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Impact of modelling intra-subject variability on tests based on non-linear mixed-effects models in cross-over pharmacokinetic trials with application to the interaction of tenofovir on atazanavir in HIV patients.

We evaluated the impact of modelling intra-subject variability on the likelihood ratio test (LRT) and the Wald test based on non-linear mixed effects models in pharmacokinetic interaction and bioequivalence cross-over trials. These tests were previously found to achieve a good power but an inflated type I error when intra-subject variability was not taken into account. Trials were simulated under H0 and several H1 and analysed with the NLME function. Different configurations of the number of subjects n and of the number of samples per subject J were evaluated for pharmacokinetic interaction and bioequivalence trials. Assuming intra-subject variability in the model dramatically improved the type I error of both interaction tests. For the Wald test, the type I error decreased from 22, 14 and 7.7 per cent for the original (n = 12, J = 10), intermediate (n = 24, J = 5) and sparse (n = 40, J = 3) designs, respectively, down to 7.5, 6.4 and 3.5 per cent when intra-subject variability was modelled. The LRT achieved very similar results. This improvement seemed mostly due to a better estimation of the standard error of the treatment effect. For J = 10, the type I error was found to be closer to 5 per cent when n increased when modelling intra-subject variability. Power was satisfactory for both tests. For bioequivalence trials, the type I error of the Wald test was 6.4, 5.7 and 4.2 per cent for the original, intermediate and sparse designs, respectively, when modelling intra-subject variability. We applied the Wald test to the pharmacokinetic interaction of tenofovir on atazanavir, a novel protease inhibitor. A significant decrease of the area under the curve of atazanavir was found when patients received tenofovir.

Adenine↗

Nonconjugate Bayesian analysis of variance component models.

We consider the usual normal linear mixed model for variance components from a Bayesian viewpoint. With conjugate priors and balanced data, Gibbs sampling is easy to implement; however, simulating from full conditionals can become difficult for the analysis of unbalanced data with possibly nonconjugate priors, thus leading one to consider alternative Markov chain Monte Carlo schemes. We propose and investigate a method for posterior simulation based on an independence chain. The method is customized to exploit the structure of the variance component model, and it works with arbitrary prior distributions. As a default reference prior, we use a version of Jeffreys' prior based on the integrated (restricted) likelihood. We demonstrate the ease of application and flexibility of this approach in familiar settings involving both balanced and unbalanced data.

Algorithms↗

Influence analysis for linear mixed-effects models.

In this paper, we extend several regression diagnostic techniques commonly used in linear regression, such as leverage, infinitesimal influence, case deletion diagnostics, Cook's distance, and local influence to the linear mixed-effects model. In each case, the proposed new measure has a direct interpretation in terms of the effects on a parameter of interest, and collapses to the familiar linear regression measure when there are no random effects. The new measures are explicitly defined functions and do not necessitate re-estimation of the model, especially for cluster deletion diagnostics. The basis for both the cluster deletion diagnostics and Cook's distance is a generalization of Miller's simple update formula for case deletion for linear models. Pregibon's infinitesimal case deletion diagnostics is adapted to the linear mixed-effects model. A simple compact matrix formula is derived to assess the local influence of the fixed-effects regression coefficients. Finally, a link between the local influence approach and Cook's distance is established. These influence measures are applied to an analysis of 5-year Medicare reimbursements to colon cancer patients to identify the most influential observations and their effects on the fixed-effects coefficients.

Cluster Analysis↗

Benefits of milk powder supplementation on bone accretion in Chinese children.

Low dietary calcium intake has been demonstrated to be a risk factor for hip and vertebral fractures in studies conducted among Hong Kong Chinese. Few studies have demonstrated the effect of milk supplementation in bone accretion in Chinese children. The aim was to examine the effects of milk powder supplementation in enhancing bone accretion in Chinese children. Three hundred and forty-four children, aged 9-10 years old, were randomized to receive milk powder equivalent to 1300 mg and 650 mg calcium, and to a control group, respectively. Bone mineral density (BMD) at the proximal femur, lumbar spine and total body were measured at 6 months, 12 months and 18 months. The treatment effects were modeled using linear mixed effect models and compared using linear contrast F-tests, by intention-to-treat. Subjects randomized to milk powder equivalent to 1300 mg calcium had significantly higher increase in BMD at both the total hip (7.4 +/- 0.4% in treatment group versus 6.3 +/- 0.4% in the control) and the spine (8.4 +/- 0.5% in the treatment group versus 7.0 +/- 0.5% in the control group). Subjects randomized to milk powder equivalent to 650 mg calcium had smaller increases in BMD at the total hip and spine, although the increase in BMD at the total body was significantly higher (3.1 +/- 0.3% in treatment group versus 2.4 +/- 0.2% in controls). It is concluded that supplementing the diet of Chinese children with milk powder was effective in enhancing bone accretion.

Animals↗

Mixed models for the analysis of replicated spatial point patterns.

The statistical methodology for the analysis of replicated spatial point patterns in complex designs such as those including replications is fairly undeveloped. A mixed model is developed in conjunction with maximum pseudolikelihood and generalized linear mixed modeling by extending Baddeley and Turner's (2000, Australian and New Zealand Journal of Statistics 42, 283-322) work on pseudolikelihood for single patterns. A simulation experiment is performed on parameter estimation. Fixed- and mixed-effect models are compared, and in some respects the mixed model is found to be superior. An example using the Strauss process for modeling neuron locations in post-mortem brain slices is shown.

Brain↗

Deprived children or deprived neighbourhoods? A public health approach to the investigation of links between deprivation and injury risk with specific reference to child road safety in Devon County, UK.

BACKGROUND: Worldwide, injuries from road traffic collisions are a rapidly growing problem in terms of morbidity and mortality. The UK has amongst the worst records in Europe with regard to child pedestrian safety. A traditional view holds that resources should be directed towards training child pedestrians. In order to reduce socio-economic differentials in child pedestrian casualty rates it is suggested that these should be directed at deprived children. This paper seeks to question whether analysis of extant routinely collected data supports this view. METHODS: Routine administrative data on road collisions has been used. A deprivation measure has been assigned to the location where a collision was reported, and the home postcode of the casualty. Aggregate data was analysed using a number of epidemiological models, concentrating on the Generalised Linear Mixed Model. RESULTS: This study confirms evidence suggesting a link between increasing deprivation and increasing casualty involvement of child pedestrians. However, suggestions are made that it may be necessary to control for the urban nature of an area where collisions occur. More importantly, the question is raised as to whether the casualty rate is more closely associated with deprivation measures of the ward in which the collision occurred than with the deprivation measures of the home address of the child. CONCLUSION: Conclusions have to be drawn with great caution. Limitations in the utility of the officially collected data are apparent, but the implication is that the deprivation measures of the area around the collision is a more important determinant of socio-economic differentials in casualty rates than the deprivation measures of the casualties' home location. Whilst this result must be treated with caution, if confirmed by individual level case-controlled studies this would have a strong implication for the most appropriate interventions.

Accidents, Traffic↗

A note on genetic variance components in mixed models.

Burton et al. ([1999] Genet. Epidemiol. 17:118-140) proposed a series of generalized linear mixed models for pedigree data that account for residual correlation between related individuals. These models may be fitted using Markov chain Monte Carlo methods, but the posterior mean for small variance components can exhibit marked positive bias. Burton et al. ([1999] Genet. Epidemiol. 17:118-140) suggested that this problem could be overcome by allowing the variance components to take negative values. We examine this idea in depth, and show that it can be interpreted as a computational device for locating the posterior mode without necessarily implying that the original random effects structure is incorrect. We illustrate the application of this technique to mixed models for familial data.

Data Interpretation, Statistical↗

Comparing trajectories of cognitive functioning in treatment-resistant and non-resistant depression: a multicentre linear mixed-effects analysis.

BACKGROUND: Impaired cognitive functioning is a severe symptom in major depressive disorder (MDD). Recent evidence suggests it may be a central characteristic in its treatment resistant form (TRD), potentially constituting a clinical marker for treatment resistance and a target amenable to intervention. To date, cognitive functioning in TRD remains poorly understood and longitudinal investigations are scarce. METHODS: This observational prospective cohort study, including 320 patients diagnosed with MDD from the multicentre PROMPT study, examined differences in cognitive functioning between 118 TRD and 202 non-TRD patients over a period of twelve weeks in a real-world setting, using linear mixed modelling. Patients that failed to respond to at least two prior antidepressants trials at baseline were classified as TRD. RESULTS: TRD patients showed significantly poorer baseline performances than non-TRD patients in attention/processing speed (β = -0.45; 95%CI[-0.70, -0.19]; FDR-p = 0.003) and verbal memory (β = -0.45; 95%CI[-0.72, -0.18]; FDR-p = 0.003). Significant time × group interactions were observed in motor speed and verbal fluency tasks. Post-hoc-analyses revealed stagnation in TRD patients and significant improvement in non-TRD patients. Across all other tasks improvement was observed in both groups, and random effects showed large heterogeneity between patients, indicating notable individual differences in cognitive performances. CONCLUSIONS: The results suggest distinct recovery patters between non-TRD and TRD patients, and diminished functioning in TRD patients at the domain level. However, intact and diminished performances likely occur in both groups, warranting further investigation of cognitive heterogeneity. These short-term findings highlight the need for more comprehensive longitudinal research on cognition in TRD.

Humans↗

The effects of Medicare Health Management Organizations on hospital operating profit in Florida.

Between 1992 and 1997, the number of members enrolled in Medicare Health Management Organizations (HMOs) nationwide in the USA more than doubled. During this period, managed care organizations wielded considerable influence over the health care of a large segment of the Medicare population in Florida. This study examined the impact on operational profit of 148 short-term, acute-care Florida hospitals in this period from Medicare HMO patients, as part of a hospital's payer mix. Three measures of hospital profitability were used: operating profit per actual bed, total operating profit with no adjustment for bed size, and operating margins. The multivariate statistical model employed in this study was a linear mixed model with an autoregressive order one (AR[1]) parametric structure on the covariance matrix. The results of the study indicate that Florida hospitals experienced greater profit pressures from Medicare HMO inpatients than from traditional Medicare inpatients. Further, these hospitals could have experienced positive profit effects with greater traditional Medicare participation and negative financial effects with greater Medicare HMO participation. Additionally, Medicare HMO patients appear to have been admitted to hospitals in worse health condition than those in traditional Medicare. Medicare HMO patients were more likely to have used emergency rooms as the source of admission than traditional Medicare patients. Also, Medicare HMO patients were more likely to have been admitted as emergent cases than traditional Medicare patients. Other research has shown that Medicare HMO patients, at the time of enrolment, are probably healthier than traditional Medicare enrollees, but here they appear to have been admitted to hospitals with higher levels of severity of illness. Explanations are offered for these findings.

Economics, Hospital↗

Shoot growth of mature Fagus sylvatica and Picea abies in relation to ozone.

Epidemiological analysis of sequential growth data may be a tool in assessing ozone sensitivity of mature trees. Annual shoot growth of mature Fagus sylvatica in 83 Swiss permanent forest observation plots and of Picea abies in 61 plots was evaluated for 11 and 8 consecutive years, respectively, using branches harvested every 4 years. The data were assessed as annual deviation from average growth and related to fructification, ozone, meteorological parameters, and modelled soil water content using a mixed linear model. In beech, a significant association between ozone and shoot growth was observed which corresponded to a 7.4% growth reduction between 0 and 10 ppm h AOT40 (accumulated ozone over threshold 40). This is in the same order of magnitude as the response observed in experiments with seedlings. No interaction was found between ozone and drought parameters. In Norway spruce, shoot growth was neither associated with ozone nor with drought.

Disasters↗

Pediatricians' intention to administer human papillomavirus vaccine: the role of practice characteristics, knowledge, and attitudes.

PURPOSE: The objective of this study was to examine pediatrician characteristics and attitudes associated with intention to recommend two hypothetical human papillomavirus (HPV) vaccines. METHODS: A survey instrument mailed to a random sample of 1000 pediatricians assessed provider characteristics, HPV knowledge, and attitudes about HPV vaccination. Intention to administer each of two HPV vaccines types (a cervical cancer/genital wart vaccine and a cervical cancer vaccine) to girls and boys of three different ages (11, 14, and 17 years) was assessed. Linear mixed modeling for repeated measures and multivariable linear regression models were performed to identify variables associated with intention to recommend vaccination. RESULTS: The mean age of participants (n = 513) was 42 years and 57% were female. Participants were more likely to recommend vaccination to girls vs. boys and older vs. younger children, and were more likely to recommend a cervical cancer/genital wart vaccine than a cervical cancer vaccine (p < .0001). Variables independently associated with intention to recommend a cervical cancer/genital wart vaccine were: higher estimate of the percentage of sexually active adolescents in one's practice (beta .084, p = .002), number of young adolescents seen weekly (beta 1.300, p = .015), higher HPV knowledge (beta 1.079, p = .015), likelihood of following the recommendations of important individuals and organizations regarding immunization (beta .834, p = .001), and fewer perceived barriers to immunization (beta -.203, p = .001). CONCLUSIONS: Vaccination initiatives directed toward pediatricians that focus on modifiable predictors of intention to vaccinate, such as HPV knowledge and attitudes about vaccination, may facilitate adherence to emerging national immunization guidelines.

Adolescent↗

The knee-ankle link: impact of knee varus severity on distal joint malalignment and concomitant pathologies.

BACKGROUND: Knee varus deformity is traditionally managed as an isolated joint pathology; however, persistent distal symptoms following proximal realignment suggest a more extensive kinetic chain dysfunction. The degree to which knee varus severity dictates distal malalignment and secondary pathologies remains poorly quantified in the current literature. METHODS: This systematic review and meta-analysis were conducted in accordance with PRISMA 2020 guidelines (PROSPERO: CRD420261363327). A comprehensive search of PubMed, Embase, Web of Science, and the Cochrane Library was performed from inception to April 2026. Studies examining the relationship between knee varus (HKA angle) and radiographic distal alignment or pathologies were included. Data synthesis utilized random-effects models, with prevalence analyzed via generalized linear mixed models (GLMM). RESULTS: Fourteen studies were included in the final synthesis. While pooling of continuous radiographic parameters was limited by high statistical heterogeneity in Talar Tilt (I2&#xa0;=&#xa0;96.5%), individual large-cohort data (Huang et al.) indicated that severe knee varus (HKA&#xa0;>&#xa0;10&#xb0;) was associated with increased odds of concomitant ankle osteoarthritis (OR 2.29; 95% CI 1.28-4.11) and a specific cohort prevalence of 37.1%. Furthermore, single-arm prevalence data revealed divergent trends across different study populations, with compensatory hindfoot valgus reaching 69.9% in some cohorts and rigid varus up to 63.9% in others. CONCLUSIONS: Severe genu varum is associated with distal kinetic chain alterations and concomitant ankle pathologies. However, due to the extreme heterogeneity and divergent distal adaptations observed across different cohorts, standardized knee-centric protocols may be insufficient. Further longitudinal and interventional studies are required to establish phenotype-specific rehabilitation guidelines.

Humans↗

Effect of herd environment on the genetic and phenotypic relationships among milk yield, conception rate, and somatic cell score in Holstein cattle.

A total of 248,230 primiparous records of Holstein cows calving from 1987 to 1994 (daughters of 588 sires in 3042 herds) was used to evaluate potential genotype by environment interactions among mature equivalent milk yield, lactation mean somatic cell score, and conception rate at first service. Herds were classified into low and high environmental groups using three different criteria: standard deviation of herd mature equivalent milk yield, a combination of herd mature equivalent milk yield mean and standard deviation, and the herd mean of body weight at first calving divided by age at first calving. Genetic parameters were modeled by using multiple-trait linear mixed models and were fitted using the multiple-trait derivative-free software. Heritabilities for mature equivalent milk yield, lactation mean somatic cell score, and conception rate at first service were 0.221, 0.106, and 0.015 in low environment herds and 0.300, 0.093, and 0.009 in high environment herds, respectively. Genetic (and phenotypic) correlations between mature equivalent milk yield and lactation mean somatic cell score, mature equivalent milk yield and conception rate at first service, and lactation mean somatic cell score and conception rate at first service were 0.277, -0.417, and -0.209, (-0.049, -0.180, and -0.040) and 0.173, -0.318, and -0.144, (-0.087, -0.166, and -0.035) in low and high environment herds, respectively. The genetic correlations between pairs of traits were consistently smaller in high environment herds, suggesting that differences in management between the two environment levels lessened the antagonistic genetic association between the traits studied. A long-range plan for low environment herds should focus on improving the level of management, which would greatly reduce the unfavorable correlated changes in lactation mean somatic cell score and conception rate at first service associated with the genetic improvement of mature equivalent milk yield.

Animals↗

Modelling spatial disease rates using maximum likelihood.

This paper concerns maximum likelihood estimation for a generalized linear mixed model (GLMM) useful for modelling spatial disease rates. The model allows for log-linear covariate adjustment and local smoothing of rates through estimation of spatially correlated random effects. The covariance structure of the random effects is based on a recently proposed model which parameterizes spatial dependence through the inverse covariance matrix. A Markov chain Monte Carlo algorithm for performing maximum likelihood estimation for this model is described. Results of a computer simulation study that compared maximum likelihood (ML) and penalized quasi-likelihood (PQL) estimators are presented. Compared with PQL, ML produced less biased estimates of the intercept but the ML estimates were slightly more variable. Estimates of the other regression coefficients were unbiased and nearly identical for the two methods. ML estimators of the random effects standard deviation and spatial correlation were more biased than the corresponding PQL estimators. The conclusion is that ML estimators for GLMMs cannot be expected to perform better than PQL for small samples.

Algorithms↗

Power calculations for generalized linear models in observational longitudinal studies: a simulation approach in SAS.

Repeated measurements arising from longitudinal studies occur frequently in applied research. Methods to calculate power in the context of repeated measures are available for experimental settings where the covariate of interest is a discrete treatment indicator. However, no closed form expression exists to calculate power for generalized linear models with non-zero within-cluster correlation that are common in epidemiological and observational studies in which the covariate of interest varies over time and is often measured on a continuous scale, and where the researchers control for several potential confounders. We describe a Monte Carlo simulation approach conducted to calculate power, and illustrate its application in two models frequently encountered in practice, the normal linear mixed model, and the logistic regression model, both with repeated measurements and non-zero within-cluster correlation. This approach can be used to calculate the effect on power of changing various simulation conditions controlled by the researcher, such as sample size, within-cluster correlation structure, smallest meaningful difference to detect, and distributional assumptions.

Child↗

Incidences and effects of diseases on the performance of Swedish dairy herds stratified by production.

Incidences of diseases and their effects on reproductive performance and risk of culling in herds stratified by production and estrus detection efficiency were studied. Data were from the Swedish milk and disease recording systems and consisted of records for 33,748 first parity Swedish Friesian cows. A standardized mixed threshold model was used for statistical analyses of categorical outcome variables, and an ordinary linear mixed model was used for continuous outcome variables. An increase in production was associated with increased frequencies of treatments of most diseases, shorter intervals from calving to first artificial insemination, fewer days open, and lower culling rates. Cows treated for metritis, silent estrus, and cystic ovaries had an increased number of days to first artificial insemination and more days open. However, the negative consequences of these diseases on reproductive performance decreased as herd production increased. The risk of culling was higher for cows treated for dystocia, cystic ovaries, and mastitis, but the increase in the risk of culling was lower for higher producing herds. Similar trends were observed when herds were stratified by estrus detection efficiency. The results support the hypothesis that herd management, as characterized by milk production or estrus detection efficiency, is important in the incidences and consequences of diseases. Herd management, measured directly or indirectly, should be considered when the health status or cost of disease for a given herd is evaluated.

Animals↗

Prediction error variance and expected response to selection, when selection is based on the best predictor - for Gaussian and threshold characters, traits following a Poisson mixed model and survival traits.

In this paper, we consider selection based on the best predictor of animal additive genetic values in Gaussian linear mixed models, threshold models, Poisson mixed models, and log normal frailty models for survival data (including models with time-dependent covariates with associated fixed or random effects). In the different models, expressions are given (when these can be found - otherwise unbiased estimates are given) for prediction error variance, accuracy of selection and expected response to selection on the additive genetic scale and on the observed scale. The expressions given for non Gaussian traits are generalisations of the well-known formulas for Gaussian traits - and reflect, for Poisson mixed models and frailty models for survival data, the hierarchal structure of the models. In general the ratio of the additive genetic variance to the total variance in the Gaussian part of the model (heritability on the normally distributed level of the model) or a generalised version of heritability plays a central role in these formulas.

Analysis of Variance↗

Analysis of a Bayesian repeated measures model for detecting differences in GP prescribing habits.

A linear mixed model is used to detect a change, if any, in the prescribing habits in the UK at the general practice (family medicine) level due to an educational intervention given repeated measures data before and after the intervention and a control group. Inferences are corrected for general practice size and fundholding status. The estimates of the model parameters are obtained using Bayesian inference by applying Gibbs sampling. We develop three different priors for the parameters of the model. These three priors correspond to 'sceptical,' 'reference' and 'enthusiastic' priors in terms of the opinion about the treatment effects that they represent. We compare the results obtained by using these three priors for the parameters in the random effects model.

Anti-Inflammatory Agents, Non-Steroidal↗