Gauss-Seidel Estimation of Generalized Linear Mixed Models with Application to Poisson Modeling of Spatially Varying Disease Rates

Generalized linear mixed models (GLMMs) provide an elegant framework for the analysis of correlated data. Due to the non-closed form of the likelihood, GLMMs are often fit by computational procedures like penalized quasi-likelihood (PQL). Special cases of these models are generalized linear models (GLMs), which are often fit using algorithms like iterative weighted least squares (IWLS). High computational costs and memory space constraints often make it difficult to apply these iterative procedures to data sets with very large number of cases. This paper proposes a computationally efficient strategy based on the Gauss-Seidel algorithm that iteratively fits sub-models of the GLMM to subsetted versions of the data. Additional gains in efficiency are achieved for Poisson models, commonly used in disease mapping problems, because of their special collapsibility property which allows data reduction through summaries. Convergence of the proposed iterative procedure is guaranteed for canonical link functions. The strategy is applied to investigate the relationship between ischemic heart disease, socioeconomic status and age/gender category in New South Wales, Australia, based on outcome data consisting of approximately 33 million records. A simulation study demonstrates the algorithm's reliability in analyzing a data set with 12 million records for a (non-collapsible) logistic regression model.

A Diagnostic Test for the Mixing Distribution in a Generalised Linear Mixed Model

We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimates of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-square distribution under the null hypothesis that the mixing distribution is correctly specified. For the important special case of the logistic regression model with random intercepts, we evaluate via simulation the power of the test in finite samples under several alternative distributional forms for the mixing distribution. We illustrate the method by applying it to data from a clinical trial investigating the effects of hormonal contraceptives in women.

On the Behaviour of Marginal and Conditional Akaike Information Criteria in Linear Mixed Models

In linear mixed models, model selection frequently includes the selection of random effects. Two versions of the Akaike information criterion (AIC) have been used, based either on the marginal or on the conditional distribution. We show that the marginal AIC is no longer an asymptotically unbiased estimator of the Akaike information, and in fact favours smaller models without random effects. For the conditional AIC, we show that ignoring estimation uncertainty in the random effects covariance matrix, as is common practice, induces a bias that leads to the selection of any random effect not predicted to be exactly zero. We derive an analytic representation of a corrected version of the conditional AIC, which avoids the high computational cost and imprecision of available numerical approximations. An implementation in an R package is provided. All theoretical results are illustrated in simulation studies, and their impact in practice is investigated in an analysis of childhood malnutrition in Zambia.

A mixed epithelial and stromal tumor of the kidney in a ringtail lemur (Lemur catta)

Primary renal tumors are rare neoplasms in nonhuman primates. This report describes a mixed epithelial and stromal tumor of the kidney (MESTK) in a 14.5-year-old female ringtail lemur. The well-demarcated, solid, and cystic mass was located in the pelvis of the left kidney and consisted histologically of both epithelial and mesenchymal components. The mesenchymal cells were arranged in fascicles around cysts lined by a well-differentiated epithelium. Neither the mesenchymal nor the epithelial parts showed significant nuclear atypia or mitotic figures. To our knowledge, only 1 similar case, classified as adenoleiomyofibromatous hamartoma, has been reported in a ringtail lemur. In humans this tumor affects predominantly perimenopausal women and can express estrogen and progesterone receptors. However, neither estrogen nor progesterone receptors could be identified by immunohistochemistry in the tumor of the present ringtail lemur. Therefore, a hormonal mechanism could not be demonstrated in this case.

[Reconstruction of a periodontally compromised dentition]

The presented case report describes a systematic treatment concept, the treatment sequence and the maintenance care of a sixty-seven-year old female patient suffering from generalized chronic periodontitis with advanced attachment loss. Due to a pretherapeutic risk assessment, several teeth were classified as "irrational to treat" or "doubtful". Therefore, a comprehensive reconstructive rehabilitation after active periodontal therapy was necessary. The restoration of a periodontally compromised dentition represents various difficulties. The patient wished to have fixed reconstructions. Depending upon anatomical conditions several different reconstructions were used: conventional bridges, partly using a resected molar root, a solely implant-retained bridge and a combined implant-tooth-retained bridge.

Success rate and efficiency of activator treatment

In a retrospective multicentre study, the success rate and efficiency of activator treatment were analysed. All patients from two University clinics (Giessen, Germany and Berne, Switzerland) that fulfilled the selection criteria (Class II division 1 malocclusion, activator treatment, no aplasia, no extraction of permanent teeth, no syndromes, no previous orthodontic treatment except transverse maxillary expansion, full available records) were included in the study. The subject material amounted to 222 patients with a mean age of 10.6 years. Patient records, lateral head films, and dental casts were evaluated. Treatment was classified as successful if the molar relationship improved by at least half to three-fourths cusp width depending on whether or not the leeway space was used during treatment. Group comparisons were carried out using Wilcoxon two-sample and Kruskal-Wallis tests. For discrete data, chi-square analysis was used and Fisher's exact test when the sample size was small. Stepwise logistic regression was also employed. The success rate was 64 per cent in Giessen and 66 per cent in Berne. The only factor that significantly (P < 0.001) influenced treatment success was the level of co-operation. In approximately 27 per cent of the patients at both centres, the post-treatment occlusion was an 'ideal' Class I. In an additional 38 per cent of the patients, marked improvements in occlusal relationships were found. In subjects with Class II division 1 malocclusions, in which orthodontic treatment is performed by means of activators, a marked improvement of the Class II dental arch relationships can be expected in approximately 65 per cent of subjects. Activator treatment is more efficient in the late than in the early mixed dentition.