Anders Skrondal

Generalized multilevel structural equation modeling

A unifying framework for generalized multilevel structural equation modeling is introduced. The models in the framework, called generalized linear latent and mixed models (GLLAMM), combine features of generalized linear mixed models (GLMM) and structural equation models (SEM) and consist of a response model and a structural model for the latent variables. The response model generalizes GLMMs to incorporate factor structures in addition to random intercepts and coefficients. As in GLMMs, the data can have an arbitrary number of levels and can be highly unbalanced with different numbers of lower-level units in the higher-level units and missing data. A wide range of response processes can be modeled including ordered and unordered categorical responses, counts, and responses of mixed types. The structural model is similar to the structural part of a SEM except that it may include latent and observed variables varying at different levels. For example, unit-level latent variables (factors or random coefficients) can be regressed on cluster-level latent variables. Special cases of this framework are explored and data from the British Social Attitudes Survey are used for illustration. Maximum likelihood estimation and empirical Bayes latent score prediction within the GLLAMM framework can be performed using adaptive quadrature in gllamm, a freely available program running in Stata.

Risk of Fetal Death after Pandemic Influenza Virus Infection or Vaccination

BACKGROUND During the 2009 influenza A (H1N1) pandemic, pregnant women were at risk for severe influenza illness. This concern was complicated by questions about vaccine safety in pregnant women that were raised by anecdotal reports of fetal deaths after vaccination. METHODS We explored the safety of influenza vaccination of pregnant women by linking Norwegian national registries and medical consultation data to determine influenza diagnosis, vaccination status, birth outcomes, and background information for pregnant women before, during, and after the pandemic. We used Cox regression models to estimate hazard ratios for fetal death, with the gestational day as the time metric and vaccination and pandemic exposure as time-dependent exposure variables. RESULTS There were 117,347 eligible pregnancies in Norway from 2009 through 2010. Fetal mortality was 4.9 deaths per 1000 births. During the pandemic, 54% of pregnant women in their second or third trimester were vaccinated. Vaccination during pregnancy substantially reduced the risk of an influenza diagnosis (adjusted hazard ratio, 0.30; 95% confidence interval [CI], 0.25 to 0.34). Among pregnant women with a clinical diagnosis of influenza, the risk of fetal death was increased (adjusted hazard ratio, 1.91; 95% CI, 1.07 to 3.41). The risk of fetal death was reduced with vaccination during pregnancy, although this reduction was not significant (adjusted hazard ratio, 0.88; 95% CI, 0.66 to 1.17). CONCLUSIONS Pandemic influenza virus infection in pregnancy was associated with an increased risk of fetal death. Vaccination during pregnancy reduced the risk of an influenza diagnosis. Vaccination itself was not associated with increased fetal mortality and may have reduced the risk of influenza-related fetal death during the pandemic. (Funded by the Norwegian Institute of Public Health.).

Regression among factor scores

Structural equation models with latent variables are sometimes estimated using an intuitive three-step approach, here denoted factor score regression. Consider a structural equation model composed of an explanatory latent variable and a response latent variable related by a structural parameter of scientific interest. In this simple example estimation of the structural parameter proceeds as follows: First, common factor models areseparately estimated for each latent variable. Second, factor scores areseparately assigned to each latent variable, based on the estimates. Third, ordinary linear regression analysis is performed among the factor scores producing an estimate for the structural parameter. We investigate the asymptotic and finite sample performance of different factor score regression methods for structural equation models with latent variables. It is demonstrated that the conventional approach to factor score regression performs very badly. Revised factor score regression, using Regression factor scores for the explanatory latent variables and Bartlett scores for the response latent variables, produces consistent estimators for all parameters.

Paternal contribution to birth weight

STUDY OBJECTIVE Understanding causes of variation in birth weight has been limited by lack of sufficient sets of data that include paternal birth weight. The objective was to estimate risks of low birth weight dependent on parental birth weights and to estimate father-mother-offspring correlations for birth weight to explain the variability in birth weight in terms of effects of genes and environmental factors. DESIGN A family design, using trios of father-mother-firstborn child. SETTING The complete birth population in Norway 1967–98. PARTICIPANTS 67 795 families. MAIN RESULTS The birth weight correlations were 0.226 for mother-child and 0.126 for father-child. The spousal correlation was low, 0.020. The relative risk of low birth weight in the first born child was 8.2 if both parents were low birth weight themselves, with both parents being above 4 kg as the reference. The estimate of heritability is about 0.25 for birth weight, under the assumption that cultural transmission on the paternal side has no effect on offspring prenatal growth. CONCLUSIONS Paternal birth weight is a significant and independent predictor of low birth weight in offspring. The estimate of the heritability of birth weight in this study is lower than previously estimated from data within one generation in the Norwegian population.

Multilevel logistic regression for polytomous data and rankings

We propose a unifying framework for multilevel modeling of polytomous data and rankings, accommodating dependence induced by factor and/or random coefficient structures at different levels. The framework subsumes a wide range of models proposed in disparate methodological literatures. Partial and tied rankings, alternative specific explanatory variables and alternative sets varying across units are handled. The problem of identification is addressed. We develop an estimation and prediction methodology for the model framework which is implemented in the generally available gllamm software. The methodology is applied to party choice and rankings from the 1987–1992 panel of the British Election Study. Three levels are considered: elections, voters and constituencies.

Early Respiratory Infections, Asthma, and Allergy: 10-Year Follow-up of the Oslo Birth Cohort

Objective. It has been hypothesized that early infections protect against the development of atopic disease, but there have been few long-term follow-up studies. We estimated the associations between early respiratory infections and doctor-diagnosed asthma, allergic rhinitis, and skin-prick sensitization in children at 10 years of age in the Oslo Birth Cohort, established in 1992–1993. We also considered birth order and attendance at a child care center as proxy measures of increased exposure to infections early in life. Methods. A total of 2540 children were followed from birth to the age of 10 years. Experiences of respiratory infections were recorded in follow-up surveys at 6 and 12 months. At age 10, questions were asked about current symptoms of asthma and allergic rhinitis and about having ever received a doctor diagnosis for these diseases. A subsample (n = 1740) of the cohort was tested for skin-prick test reactivity. Results. Current asthma was related to lower respiratory tract infection (adjusted odds ratio [OR]: 2.1; 95% confidence interval: 1.3–3.0) and croup (adjusted OR: 2.3; 95% confidence interval: 1.3–4.2) in the first year. ORs for allergic rhinitis and skin-prick sensitization were smaller but mainly positive. Birth order and child care attendance at age 1 year were not significantly associated with any of the studied outcomes. Conclusions. Early respiratory infections did not protect against the development of asthma, allergic rhinitis, or sensitization to common allergens during the first 10 years of life but increased the risk for asthma symptoms at age 10 in this population.

A simulation study of three methods for detecting disease clusters.

BackgroundCluster detection is an important part of spatial epidemiology because it can help identifying environmental factors associated with disease and thus guide investigation of the aetiology of diseases. In this article we study three methods suitable for detecting local spatial clusters: (1) a spatial scan statistic (SaTScan), (2) generalized additive models (GAM) and (3) Bayesian disease mapping (BYM). We conducted a simulation study to compare the methods. Seven geographic clusters with different shapes were initially chosen as high-risk areas. Different scenarios for the magnitude of the relative risk of these areas as compared to the normal risk areas were considered. For each scenario the performance of the methods were assessed in terms of the sensitivity, specificity, and percentage correctly classified for each cluster.ResultsThe performance depends on the relative risk, but all methods are in general suitable for identifying clusters with a relative risk larger than 1.5. However, it is difficult to detect clusters with lower relative risks. The GAM approach had the highest sensitivity, but relatively low specificity leading to an overestimation of the cluster area. Both the BYM and the SaTScan methods work well. Clusters with irregular shapes are more difficult to detect than more circular clusters.ConclusionBased on our simulations we conclude that the methods differ in their ability to detect spatial clusters. Different aspects should be considered for appropriate choice of method such as size and shape of the assumed spatial clusters and the relative importance of sensitivity and specificity. In general, the BYM method seems preferable for local cluster detection with relatively high relative risks whereas the SaTScan method appears preferable for lower relative risks. The GAM method needs to be tuned (using cross-validation) to get satisfactory results.

The problem of structural indeterminacy in multidimensional symptom report instruments. The case of SCL-90-R

The factor structure of SCL-90-R items and scales was analyzed using both exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). Results of CFA studies at the item-level failed to support the original nine-factor model, as well as several alternative models and EFA suggested very different dimensionality, depending on which criteria were used. Analyses at the scale-level (i.e. the nine original symptom dimensions) suggested that a one- or two-factor model was satisfactory according to descriptive goodness of fit criteria. However, using the likelihood ratio test, specification of four factors was necessary to avoid rejection. According to the likelihood ratio test in a multi-group analysis, a lack of factorial invariance across gender was indicated. Moreover, the factorial structure of the instrument was clearly different across levels of negative affectivity (NA); the dimensionality was substantially higher in the low-NA group as compared to the high-NA group. It is concluded that we are confronted with a profound structural indeterminacy problem and that factor analytic methods and model acceptance criteria alone are insufficient to solve this problem. The indeterminacy problem can be accounted for, at least in part, by the complex logical-semantical structure of SCL-90-R items and scales and the role of the NA trait as a structure generating factor.

Water chlorination and birth defects.

Chlorination of drinking water that contains organic compounds leads to the formation of by-products, some of which have been shown to have mutagenic or carcinogenic effects. As yet, too little is known about the possible teratogenic effects on the human fetus. We linked the Norwegian waterwork registry, containing 1994 data on chlorination practice and color (an indicator for natural organic matter), with the Medical Birth Registry for 1993-1995. The proportion of the population exposed to chlorination and a weighted mean color number in drinking water was computed for each municipality. Among 141,077 births, 2,608 (1.8%) had birth defects. In a comparison between exposed (high color; chlorination) and reference groups (low color; no chlorination), the adjusted odds ratio was 1.14 (0.99-1.31) for any malformation, 1.26 (0.61-2.62) for neural tube defects, and 1.99 (1.10-3.57) for urinary tract defects. This study provides further evidence of the role of chlorination of humic water as a potential cause of birth defects, in a country with relatively low levels of chlorination byproducts.

CONSANGUINITY AND RECURRENCE RISK OF STILLBIRTH AND INFANT DEATH

OBJECTIVES The aim of this study was to estimate the recurrence risk for stillbirth and infant death and compare results for offspring of first-cousin parents with results for offspring of unrelated parents. METHODS The study population consisted of all single births with a previous sibling born in Norway between 1967 and 1994. Altogether, 629,888 births were to unrelated parents, and 3466 births were to parents who were first cousins. The risk of stillbirth and infant death was estimated for subsequent siblings contingent on parental consanguinity and survival of the previous sibling. RESULTS For unrelated parents, the risk of early death (stillbirth plus infant death) for the subsequent sibling was 17 of 1000 if the previous child survived and 67 of 1000 if the previous child died before 1 year of age. For parents who were first cousins, the risk of early death for the subsequent sibling was 29 of 1000 if the previous child survived and 116 of 1000 if the previous child died. CONCLUSIONS The risk of recurrence of stillbirth and infant death is higher for offspring of first-cousin parents compared with offspring of unrelated parents.