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.

RANDOM EFFECTS MODELS IN A META-ANALYSIS OF THE ACCURACY OF DIAGNOSTIC TESTS WITHIN A GOLD STANDARD IN THE PRESENCE OF MISSING DATA

In evaluating the accuracy of diagnosis tests, it is common to apply two imperfect tests jointly or sequentially to a study population. In a recent meta-analysis of the accuracy of microsatellite instability testing (MSI) and traditional mutation analysis (MUT) in predicting germline mutations of the mismatch repair (MMR) genes, a Bayesian approach (Chen, Watson, and Parmigiani 2005) was proposed to handle missing data resulting from partial testing and the lack of a gold standard. In this paper, we demonstrate an improved estimation of the sensitivities and specificities of MSI and MUT by using a nonlinear mixed model and a Bayesian hierarchical model, both of which account for the heterogeneity across studies through study-specific random effects. The methods can be used to estimate the accuracy of two imperfect diagnostic tests in other meta-analyses when the prevalence of disease, the sensitivities and/or the specificities of diagnostic tests are heterogeneous among studies. Furthermore, simulation studies have demonstrated the importance of carefully selecting appropriate random effects on the estimation of diagnostic accuracy measurements in this scenario.

Impact of vessel size on outcome after implantation of sirolimus-eluting and paclitaxel-eluting stents: a subgroup analysis of the SIRTAX trial

OBJECTIVES: We assessed the impact of vessel size on angiographic and long-term clinical outcome after percutaneous coronary intervention (PCI) with sirolimus-eluting stents (SES) and paclitaxel-eluting stents (PES) within a randomized trial (SIRTAX [Sirolimus-Eluting Stent Compared With Paclitaxel-Eluting Stent for Coronary Revascularization]). BACKGROUND: Percutaneous coronary intervention in small-vessel disease is associated with an increased risk of major adverse cardiac events (MACE). METHODS: A total of 1,012 patients were randomly assigned to treatment with SES (n = 503) or PES (n = 509). A stratified analysis of angiographic and clinical outcome was performed up to 2 years after PCI according to size of the treated vessel (reference vessel diameter < or =2.75 vs. >2.75 mm). RESULTS: Of 1,012 patients, 370 patients (37%) with 495 lesions underwent stent implantation in small vessels only, 504 patients (50%) with 613 lesions in large vessels only, and 138 patients (14%) with 301 lesions in both small and large vessels (mixed). In patients with small-vessel stents, SES reduced MACE by 55% (10.4% vs. 21.4%; p = 0.004), mainly driven by a 69% reduction of target lesion revascularization (TLR) (6.0% vs. 17.7%; p = 0.001) compared with PES at 2 years. In patients with large- and mixed-vessel stents, rates of MACE (large: 10.4% vs. 13.1%; p = 0.33; mixed: 16.7% vs. 18.0%; p = 0.83) and TLR (large: 6.9% vs. 8.6%; p = 0.47; mixed: 16.7% vs. 15.4%; p = 0.86) were similar for SES and PES. There were no significant differences with respect to death and myocardial infarction between the 3 groups. CONCLUSIONS: Compared with PES, SES more effectively reduced MACE and TLR in small-vessel disease. Differences between SES and PES appear less pronounced in patients with large- and mixed-vessel disease. (The SIRTAX trial; http://clinicaltrials.gov/ct/show/NCT00297661?order=1; NCT00297661).

Stability measurements of 1-stage implants in the edentulous mandible by means of resonance frequency analysis

OBJECTIVE: Resonance frequency analysis (RFA) is a method of measuring implant stability. However, little is known about RFA of implants with long loading periods. The objective of the present study was to determine standard implant stability quotients (ISQs) for clinical successfully osseointegrated 1-stage implants in the edentulous mandible. MATERIALS AND METHODS: Stability measurements by means of RFA were performed in regularly followed patients who had received 1- stage implants for overdenture support. The time interval between implant placement and measurement ranged from 1 year up to 10 years. The short-term group comprised patients who were followed up to 5 years, while the long-term group included patients with an observation time of > 5 years up to 10 years. For further comparison RFA measurements were performed in a matching group with unloaded implants at the end of the surgical procedure. For statistical analysis various parameters that might influence the ISQs of loaded implants were included, and a mixed-effects model applied (regression analysis, P <.0125). RESULTS: Ninety-four patients were available with a total of 205 loaded implants, and 16 patients with 36 implants immediately after the surgical procedure. The mean ISQ of all measured implants was 64.5 +/- 7.9 (range, 58 to 72). Statistical analysis did not reveal significant differences in the mean ISQ related to the observation time. The parameters with overall statistical significance were the diameter of the implants and changes in the attachment level. In the short-term group, the gender and the clinically measured attachment level had a significant effect. Implant diameter had a significant effect in the long-term group. CONCLUSIONS: A mean ISQ of 64.5 +/- 7.9 was found to be representative for stable asymptomatic interforaminal implants measured by the RFA instrument at any given time point. No significant differences in ISQ values were found between implants with different postsurgical time intervals. Implant diameter appears to influence the ISQ of interforaminal implants.

Drug eluting and bare metal stents in people with and without diabetes: collaborative network meta-analysis

Objective To compare the effectiveness and safety of three types of stents (sirolimus eluting, paclitaxel eluting, and bare metal) in people with and without diabetes mellitus. Design Collaborative network meta-analysis. Data sources Electronic databases (Medline, Embase, the Cochrane Central Register of Controlled Trials), relevant websites, reference lists, conference abstracts, reviews, book chapters, and proceedings of advisory panels for the US Food and Drug Administration. Manufacturers and trialists provided additional data. Review methods Network meta-analysis with a mixed treatment comparison method to combine direct within trial comparisons between stents with indirect evidence from other trials while maintaining randomisation. Overall mortality was the primary safety end point, target lesion revascularisation the effectiveness end point. Results 35 trials in 3852 people with diabetes and 10 947 people without diabetes contributed to the analyses. Inconsistency of the network was substantial for overall mortality in people with diabetes and seemed to be related to the duration of dual antiplatelet therapy (P value for interaction 0.02). Restricting the analysis to trials with a duration of dual antiplatelet therapy of six months or more, inconsistency was reduced considerably and hazard ratios for overall mortality were near one for all comparisons in people with diabetes: sirolimus eluting stents compared with bare metal stents 0.88 (95% credibility interval 0.55 to 1.30), paclitaxel eluting stents compared with bare metal stents 0.91 (0.60 to 1.38), and sirolimus eluting stents compared with paclitaxel eluting stents 0.95 (0.63 to 1.43). In people without diabetes, hazard ratios were unaffected by the restriction. Both drug eluting stents were associated with a decrease in revascularisation rates compared with bare metal stents in people both with and without diabetes. Conclusion In trials that specified a duration of dual antiplatelet therapy of six months or more after stent implantation, drug eluting stents seemed safe and effective in people both with and without diabetes.

Long-term immunologic response to antiretroviral therapy in low-income countries: a collaborative analysis of prospective studies

BACKGROUND: Few data are available on the long-term immunologic response to antiretroviral therapy (ART) in resource-limited settings, where ART is being rapidly scaled up using a public health approach, with a limited repertoire of drugs. OBJECTIVES: To describe immunologic response to ART among ART patients in a network of cohorts from sub-Saharan Africa, Latin America, and Asia. STUDY POPULATION/METHODS: Treatment-naive patients aged 15 and older from 27 treatment programs were eligible. Multilevel, linear mixed models were used to assess associations between predictor variables and CD4 cell count trajectories following ART initiation. RESULTS: Of 29 175 patients initiating ART, 8933 (31%) were excluded due to insufficient follow-up time and early lost to follow-up or death. The remaining 19 967 patients contributed 39 200 person-years on ART and 71 067 CD4 cell count measurements. The median baseline CD4 cell count was 114 cells/microl, with 35% having less than 100 cells/microl. Substantial intersite variation in baseline CD4 cell count was observed (range 61-181 cells/microl). Women had higher median baseline CD4 cell counts than men (121 vs. 104 cells/microl). The median CD4 cell count increased from 114 cells/microl at ART initiation to 230 [interquartile range (IQR) 144-338] at 6 months, 263 (IQR 175-376) at 1 year, 336 (IQR 224-472) at 2 years, 372 (IQR 242-537) at 3 years, 377 (IQR 221-561) at 4 years, and 395 (IQR 240-592) at 5 years. In multivariable models, baseline CD4 cell count was the most important determinant of subsequent CD4 cell count trajectories. CONCLUSION: These data demonstrate robust and sustained CD4 response to ART among patients remaining on therapy. Public health and programmatic interventions leading to earlier HIV diagnosis and initiation of ART could substantially improve patient outcomes in resource-limited settings.

Bayesian change-point analysis in linear regression model with scale mixtures of normal distributions

In this thesis, we consider Bayesian inference on the detection of variance change-point models with scale mixtures of normal (for short SMN) distributions. This class of distributions is symmetric and thick-tailed and includes as special cases: Gaussian, Student-t, contaminated normal, and slash distributions. The proposed models provide greater flexibility to analyze a lot of practical data, which often show heavy-tail and may not satisfy the normal assumption. As to the Bayesian analysis, we specify some prior distributions for the unknown parameters in the variance change-point models with the SMN distributions. Due to the complexity of the joint posterior distribution, we propose an efficient Gibbs-type with Metropolis- Hastings sampling algorithm for posterior Bayesian inference. Thereafter, following the idea of [1], we consider the problems of the single and multiple change-point detections. The performance of the proposed procedures is illustrated and analyzed by simulation studies. A real application to the closing price data of U.S. stock market has been analyzed for illustrative purposes.

The MIRELA framework: modeling and analyzing mixed reality applications using timed automata

Mixed Reality (MR) aims to link virtual entities with the real world and has many applications such as military and medical domains [JBL+00, NFB07]. In many MR systems and more precisely in augmented scenes, one needs the application to render the virtual part accurately at the right time. To achieve this, such systems acquire data related to the real world from a set of sensors before rendering virtual entities. A suitable system architecture should minimize the delays to keep the overall system delay (also called end-to-end latency) within the requirements for real-time performance. In this context, we propose a compositional modeling framework for MR software architectures in order to specify, simulate and validate formally the time constraints of such systems. Our approach is first based on a functional decomposition of such systems into generic components. The obtained elements as well as their typical interactions give rise to generic representations in terms of timed automata. A whole system is then obtained as a composition of such defined components. To write specifications, a textual language named MIRELA (MIxed REality LAnguage) is proposed along with the corresponding compilation tools. The generated output contains timed automata in UPPAAL format for simulation and verification of time constraints. These automata may also be used to generate source code skeletons for an implementation on a MR platform. The approach is illustrated first on a small example. A realistic case study is also developed. It is modeled by several timed automata synchronizing through channels and including a large number of time constraints. Both systems have been simulated in UPPAAL and checked against the required behavioral properties.

CD4 count slope and mortality in HIV-infected patients on antiretroviral therapy: multicohort analysis from South Africa

BACKGROUND In many resource-limited settings monitoring of combination antiretroviral therapy (cART) is based on the current CD4 count, with limited access to HIV RNA tests or laboratory diagnostics. We examined whether the CD4 count slope over 6 months could provide additional prognostic information. METHODS We analyzed data from a large multicohort study in South Africa, where HIV RNA is routinely monitored. Adult HIV-positive patients initiating cART between 2003 and 2010 were included. Mortality was analyzed in Cox models; CD4 count slope by HIV RNA level was assessed using linear mixed models. RESULTS About 44,829 patients (median age: 35 years, 58% female, median CD4 count at cART initiation: 116 cells/mm) were followed up for a median of 1.9 years, with 3706 deaths. Mean CD4 count slopes per week ranged from 1.4 [95% confidence interval (CI): 1.2 to 1.6] cells per cubic millimeter when HIV RNA was <400 copies per milliliter to -0.32 (95% CI: -0.47 to -0.18) cells per cubic millimeter with >100,000 copies per milliliter. The association of CD4 slope with mortality depended on current CD4 count: the adjusted hazard ratio (aHRs) comparing a >25% increase over 6 months with a >25% decrease was 0.68 (95% CI: 0.58 to 0.79) at <100 cells per cubic millimeter but 1.11 (95% CI: 0.78 to 1.58) at 201-350 cells per cubic millimeter. In contrast, the aHR for current CD4 count, comparing >350 with <100 cells per cubic millimeter, was 0.10 (95% CI: 0.05 to 0.20). CONCLUSIONS Absolute CD4 count remains a strong risk for mortality with a stable effect size over the first 4 years of cART. However, CD4 count slope and HIV RNA provide independently added to the model.

Zidovudine impairs immunological recovery on first-line antiretroviral therapy: collaborative analysis of cohort studies in southern Africa

OBJECTIVES Zidovudine (ZDV) is recommended for first-line antiretroviral therapy (ART) in resource-limited settings. ZDV may, however, lead to anemia and impaired immunological response. We compared CD4+ cell counts over 5 years between patients starting ART with and without ZDV in southern Africa. DESIGN Cohort study. METHODS Patients aged at least 16 years who started first-line ART in South Africa, Botswana, Zambia, or Lesotho were included. We used linear mixed-effect models to compare CD4+ cell count trajectories between patients on ZDV-containing regimens and patients on other regimens, censoring follow-up at first treatment change. Impaired immunological recovery, defined as a CD4+ cell count below 100 cells/μl at 1 year, was assessed in logistic regression. Analyses were adjusted for baseline CD4+ cell count and hemoglobin level, age, sex, type of regimen, viral load monitoring, and calendar year. RESULTS A total of 72,597 patients starting ART, including 19,758 (27.2%) on ZDV, were analyzed. Patients on ZDV had higher CD4+ cell counts (150 vs.128 cells/μl) and hemoglobin level (12.0 vs. 11.0 g/dl) at baseline, and were less likely to be women than those on other regimens. Adjusted differences in CD4+ cell counts between regimens containing and not containing ZDV were -16 cells/μl [95% confidence interval (CI) -18 to -14] at 1 year and -56 cells/μl (95% CI -59 to -52) at 5 years. Impaired immunological recovery was more likely with ZDV compared to other regimens (odds ratio 1.40, 95% CI 1.22-1.61). CONCLUSION In southern Africa, ZDV is associated with inferior immunological recovery compared to other backbones. Replacing ZDV with another nucleoside reverse transcriptase inhibitor could avoid unnecessary switches to second-line ART.

Executive Stock Ownership and Performance: Tracking Faint Traces

We examine the relation between managers' financial interests and firm performance. Since the relation could go in either direction, we cast the analysis in a simultaneous equations framework. For firms involved in acquisitions, we find that acquisition performance and Tobin's Q ratios affect the size of managers' stockholdings. We find no evidence, however, that larger stockholdings lead to better performance. Perhaps management is effectively disciplined by competition in product and labor markets. Alternatively, it may not be necessary for top executives to own stock to the residual claimants. And finally, higher ownership might multiply the opportunities to appropriate corporate wealth.

Accounting for baseline differences and measurement error in the analysis of change over time

If change over time is compared in several groups, it is important to take into account baseline values so that the comparison is carried out under the same preconditions. As the observed baseline measurements are distorted by measurement error, it may not be sufficient to include them as covariate. By fitting a longitudinal mixed-effects model to all data including the baseline observations and subsequently calculating the expected change conditional on the underlying baseline value, a solution to this problem has been provided recently so that groups with the same baseline characteristics can be compared. In this article, we present an extended approach where a broader set of models can be used. Specifically, it is possible to include any desired set of interactions between the time variable and the other covariates, and also, time-dependent covariates can be included. Additionally, we extend the method to adjust for baseline measurement error of other time-varying covariates. We apply the methodology to data from the Swiss HIV Cohort Study to address the question if a joint infection with HIV-1 and hepatitis C virus leads to a slower increase of CD4 lymphocyte counts over time after the start of antiretroviral therapy.