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PubMed1999

A GEE moving average analysis of the relationship between air pollution and mortality for asthma in Barcelona, Spain.

Several studies have assessed the association between air pollution and hospital admissions or emergency room visits for asthma. Because of both the presence of missing data and the small number of observations, the relationship between air pollution and mortality for respiratory causes has been rarely analysed, and when it has, the results are very inconclusive or even inconsistent. The objective of this study is to assess the relation between levels of air pollutants (black smoke, sulphur dioxide, nitrogen dioxide and ozone), meteorological variables (24th average temperature and relative humidity) and daily mortality for asthma (ICD-9 493, 2 to 45 years old) in Barcelona, Spain, during the period 1986-1989. Since the range of daily mortality for asthma (2 to 45 years old) during the period 1986-1989 was 0-1), we have preferred to consider this variable as dichotomous. First, the relationship between air pollutants, meteorological variables and daily mortality (controlled for the occurrence of asthma epidemics) was estimated using logistic regression models. As was expected, the residuals from this regression were autocorrelated, showing a complex moving average (MA) structure. If covariates were not time dependent the so-called generalized linear mixed models, could be applied. In our case the covariates vary. As a consequence the likelihood is numerically intractable because it involves the evaluation of n-fold integral. An alternative method that avoids these numerical problems is the generalized estimating equations method (GEE). It is a multivariate analogue of quasi-likelihood estimation. In the absence of a likelihood function the parameters can be estimated by solving a multivariate analogue of the quasi score function. We have modified the GEE method in this paper, allowing for a different structure in the error covariance matrix (MA). Both air pollutants and meteorological variables are related with the occurrence of a death for asthma. In this sense, nitrogen dioxide, NO(2) (ss=0.037, p<0. 05), ozone, O(3) (ss=0.021, p<0.06) and high temperature (the ss's were in the range (0.098-0.182), p<0.05) increased the probability of dying for asthma in Barcelona during the period 1986-1989.

Adolescent↗

PubMed2000

When should epidemiologic regressions use random coefficients?

Regression models with random coefficients arise naturally in both frequentist and Bayesian approaches to estimation problems. They are becoming widely available in standard computer packages under the headings of generalized linear mixed models, hierarchical models, and multilevel models. I here argue that such models offer a more scientifically defensible framework for epidemiologic analysis than the fixed-effects models now prevalent in epidemiology. The argument invokes an antiparsimony principle attributed to L. J. Savage, which is that models should be rich enough to reflect the complexity of the relations under study. It also invokes the countervailing principle that you cannot estimate anything if you try to estimate everything (often used to justify parsimony). Regression with random coefficients offers a rational compromise between these principles as well as an alternative to analyses based on standard variable-selection algorithms and their attendant distortion of uncertainty assessments. These points are illustrated with an analysis of data on diet, nutrition, and breast cancer.

Breast Neoplasms↗

PubMed2004

Mixed models for longitudinal left-censored repeated measures.

Longitudinal studies could be complicated by left-censored repeated measures. For example, in Human Immunodeficiency Virus infection, there is a detection limit of the assay used to quantify the plasma viral load. Simple imputation of the limit of the detection or of half of this limit for left-censored measures biases estimations and their standard errors. In this paper, we review two likelihood-based methods proposed to handle left-censoring of the outcome in linear mixed model. We show how to fit these models using SAS Proc NLMIXED and we compare this tool with other programs. Indications and limitations of the programs are discussed and an example in the field of HIV infection is shown.

HIV Infections↗

PubMedDate not supplied

A change point model for estimating the onset of cognitive decline in preclinical Alzheimer's disease.

Dementia is characterized by accelerated cognitive decline before and after diagnosis as compared to normal ageing. Determining the time at which that rate of decline begins to accelerate in persons who will develop dementia is important both in describing the natural history of the disease process and in identifying the optimal time window for which treatments might be useful. We model that time at which the rate of decline begins to accelerate in persons who develop dementia relative to those who do not by using a change point in a mixed linear model. A profile likelihood method is proposed to draw inferences about the change point. The method is applied to data from the Bronx Ageing Study, a cohort study of 488 initially non-demented community-dwelling elderly individuals who have been examined at approximately 12-month intervals over 15 years. Cognitive function was measured using the Buschke Selective Reminding test, a memory test with high reliability and known discriminative validity for detecting dementia. We found that the rate of cognitive decline as measured by this test in this cohort increases on average 5.1 years before the diagnosis of dementia.

Aged↗

PubMed2002

Frailty models with missing covariates.

We present a method for estimating the parameters in random effects models for survival data when covariates are subject to missingness. Our method is more general than the usual frailty model as it accommodates a wide range of distributions for the random effects, which are included as an offset in the linear predictor in a manner analogous to that used in generalized linear mixed models. We propose using a Monte Carlo EM algorithm along with the Gibbs sampler to obtain parameter estimates. This method is useful in reducing the bias that may be incurred using complete-case methods in this setting. The methodology is applied to data from Eastern Cooperative Oncology Group melanoma clinical trials in which observations were believed to be clustered and several tumor characteristics were not always observed.

Clinical Trials, Phase III as Topic↗

PubMed2002

National evaluation for calving ease, gestation length and birth weight by linear and threshold model methodologies.

Data included 393,097 calving ease, 129,520 gestation length, and 412,484 birth weight records on 412,484 Gelbvieh cattle. Additionally, pedigrees were available on 72,123 animals. Included in the models were effects of sex and age of dam, treated as fixed, as well as direct, maternal genetic and permanent environmental effects and effects of contemporary group (herd-year-season), treated as random. In all analyses, birth weight and gestation length were treated as continuous traits. Calving ease (CE) was treated either as a continuous trait in a mixed linear model (LM), or as a categorical trait in linear-threshold models (LTM). Solutions in TM obtained by empirical Bayes (TMEB) and Monte Carlo (TMMC) methodologies were compared with those by LM. Due to the computational cost, only 10,000 samples were obtained for TMMC. For calving ease, correlations between LM and TMEB were 0.86 and 0.78 for direct and maternal genetic effects, respectively. The same correlations but between TMEB and TMMC were 1.00 and 0.98, respectively. The correlations between LM and TMMC were 0.85 and 0.75, respectively. The correlations for the linear traits were above.97 between LM and TMEB but as low as 0.91 between LM and TMMC, suggesting insufficient convergence of TMMC. Computing time required was about 2 hrs, 5 hrs, and 6 days for LM, TMEB and TMMC, respectively, and memory requirements were 169, 171, and 445 megabytes, respectively. Bayesian implementation of threshold model is simple, can be extended to multiple categorical traits, and allows easy calculation of accuracies; however, computing time is prohibitively long for large models.

Animals↗

PubMedDate not supplied

Modelling geographic variations in West Nile virus.

BACKGROUND: This paper applies a method for modelling the spatial variation of West Nile virus (WNv) in humans using bird, environmental and human testing data. METHODS: We used data collected from 503 Alberta municipalities. In order to manage the effects of residual spatial autocorrelation, we used generalized linear mixed models (GLMM) to model the incidence of infection. RESULTS: There were 275 confirmed cases of WNv in the 2003 calendar year in Alberta. Our spatial model indicates that living in the grasslands natural region and levels of human testing are significant positive predictors of WNv; living in an urban area is a significant negative predictor. CONCLUSION: Infected bird data contribute little to our model. The variability of West Nile virus incidence in Alberta may be partly confounded by the variations in the rate of testing in different parts of the province. However, variation in infection is also associated with known environmental risk factors. Our findings are consistent with existing knowledge of WNv in North America.

Alberta↗

PubMed2006

Simultaneous fine mapping of multiple closely linked quantitative trait Loci using combined linkage disequilibrium and linkage with a general pedigree.

Within a small region (e.g., <10 cM), there can be multiple quantitative trait loci (QTL) underlying phenotypes of a trait. Simultaneous fine mapping of closely linked QTL needs an efficient tool to remove confounded shade effects among QTL within such a small region. We propose a variance component method using combined linkage disequilibrium (LD) and linkage information and a reversible jump Markov chain Monte Carlo (MCMC) sampling for model selection. QTL identity-by-descent (IBD) coefficients between individuals are estimated by a hybrid MCMC combining the random walk and the meiosis Gibbs sampler. These coefficients are used in a mixed linear model and an empirical Bayesian procedure combines residual maximum likelihood (REML) to estimate QTL effects and a reversible jump MCMC that samples the number of QTL and the posterior QTL intensities across the tested region. Note that two MCMC processes are used, i.e., an (internal) MCMC for IBD estimation and an (external) MCMC for model selection. In a simulation study, the use of the multiple-QTL model clearly removes the shade effects between three closely linked QTL located at 1.125, 3.875, and 7.875 cM across the region of 10 cM, using 40 markers at 0.25-cM intervals. It is shown that the use of combined LD and linkage information gives much more useful information compared to using linkage information alone for both single- and multiple-QTL analyses. When using a lower marker density (11 markers at 1-cM intervals), the signal of the second QTL can disappear. Extreme values of past effective size (resulting in extreme levels of LD) decrease the mapping accuracy.

Chromosome Mapping↗

PubMed2000

Hemodialysis causes changes in dynamic vectorcardiographic ischemia monitoring parameters.

AIMS: The aim of this study was to establish whether changes in parameters reflecting myocardial ischemia QRS vector difference (QRS-VD), ST change vector magnitude (STC-VM) and ST vector magnitude (ST-VM6) during hemodialysis (HD) registered by MIDA (myocardial infarction dynamic analysis) are related to changes in blood volume (BV), extracellular water (ECW) and blood biochemistry. PATIENTS AND METHODS: Fifteen hemodialysis (HD) patients were studied. Computerized vectorcardiography was used for on-line dynamic analysis of ST segment and QRS complex changes. BV changes were monitored non-invasively and continuously with the CRIT-LINE instrument. Bioelectric impedance analysis (BIA) was used for ECW estimation. Blood samples were taken before and after hemodialysis for hemoglobin (B-Hb), hematocrit (B-Hcr), sodium (P-Na), chloride (P-Cl), magnesium (P-Mg), potassium (P-K), ionized calcium (P-iCa), phosphate (P-Pi) and astrup measurement. RESULTS: During dialysis treatment QRS-VD, ST-VM6 and STC-VM did not change in parallel. According to the linear mixed model, no statistically significant changes were noted in ST-VM6 during dialysis (time effect p = 0.5635). On the other hand, QRS-VD and STC-VM showed a statistically significant linear trend (time effect for QRS-VD p = 0.0001 and for STC-VM p = 0.0004). Changes in both ECW and BV affected the change in QRS-VD and in STC-VM. CONCLUSION: During HD treatment changes in the vectorcardiographic ischemia monitoring parameters QRS-VD and STC-VM are mostly related to ECW and BV changes and may give a false positive impression of myocardial ischemia. The ST-VM6 trend is less markedly influenced by volume changes.

Adult↗

PubMed2004

Application of a mixed model approach for assessment of interventions and evaluation of programs.

Many social programs and programs for prevention of drug use are designed to affect a wide variety of targets, including individuals, families and neighborhoods, and organizations such as schools, companies, or hospitals. The nature of the intervention and the design of the particular study determine the choice of the appropriate unit of analysis in assessments of outcome. When the units of assignment and units of observation differ from one another, that is, when clusters of persons rather than persons are assigned at random to treatments, analyses performed at lower levels in the study hierarchy provide inefficient estimates of parameters and often lead to inappropriate significance tests. The present goal was to illustrate the applications of linear mixed models for evaluating statistically the effectiveness of programs.

Alcoholism↗

PubMed2026

Effects of intensive lifestyle interventions with calorie-carbohydrate-restricted diet versus time-restricted eating on appetite and binge eating in type 2 diabetes: A randomized controlled trial.

The impact of intensive lifestyle interventions on appetite regulation and binge eating in individuals with type 2 diabetes (T2D) remains unclear. This study evaluated the effects of combined lifestyle interventions on appetite responses and binge eating in overweight or obese adults with T2D. In a randomized trial, 120 participants with T2D were allocated to three groups (n = 40 each): (1) Calorie-carbohydrate restriction (CCR), (2) Time-restricted eating with CCR (TRE + CCR), or (3) Control. Intervention groups received structured exercise and behavioral education based on the Information-Motivation-Behavioral Skills model. Appetite perceptions (hunger, satiety, desire to eat, and prospective food consumption) and binge eating (Binge Eating Scale; BES and objective binge episodes) were evaluated at baseline, week 12, and week 24 using linear mixed models. Both CCR and TRE + CCR significantly improved subjective appetite compared with the control group at 12 and 24 weeks (all p < 0.01). At 24 weeks, hunger decreased by -24.1 mm (95% CI: -35.8, -12.5) in the CCR group and -32.7 mm (95% CI: -44.2, -21.3) in the TRE + CCR group. Satiety also increased by 21.7 mm (95% CI: 9.46, 33.9) and 29.4 mm (95% CI: 17.4, 41.4), respectively. Significant reductions were observed for desire to eat and prospective food consumption. In contrast, changes in BES and objective binge episodes were not significantly different between groups at any time point. No significant differences were detected between the CCR and the TRE + CCR groups. Intensive lifestyle interventions incorporating CCR or TRE + CCR effectively reduced appetite in adults with T2D but did not significantly affect binge eating. Future research should target individuals with higher baseline BES scores to clarify potential benefits for binge eating behavior.

Humans↗

PubMed2000

Modern statistical techniques for the analysis of longitudinal data in biomedical research.

Longitudinal study designs in biomedical research are motivated by the need or desire of a researcher to assess the change over time of an outcome and what risk factors may be associated with the outcome. The outcome is measured repeatedly over time for every individual in the study, and risk factors may be measured repeatedly over time or they may be static. For example, many clinical studies involving chronic obstructive pulmonary disease (COPD) use pulmonary function as a primary outcome and measure it repeatedly over time for each individual. There are many issues, both practical and theoretical, which make the analysis of longitudinal data complicated. Fortunately, advances in statistical theory and computer technology over the past two decades have made techniques for the analysis of longitudinal data more readily available for data analysts. The aim of this paper is to provide a discussion of the important features of longitudinal data and review two popular modern statistical techniques used in biomedical research for the analysis of longitudinal data: the general linear mixed model, and generalized estimating equations. Examples are provided, using the study of pulmonary function in cystic fibrosis research.

Biometry↗

PubMed2002

Should a mucoadhesive patch (DentiPatch) be used for gingival anesthesia in children?

A local anesthetic-impregnated mucosal adhesive patch (DentiPatch) was compared with topical anesthetic (Hurricaine Dry Handle Swab) for gingival anesthesia before rubber dam clamp placement in children. Twenty-eight children needing sealants on their posterior teeth were enrolled in this study. Topical anesthesia was provided using either the mucoadhesive patch (20% lidocaine) or topical anesthetic (20% benzocaine). Subjects were randomized using a split mouth model. Either the patch or topical anesthetic was applied to the gingiva for 5 minutes or 1 minute, respectively. Subjects used a visual analog scale to describe their pain during the procedure. Linear regression and mixed linear models were used for data analysis. The visual analog scale results (pain scores) showed no significant difference between treatments. The mean per-child patch-sticking fraction was 29.7%. Patch adherence to oral mucosa increased with age in girls (P = .0045), but not in boys. The DentiPatch is as effective as, although not superior to, the Hurricaine Dry Handle Swab for gingival anesthesia before rubber dam clamp placement in children. These study results would not support the use of the DentiPatch for gingival anesthesia in children because of poor adherence to oral mucosa and the extra time necessary to apply and retain the device.

Adhesiveness↗

PubMed2001

A multiple imputation method for missing covariates in non-linear mixed-effects models with application to HIV dynamics.

We propose a three-step multiple imputation method, implemented by Gibbs sampler, for estimating parameters in non-linear mixed-effects models with missing covariates. Estimates obtained by the proposed multiple imputation method are compared to those obtained by the mean-value imputation method and the complete-case method through simulations. We find that the proposed multiple imputation method offers smaller biases and smaller mean-squared errors for the estimates of covariate coefficients compared to other two methods. We apply the three missing data methods to modelling HIV viral dynamics from an AIDS clinical trial. We believe that the results from the proposed multiple imputation method are more reliable than that from the other two commonly used methods.

Antiretroviral Therapy, Highly Active↗

PubMed2004

Two macroscopic and microscopic brain imaging studies of human hippocampus in early Alzheimer's disease and schizophrenia research.

Among the many diseases that affect the hippocampus, a small yet highly important brain region responsible for memory and identity, Alzheimer's disease and schizophrenia are among the most devastating. We describe a two-stage, region-of-interest based linear mixed model approach to the analysis of a longitudinal functional magnetic resonance (FMRI) study of human memory function under several drug challenges. We then describe a Monte Carlo approach to testing members of nested hierarchies of linear models in a stereological study of different types and locations of human hippocampal neurons. Last, we attempt to draw the attention of the biostatistical community interested in imaging neuroscience to the intriguing complexities of human hippocampal research in early Alzheimer's disease, schizophrenia and other brain diseases via brain imaging methods.

Alzheimer Disease↗

PubMed2005

Regression models for twin studies: a critical review.

Twin studies have long been recognized for their value in learning about the aetiology of disease and specifically for their potential for separating genetic effects from environmental effects. The recent upsurge of interest in life-course epidemiology and the study of developmental influences on later health has provided a new impetus to study twins as a source of unique insights. Twins are of special interest because they provide naturally matched pairs where the confounding effects of a large number of potentially causal factors (such as maternal nutrition or gestation length) may be removed by comparisons between twins who share them. The traditional tool of epidemiological 'risk factor analysis' is the regression model, but it is not straightforward to transfer standard regression methods to twin data, because the analysis needs to reflect the paired structure of the data, which induces correlation between twins. This paper reviews the use of more specialized regression methods for twin data, based on generalized least squares or linear mixed models, and explains the relationship between these methods and the commonly used approach of analysing within-twin-pair difference values. Methods and issues of interpretation are illustrated using an example from a recent study of the association between birth weight and cord blood erythropoietin. We focus on the analysis of continuous outcome measures but review additional complexities that arise with binary outcomes. We recommend the use of a general model that includes separate regression coefficients for within-twin-pair and between-pair effects, and provide guidelines for the interpretation of estimates obtained under this model.

Birth Weight↗

PubMed2005

Mixed models applied to the study of variation of grower-finisher mortality and culling rates of a large swine production system.

Large scale production systems for swine are frequently organized in a hierarchical structure. Consequently, important production parameters, such as mortality and culling, can be analyzed at different levels. The major aims of this study were to assess variance components (VC) of mortality and culling rates attributed to sites and to barns within a site, and subsequently to investigate the impact of average entry weight, days on feed (length of the production turn), and season on the magnitude of the VC. Then, data from a large farm with 3 sites were collected during 5 y. In total, 1720040 pigs distributed in 1502 all-in/all-out grower-finisher groups were included. Linear mixed models were fitted for mortality and culling rates. The barn was modeled as the residual component (barn-to-barn variations) with production turn and site nested within production turn as random intercept variance components. Barn-to-barn pig group variation was the largest VC for mortality (63.08%), when no predictors were included in the models. Predictors, such as pigs placed on quarters 2 and 3, low average entry weight, and shorter production turn length, were associated together with higher mortality. The explained proportion of variance due to these predictors was about 12.05% and the VC for barn, site, and production turn were 67.6%, 17.6%, and 14.8%, respectively. Barn-to-barn variation was also the largest VC for culling rate (46.2%), but the same predictor mentioned above explained only about 1.4% of the variation. The VC for barn, site, and production turn were 46.8%, 21.3%, and 31.8%, respectively. Since the variability among barns far exceeded the variability among sites, the barn should be used as experimental unit in studies with grower-finisher mortality, culling rate, or both, as outcome variables.

Analysis of Variance↗

PubMed2005

Random-effects models in investigating the effect of vitamin A in childhood diarrhea.

PURPOSE: By adopting more appropriate and powerful statistical methods that fully exploit longitudinal structure, we re-analyze and extend previously published results from a large community trial to investigate the effect of vitamin A supplementation on the prevalence and severity of diarrhea in young children. METHODS: Generalized linear mixed models were used to allow for repeated measures in a reanalysis of a double-blind, randomized, placebo-controlled community trial conducted in a cohort of children in northeastern Brazil during 1 year. The response variable was weekly number of days with diarrhea for each child, and Markov Chain Monte Carlo methods were used to estimate model parameters. RESULTS AND CONCLUSIONS: Random effects suitably accounted for the underlying heterogeneity between and within children, and our longitudinal analysis shows a significant beneficial effect of vitamin A supplementation that was inconclusive in previously reported simple summary analyses of these data. Risk for diarrhea infection was estimated to be 1.57 times greater for a child administered a placebo as opposed to vitamin A (95% credible interval, 1.17-2.12). Additionally, we identified previously unreported temporal effects in these data, showing a decreasing daily probability of diarrhea for both groups during the trial and treatment-time interaction.

Bayes Theorem↗