to have a large effect, but several policy combinations were associated with substantially reduced educational gaps between children from different family structures.

Long-term Effects of Child Death on Parents' Health Related Quality of Life: A Dyadic Analysis

This study examines the long-term effects of child death on bereaved parents' health-related quality of life (HRQoL). Using data from the Wisconsin Longitudinal Study, we compared 233 bereaved couples and 229 comparison couples (mean age = 65.11 years) and examined the life course effects of child death on parents' HRQoL. Variations in bereavement effects were examined by gender and for different causes of death. Bereaved parents had significantly worse HRQoL than comparison group parents, and there was no evidence of gender differences for this effect. With respect to the cause of a child's death, bereaved parents whose child died in violent circumstances had particularly low levels of HRQoL. Multilevel models indicated that marital closeness mitigated the negative effects of bereavement.

Direct and indirect effects for neighborhood-based clustered and longitudinal data

Definitions of direct and indirect effects are given for settings in which individuals are clustered in groups or neighborhoods and in which treatments are administered at the group level. A particular intervention may affect individual outcomes both through its effect on the individual and by changing the group or neighborhood itself. Identification conditions are given for controlled direct effects and for natural direct and indirect effects. The interpretation of these identification conditions are discussed within the context of neighborhood research and multilevel modeling. Interventions at a single point in time and time-varying interventions are both considered. The definition of direct and indirect effects requires certain stability or no-interference conditions; some discussion is given as to how these no-interference conditions can be relaxed.

Estimating multilevel logistic regression models when the number of clusters is low: a comparison of different statistical software procedures

Multilevel logistic regression models are increasingly being used to analyze clustered data in medical, public health, epidemiological, and educational research. Procedures for estimating the parameters of such models are available in many statistical software packages. There is currently little evidence on the minimum number of clusters necessary to reliably fit multilevel regression models. We conducted a Monte Carlo study to compare the performance of different statistical software procedures for estimating multilevel logistic regression models when the number of clusters was low. We examined procedures available in BUGS, HLM, R, SAS, and Stata. We found that there were qualitative differences in the performance of different software procedures for estimating multilevel logistic models when the number of clusters was low. Among the likelihood-based procedures, estimation methods based on adaptive Gauss-Hermite approximations to the likelihood (glmer in R and xtlogit in Stata) or adaptive Gaussian quadrature (Proc NLMIXED in SAS) tended to have superior performance for estimating variance components when the number of clusters was small, compared to software procedures based on penalized quasi-likelihood. However, only Bayesian estimation with BUGS allowed for accurate estimation of variance components when there were fewer than 10 clusters. For all statistical software procedures, estimation of variance components tended to be poor when there were only five subjects per cluster, regardless of the number of clusters.

Automobile traffic around the home and attained body mass index: a longitudinal cohort study of children aged 10-18 years

OBJECTIVES

The objective of this study is to examine the relationship between measured traffic density near the homes of children and attained body mass index (BMI) over an eight-year follow up.

METHODS

Children aged 9-10 years were enrolled across multiple communities in Southern California in 1993 and 1996 (n=3318). Children were followed until age 18 or high school graduation to collect longitudinal information, including annual height and weight measurements. Multilevel growth curve models were used to assess the association between BMI levels at age 18 and traffic around the home.

RESULTS

For traffic within 150 m around the child's home, there were significant positive associations with attained BMI for both sexes at age 18. With the 300 m traffic buffer, associations for both male and female growth in BMI were positive, but significantly elevated only in females. These associations persisted even after controlling for numerous potential confounding variables.

CONCLUSIONS

This analysis yields the first evidence of significant effects from traffic density on BMI levels at age 18 in a large cohort of children. Traffic is a pervasive exposure in most cities, and our results identify traffic as a major risk factor for the development of obesity in children.

The effect of area of residence over the life course on subsequent mortality

Life course epidemiology concentrates on the contribution that social or physical exposures have across the life course on adult health. It is known that the area of residence can affect health, but little is known about the effect of the area of residence across the life course. We examine the contribution that area of residence in 1960, 1970, 1980 and 1990 made on subsequent mortality for 49736 male inhabitants of Oslo in 1990. We compare the performance of multiple-membership and cross-classified multilevel models on these data with a correlated cross-classified model that was developed for this.

Analysis of early life influences on cognitive development in childhood using multilevel ordinal models

Studies of cognitive development in children are often based on tests designed for specific ages. Examination of the changes of these scores over time may not be meaningful. This paper investigates the influence of early life factors on cognitive development using maths and reading test scores at ages 7, 11, and 16 years in a British birth cohort born in 1958. The distributions of these test scores differ between ages, for example, 20% participants scored the top mark in the reading test at 7 and the distribution of reading score at 16 is heavily skewed. In this paper, we group participants into 5 ordered categories, approximately 20% in each category according to their test scores at each age. Multilevel models for a repeated ordinal outcome are applied to relate the ordinal scale of maths and reading ability to early life factors.

Methods for testing theory and evaluating impact in randomized field trials: intent-to-treat analyses for integrating the perspectives of person, place, and time

Randomized field trials provide unique opportunities to examine the effectiveness of an intervention in real world settings and to test and extend both theory of etiology and theory of intervention. These trials are designed not only to test for overall intervention impact but also to examine how impact varies as a function of individual level characteristics, context, and across time. Examination of such variation in impact requires analytical methods that take into account the trial's multiple nested structure and the evolving changes in outcomes over time. The models that we describe here merge multilevel modeling with growth modeling, allowing for variation in impact to be represented through discrete mixtures--growth mixture models--and nonparametric smooth functions--generalized additive mixed models. These methods are part of an emerging class of multilevel growth mixture models, and we illustrate these with models that examine overall impact and variation in impact. In this paper, we define intent-to-treat analyses in group-randomized multilevel field trials and discuss appropriate ways to identify, examine, and test for variation in impact without inflating the Type I error rate. We describe how to make causal inferences more robust to misspecification of covariates in such analyses and how to summarize and present these interactive intervention effects clearly. Practical strategies for reducing model complexity, checking model fit, and handling missing data are discussed using six randomized field trials to show how these methods may be used across trials randomized at different levels.

Let's not talk about it: suicide inquiry in primary care

PURPOSE

The purpose of this study was to ascertain physician characteristics associated with exploring suicidality in patients with depressive symptoms and the influence of patient antidepressant requests.

METHODS

Primary care physicians were randomly recruited from 4 sites in northern California and Rochester, NY; 152 physicians participated (53%-61% of those approached). Standardized patients portraying 2 conditions (major depression and adjustment disorder) and 3 antidepressant request types (brand specific, general, or none) made unannounced visits to these physicians between May 2003 and May 2004. We examined factors associated with physician exploration of suicidality.

RESULTS

Suicide was explored in 36% of 298 encounters. Exploration was more common when the patient portrayed major depression (vs adjustment disorder) (P = .03), with an antidepressant request (vs no request) (P=.02), in academic settings (P <.01), and among physicians with personal experience with depression (P <.01). The random effects logistic model revealed a significant physician variance component with rho = 0.57 (95% confidence interval, 0.45-0.68) indicating that there were additional, unspecified physician factors determining the tendency to explore suicide risk. These factors are unrelated to physician specialty (family medicine or internal medicine), sex, communication style, or perceived barriers to or confidence in treating depression.

CONCLUSIONS

When seeing patients with depressive symptoms, primary care physicians do not consistently inquire about suicidality. Their inquiries into suicidal thinking may be enhanced through advertising or public service messaging that prompts patients to ask for help. Research is needed to further elucidate physician characteristics associated with the assessment of suicidality.

A Genetically Informed Study of the Intergenerational Transmission of Marital Instability

Environmental or genetic influences, or both could account for the increased risk of divorce among the offspring of separated parents. Previous studies have used covariates to statistically control for confounds, but the present research is the first genetically informed study of the topic. The investigation used the Children of Twins Design with twins, their spouses, and their young adult offspring (n = 2,310) from the Australian Twin Registry to test whether selection on the basis of genetic or shared environment factors accounted for part of the inter-generational association. The analyses also controlled for measured characteristics of both parents. The results suggest that both environmentally mediated and genetic risk account for the intergenerational transmission, supporting the roles of both selection and causation.

Mapping and measuring social disparities in premature mortality: the impact of census tract poverty within and across Boston neighborhoods, 1999-2001

The identification and documentation of health disparities are important functions of public health surveillance. These disparities, typically falling along lines defined by gender, race/ethnicity, and social class, are often made visible in urban settings as geographic disparities in health between neighborhoods. Recognizing that premature mortality is a powerful indicator of disparities in both health status and access to health care that can readily be monitored using routinely available public health surveillance data, we undertook a systematic analysis of spatial variation in premature mortality in Boston (1999-2001) across neighborhoods and sub-neighborhoods in relation to census tract (CT) poverty. Using a multilevel model based framework, we estimated that the incidence of premature mortality was 1.39 times higher (95% credible interval 1.09-1.78) among persons living in the most economically deprived CTs (>/=20% below poverty) compared to those in the least impoverished tracts (<5% below poverty). We present maps of model-based standardized mortality ratios that show substantial within-neighborhood variation in premature mortality and a sizeable decrease in spatial variation after adjustment for CT poverty. Additionally, we present maps of model-based direct standardized rates that can more readily be compared to externally published rates and targets, as well as maps of the population attributable fraction that show that in some of Boston's poorest neighborhoods, the proportion of excess deaths associated with CT poverty reaches 25-30%. We recommend that these methods be incorporated into routine analyses of public health surveillance data to highlight continuing social disparities in premature mortality.