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.

rCBF in hemorrhagic, non-hemorrhagic and mixed contusions after severe head injury and its effect on perilesional cerebral blood flow

Intracerebral contusions can lead to regional ischemia caused by extensive release of excitotoxic aminoacids leading to increased cytotoxic brain edema and raised intracranial pressure. rCBF measurements might provide further information about the risk of ischemia within and around contusions. Therefore, the aim of the presented study was to compare the intra- and perilesional rCBF of hemorrhagic, non-hemorrhagic and mixed intracerebral contusions. In 44 patients, 60 stable Xenon-enhanced CT CBF-studies were performed (EtCO2 30 +/- 4 mmHg SD), initially 29 hours (39 studies) and subsequent 95 hours after injury (21 studies). All lesions were classified according to localization and lesion type using CT/MRI scans. The rCBF was calculated within and 1-cm adjacent to each lesion in CT-isodens brain. The rCBF within all contusions (n = 100) of 29 +/- 11 ml/100 g/min was significantly lower (p < 0.0001, Mann-Whitney U) compared to perilesional rCBF of 44 +/- 12 ml/100 g/min and intra/perilesional correlation was 0.4 (p < 0.0005). Hemorrhagic contusions showed an intra/perilesional rCBF of 31 +/- 11/44 +/- 13 ml/100 g/min (p < 0.005), non-hemorrhagic contusions 35 +/- 13/46 +/- 10 ml/100 g/min (p < 0.01). rCBF in mixed contusions (25 +/- 9/44 +/- 12 ml/100 g/min, p < 0.0001) was significantly lower compared to hemorrhagic and non-hemorrhagic contusions (p < 0.02). Intracontusional rCBF is significantly reduced to 29 +/- 11 ml/100 g/min but reduced below ischemic levels of 18 ml/100 g/min in only 16% of all contusions. Perilesional CBF in CT normal appearing brain closed to contusions is not critically reduced. Further differentiation of contusions demonstrates significantly lower rCBF in mixed contusions (defined by both hyper- and hypodense areas in the CT-scan) compared to hemorrhagic and non-hemorrhagic contusions. Mixed contusions may evolve from hemorrhagic contusions with secondary increased perilesional cytotoxic brain edema leading to reduced cerebral blood flow and altered brain metabolism. Therefore, the treatment of ICP might be individually modified by the measurement of intra- and pericontusional cerebral blood.

Training Volume and Methods of Athletes Competing at a Mixed Martial Arts Events

This study surveyed 32 athletes competing at a mixed martial arts (MMA) event held in Butte, Montana. The survey attempted to gather information regarding overall training volume, supplement use, volume change and specific exercises used. The survey return rate was 100 percent (32/32). Twenty-five of 32 athletes supplemented their training with strength training. Overall frequency of strength training ranged from one to six sessions/week, and overall frequency of fighting-specific training sessions/weel ranged from two to 10. Two of the 32 athletes used/had used anabolic-androgenic steroids. Sixteen MMA athletes performed exercises specifically for the neck musculature, and eight use the power clean within their strength-training program. Results suggested that strength and conditioning speciialists should educate the importance of, volume variation and periodization, balanced training, effective exercises, and the side effects of anabolic steroid use.