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.

Dynamic changes of cardiac conduction during rapid pacing

Slow conduction and unidirectional conduction block (UCB) are key mechanisms of reentry. Following abrupt changes in heart rate, dynamic changes of conduction velocity (CV) and structurally determined UCB may critically influence arrhythmogenesis. Using patterned cultures of neonatal rat ventricular myocytes grown on microelectrode arrays, we investigated the dynamics of CV in linear strands and the behavior of UCB in tissue expansions following an abrupt decrease in pacing cycle length (CL). Ionic mechanisms underlying rate-dependent conduction changes were investigated using the Pandit-Clark-Giles-Demir model. In linear strands, CV gradually decreased upon a reduction of CL from 500 ms to 230-300 ms. In contrast, at very short CLs (110-220 ms), CV first decreased before increasing again. The simulations suggested that the initial conduction slowing resulted from gradually increasing action potential duration (APD), decreasing diastolic intervals, and increasing postrepolarization refractoriness, which impaired Na(+) current (I(Na)) recovery. Only at very short CLs did APD subsequently shorten again due to increasing Na(+)/K(+) pump current secondary to intracellular Na(+) accumulation, which caused recovery of CV. Across tissue expansions, the degree of UCB gradually increased at CLs of 250-390 ms, whereas at CLs of 180-240 ms, it first increased and subsequently decreased. In the simulations, reduction of inward currents caused by increasing intracellular Na(+) and Ca(2+) concentrations contributed to UCB progression, which was reversed by increasing Na(+)/K(+) pump activity. In conclusion, CV and UCB follow intricate dynamics upon an abrupt decrease in CL that are determined by the interplay among I(Na) recovery, postrepolarization refractoriness, APD changes, ion accumulation, and Na(+)/K(+) pump function.

Adenoviral expression of IKs contributes to wavebreak and fibrillatory conduction in neonatal rat ventricular cardiomyocyte monolayers

Previous studies have shown that the gating kinetics of the slow component of the delayed rectifier K(+) current (I(Ks)) contribute to postrepolarization refractoriness in isolated cardiomyocytes. However, the impact of such kinetics on arrhythmogenesis remains unknown. We surmised that expression of I(Ks) in rat cardiomyocyte monolayers contributes to wavebreak formation and facilitates fibrillatory conduction by promoting postrepolarization refractoriness. Optical mapping was performed in 44 rat ventricular myocyte monolayers infected with an adenovirus carrying the genomic sequences of KvLQT1 and minK (molecular correlates of I(Ks)) and 41 littermate controls infected with a GFP adenovirus. Repetitive bipolar stimulation was applied at increasing frequencies, starting at 1 Hz until loss of 1:1 capture or initiation of reentry. Action potential duration (APD) was significantly shorter in I(Ks)-infected monolayers than in controls at 1 to 3 Hz (P<0.05), whereas differences at higher pacing frequencies did not reach statistical significance. Stable rotors occurred in both groups, with significantly higher rotation frequencies, lower conduction velocities, and shorter action potentials in the I(Ks) group. Wavelengths in the latter were significantly shorter than in controls at all rotation frequencies. Wavebreaks leading to fibrillatory conduction occurred in 45% of the I(Ks) reentry episodes but in none of the controls. Moreover, the density of wavebreaks increased with time as long as a stable source sustained the fibrillatory activity. These results provide the first demonstration that I(Ks)-mediated postrepolarization refractoriness can promote wavebreak formation and fibrillatory conduction during pacing and sustained reentry and may have important implications in tachyarrhythmias.

Wide QRS-complex tachycardia with variable VA-conduction: what is the mechanism?

We describe the case of a 16-year-old woman with a surgically corrected tetralogy of Fallot presenting with recurrent wide-QRS-complex tachycardia. The tachycardia could be induced and terminated with ventricular stimulation only. QRS morphology during sinus rhythm and tachycardia was identical and variable VA-conduction was observed. Mapping of the tachycardia showed that variations of HH intervals preceded VV intervals. Therefore, a mechanism involving re-entry within the bundle branches was suggested. However, detailed mapping showed cranial to caudal depolarization of the His bundle, leading to the diagnosis of atrioventricular node re-entrant tachycardia. The tachycardia was abolished by radiofrequency catheter ablation of the slow AV nodal pathway. We conclude that variable VA conduction can occur in patients with atrioventricular node re-entrant tachycardia. The atrial tissue is not always an integral part of the re-entrant circuit.

A Novel Implantable Hearing System with Direct Acoustic Cochlear Stimulation

A new implantable hearing system, the direct acoustic cochlear stimulator (DACS) is presented. This system is based on the principle of a power-driven stapes prosthesis and intended for the treatment of severe mixed hearing loss due to advanced otosclerosis. It consists of an implantable electromagnetic transducer, which transfers acoustic energy directly to the inner ear, and an audio processor worn externally behind the implanted ear. The device is implanted using a specially developed retromeatal microsurgical approach. After removal of the stapes, a conventional stapes prosthesis is attached to the transducer and placed in the oval window to allow direct acoustical coupling to the perilymph of the inner ear. In order to restore the natural sound transmission of the ossicular chain, a second stapes prosthesis is placed in parallel to the first one into the oval window and attached to the patient's own incus, as in a conventional stapedectomy. Four patients were implanted with an investigational DACS device. The hearing threshold of the implanted ears before implantation ranged from 78 to 101 dB (air conduction, pure tone average, 0.5-4 kHz) with air-bone gaps of 33-44 dB in the same frequency range. Postoperatively, substantial improvements in sound field thresholds, speech intelligibility as well as in the subjective assessment of everyday situations were found in all patients. Two years after the implantations, monosyllabic word recognition scores in quiet at 75 dB improved by 45-100 percent points when using the DACS. Furthermore, hearing thresholds were already improved by the second stapes prosthesis alone by 14-28 dB (pure tone average 0.5-4 kHz, DACS switched off). No device-related serious medical complications occurred and all patients have continued to use their device on a daily basis for over 2 years. Copyright (c) 2008 S. Karger AG, Basel.

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.