Estimation of Daily Smoking Prevalence for Disaggregated Statistical Areas in Australia

Summary - A method is described for the simultaneous estimation of variance components due to several genetic and environmental effects from unbalanced data by restricted maximum likelihood (REML). Estimates are obtained by evaluating the likelihood explicitly and using standard, derivative-free optimization procedures to locate its maximum. The model of analysis considered is the so-called Animal Model which includes the additive genetic merit of animals as a random effect, and incorporates all information on relationships between animals. Furthermore, random effects in addition to animals’ additive genetic effects, such as maternal genetic, dominance or permanent environmental effects are taken into account. Emphasis is placed entirely upon univariate analyses. Simulation is employed to investigate the efficacy of three different maximization techniques and the scope for approximation of sampling errors. Computations are illustrated with a numerical example. variance components - restricted maximum likelihood - animal model - additional random effects - derivative - free approach

Many statistical models have been proposed in the literature for the analysis of longitudinal data. One may propose to model two or more correlated longitudinal processes simultaneously, with a goal of understanding their association over time. Joint modeling is then required to carefully study the association structure among the outcomes as well as drawing joint inferences about the different outcomes. In this study, we sought to model the associations among six nutrition outcomes while circumventing the computational challenge posed by their clustered and high-dimensional nature. We analyzed data from a 2 2 randomized crossover trial conducted in Kenya, to compare the effect of high-dose and low-dose iodine in household salt on systolic blood pressure (SBP) and diastolic blood pressure (DBP) in women of reproductive age and their household matching pair of school-aged children. Two additional outcomes, namely, urinary iodine concentration (UIC) in women and children were measured repeatedly to monitor the amount of iodine excreted through urine. We extended the model proposed by Mwangi etal. (2021, Communications in Statistics: Case Studies, Data Analysis and Applications, 7(3), 413-431) allowing flexible piecewise joint models for six outcomes to depend on separate random effects, which are themselves correlated. This entailed fitting 15 bivariate general linear mixed models and deriving inference for the joint model using pseudo-likelihood theory. We analyzed the outcomes separately and jointly using piecewise linear mixed-effects (PLME) model and further validated the results using current state-of-the-art Jones and Kenward methodology (JKME model) used for analyzing randomized crossover trials. The results indicate that high-dose iodine in salt significantly reduced blood pressure (BP) compared to low-dose iodine in salt. Estimates for the random effects and residual error components showed that SBP and DBP had strong positive correlation, with effect of the random slope indicating that significantly related outcomes are strongly associated in their evolution. There was a moderately strong inverse relationship between evolutions of UIC and BP both in women and children. These findings confirmed the original hypothesis that high-dose iodine salt has significant lowering effect on BP. We further sought to evaluate the performance of our proposed PLME model against the widely used JKME model, within the multivariate joint modeling framework through a simulation study mimicking a crossover design. From our findings, the multivariate joint PLME model performed exceptionally well both in estimation of random-effects matrix (G) and Hessian matrix (H), allowing satisfactory model convergence during estimation. It allowed a more complex fit to the data with both random intercepts and slopes effects compared to the multivariate joint JKME model that allowed for random intercepts only. When a hierarchical viewpoint is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive definite. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters. The key highlight in this evaluation shows that multivariate joint JKME model is a powerful tool especially while fitting mixed models with random intercepts only, in crossover design settings. Addition of random slopes may lead to model complexities in most cases, resulting in unsatisfactory model convergence during estimation. To circumvent convergence pitfalls, extention of JKME model to PLME model allows a more flexible fit to the data (generated from crossover design settings), especially in the multivariate joint modelingframework.

In meta-analysis, study participants are nested within studies, leading to a multilevel data structure. The traditional random effects model can be considered as a model with a random study effect, but additional random effects can be added in order to account for dependent effects sizes within or across studies. The goal of this systematic review is three-fold. First, we will describe how multilevel models with multiple random effects (i.e., hierarchical three-, four-, five-level models and cross-classified random effects models) are applied in meta-analysis. Second, we will illustrate how in some specific three-level meta-analyses, a more sophisticated model could have been used to deal with additional dependencies in the data. Third and last, we will describe the distribution of the characteristics of multilevel meta-analyses (e.g., distribution of the number of outcomes across studies or which dependencies are typically modeled) so that future simulation studies can simulate more realistic conditions. Results showed that four- or five-level or cross-classified random effects models are not often used although they might account better for the meta-analytic data structure of the analyzed datasets. Also, we found that the simulation studies done on multilevel meta-analysis with multiple random factors could have used more realistic simulation factor conditions. The implications of these results are discussed, and further suggestions are given.

The probability of breeding is known to increase with age early in life in many long-lived species. This increase may be due to experience accumulated through past breeding attempts. Recent methodological advances allowing accounting for unobserved breeding episodes, we analyzed the encounter histories of 14716 greater flamingos over 25 years to get a detailed picture of the interactions of age and experience. Survival did not improve with experience, seemingly ruling out the selection hypothesis. Breeding probability varied within three levels of experience : no breeding experience, 1 experience, 2+ experiences. We fitted models with and without among-individual differences in breeding probabilities by including or not an additive individual random effect. Including the individual random effect improved the model fit less than including experience but the best model retained both. However, because modeling individual heterogeneity by means of an additive static individual random effect is currently criticized and may not be appropriate, we discuss the results with and without random effect. Without random effect, breeding probability of inexperienced birds was always times lower than that of same age experienced birds, and breeding probability increased more with one additional experience than with one additional year of age. With random effects, the advantage of experience was unequivocal only after age 9 while in young having experience was penalizing. Another pattern, that breeding probability of birds with experiences dropped after some age (8 without random effect; up to 11 with it), may point to differences in the timing of reproductive senescence or to the existence of a sensitive period for acquiring behavioral skills. Overall, the role of experience appears strong in this long-lived species. We argue that overlooking the role of experience may hamper detection of trade-offs and assessment of individual heterogeneity. However, manipulative experiments are desirable to confirm our finding.

In a meta-analysis combining survival data from different clinical trials, an important issue is the possible heterogeneity between trials. Such intertrial variation can not only be explained by heterogeneity of treatment effects across trials but also by heterogeneity of their baseline risk. In addition, one might examine the relationship between magnitude of the treatment effect and the underlying risk of the patients in the different trials. Such a scenario can be accounted for by using additive random effects in the Cox model, with a random trial effect and a random treatment-by-trial interaction. We propose to use this kind of model with a general correlation structure for the random effects and to estimate parameters and hazard function using a semi-parametric penalized marginal likelihood method (maximum penalized likelihood estimators). This approach gives smoothed estimates of the hazard function, which represents incidence in epidemiology. The idea for the approach in this paper comes from the study of heterogeneity in a large meta-analysis of randomized trials in patients with head and neck cancers (meta-analysis of chemotherapy in head and neck cancers) and the effect of adding chemotherapy to locoregional treatment. The simulation study and the application demonstrate that the proposed approach yields satisfactory results and they illustrate the need to use a flexible variance-covariance structure for the random effects.

به منظور تخمین پارامترهاو روند ژنتیکی تداوم شیردهی از تعداد 2487378 رکورد روز آزمون متعلق به336164 راس گاو هلشتاین شکم اول ایران متعلق به 2581 گله که در طی سال‌های 1371 تا 1391 زایش داشتند، استفاده شد. برای محاسبه تداوم شیردهی از پارامترهای برآورد شده تابع وود، توسط نرم‌افزار R استفاده گردید. آنالیز عوامل موجود در مدل جهت ارزیابی ژنتیکی تداوم شیردهی با کمک نرم‌افزار SASانجام گردید که همگی معنی‌دار بودند. اجزای واریانس ژنتیکی افزایشی، فنوتیپی و وراثت پذیری براساس مدل دام تک صفته با استفاده از نرم‌افزار WOMBAT محاسبه گردیدند. واریانس ژنتیکی افزایشی، فنوتیپی ووراثت پذیری صفت مزبور به ترتیب 03/0، 37/0 و 08/0 برآورد شدند. مقادیر روندهای ژنتیکی و فنوتیپی به ترتیب حدود 01/ و 022/0 برآورد شدند که هر دو از لحاظ آماری معنی دار بودند. نتایج این پژوهش نشان داد که روند ژنتیکی و فنوتیپی تداوم شیردهی در گاوهای هلشتاین ایران مثبت و مطلوب بوده است.

Assessing infections at multiple levels of aggregation

Variance components for production traits were estimated using different models to evaluate maternal effects. Data analysed were records from the South African pig performance testing scheme on 22224 pigs from 18 herds, tested between 1990 and 2008. The traits analysed were backfat thickness (BFAT), test period weight gain (TPG), lifetime weight gain (LTG), test period feed conversion ratio (FCR) and age at slaughter (AGES). Data analyses were performed by REML procedures in ASREML, where random effects were successively fitted into animal and sire models to produce different models. The first animal model had one random effect, the direct genetic effects, while the additional random effects were maternal genetic and maternal permanent environmental effects. In the sire model, the random effects fitted were sire and maternal grand sire effects. The best model considered the covariance between direct and maternal genetic effects or between sire and maternal grand sire effects. Fitting maternal genetic effects into the animal model reduced total additive variance, while the total additive variance increased when maternal grand sire effects were fitted into the sire model. The correlations between direct and maternal genetic effects were all negative, indicating antagonism between these effects, hence the need to consider both effects in selection programmes. Direct genetic correlations were higher than other correlations, except for maternal genetic correlations of FCR with TPG, LTG and AGES. There has been direct genetic improvement and almost constant maternal ability in production traits as shown by trends for estimated (EBVs) and maternal breeding values (MBVs), while phenotypic trends were similar to those for EBVs. These results suggest that maternal genetic effects should be included in selection programmes for these production traits. Therefore, the animal-maternal model may be the most appropriate model to use when estimating genetic parameters for production traits in this population.

Nonparametric estimation for stochastic differential equations with random effects

Cross-over designs are commonly used in randomized clinical trials to estimate efficacy of a new treatment. They have received a lot of attention, particularly in connection with regulatory requirements for new drugs. The main advantage of using cross-over designs over conventional parallel designs is increased precision, thanks to within-subject comparisons. In the statistical literature, more recent developments are discussed in the analysis of cross-over trials, in particular regarding repeated measures. A piecewise linear model within the framework of mixed effects has been proposed in the analysis of cross-over trials. In this article, we report on a simulation study comparing performance of a piecewise linear mixed-effects (PLME) model against two commonly cited models-Grizzle's mixed-effects (GME) and Jones & Kenward's mixed-effects (JKME) models-used in the analysis of cross-over trials. Our simulation study tried to mirror real-life situation by deriving true underlying parameters from empirical data. The findings from real-life data confirmed the original hypothesis that high-dose iodine salt have significantly lowering effect on diastolic blood pressure (DBP). We further sought to evaluate the performance of PLME model against GME and JKME models, within univariate modeling framework through a simulation study mimicking a 2 × 2 cross-over design. The fixed-effects, random-effects and residual error parameters used in the simulation process were estimated from DBP data, using a PLME model. The initial results with full specification of random intercept and slope(s), showed that the univariate PLME model performed better than the GME and JKME models in estimation of variance-covariance matrix (G) governing the random effects, allowing satisfactory model convergence during estimation. When a hierarchical view-point is adopted, in the sense that outcomes are specified conditionally upon random effects, the variance-covariance matrix of the random effects must be positive-definite. The PLME model is preferred especially in modeling an increased number of random effects, compared to the GME and JKME models that work equally well with random intercepts only. In some cases, additional random effects could explain much variability in the data, thus improving precision in estimation of the estimands (effect size) parameters.

ABSTRACTMixtures of linear mixed models are widely used for modeling longitudinal data for which observation times differ between subjects. In typical applications, temporal trends are described using a basis expansion, with basis coefficients treated as random effects varying by subject. Additional random effects can describe variation between mixture components or other known sources of variation in complex designs. A key advantage of these models is that they provide a natural mechanism for clustering. Current versions of mixtures of linear mixed models are not specifically designed for the case where there are many observations per subject and complex temporal trends, which require a large number of basis functions to capture. In this case, the subject‐specific basis coefficients are a high‐dimensional random effects vector, for which the covariance matrix is hard to specify and estimate, especially if it varies between mixture components. To address this issue, we consider the use of deep mixture of factor analyzers models as a prior for the random effects. The resulting deep mixture of linear mixed models is well suited for high‐dimensional settings, and we describe an efficient variational inference approach to posterior computation. The efficacy of the method is demonstrated in biomedical applications and on simulated data.

This paper discusses the tests for departures from nominal dispersion in the framework of generalized nonlinear models with varying dispersion and/or additive random effects. We consider two classes of exponential family distributions. The first is discrete exponential family distributions, such as Poisson, binomial, and negative binomial distributions. The second is continuous exponential family distributions, such as normal, gamma, and inverse Gaussian distributions. Correspondingly, we develop a unifying approach and propose several tests for testing for departures from nominal dispersion in two classes of generalized nonlinear models. The score test statistics are constructed and expressed in simple, easy to use, matrix formulas, so that the tests can easily be implemented using existing statistical software. The properties of test statistics are investigated through Monte Carlo simulations.

The aim of the current research was to estimate variance components and genetic parameters of weaning weight in Hungarian Simmental cattle. Weaning weight records were obtained from the Association of Hungarian Simmental Breeders. The dataset comprised of 44,278 animals born from 1975 to 2020. The data was analyzed using the restricted maximum likelihood methodology of the Wombat software. We fitted a total of six models to the weaning weight data of Hungarian Simmental cattle. Models ranged from a simple model with animals as the only random effect to a model that had maternal environmental effects as additional random effects as well as direct maternal genetic covariance. Fixed effects in the model comprised of herd, birth year, calving order and sex. Likelihood ratio test was used to determine the best fit model for the data. Results indicated that allowing for direct-maternal genetic covariance increases the direct and maternal effect dramatically. The best fit model had direct and maternal genetic effects as the only random effect with non-zero direct-maternal genetic correlation. Direct heritability, maternal heritability and direct maternal correlation of the best fit model was 0.57, 0.16 and -0.78 respectively. The result indicates that problem of (co-)sampling variation occurs when attempting to partition additive genetic variance into direct and maternal components.

In applied statistical data analysis, overdispersion is a common feature. It can be addressed using both multiplicative and additive random effects. A multiplicative model for count data incorporates a gamma random effect as a multiplicative factor into the mean, whereas an additive model assumes a normally distributed random effect, entered into the linear predictor. Using Bayesian principles, these ideas are applied to longitudinal count data, based on the so-called combined model. The performance of the additive and multiplicative approaches is compared using a simulation study.

The aim of the study was to partition the total phenotypic variation in the weaning weight of Hungarian Simmental calves into their various causal components. The data used was provided by the Association of Hungarian Simmental Breeders. The dataset comprised of the weaning weight records of 44,278 calves (sire = 879, dam = 14,811) born from 1975 to 2020. A total of six models were fitted to the weaning weight data. Herd, birth year, calving order and sex were included as fixed effects in the models. Model 1 had direct genetic effect as the only random effect. Model 2 had a permanent maternal environment as an additional random effect. Model 3 had both direct and maternal genetic effects, with their covariance is being zero. Model 4 was similar to Model 3 but with non-zero direct-maternal genetic covariance. Model 5 had direct, maternal genetic and permanent environmental effects and a zero direct-maternal genetic covariance. Model 6 was similar to model 5 but the direct-maternal genetic effect was assumed to be correlated. Variance components and genetic parameters were estimated using restricted maximum likelihood method with the Wombat software. The best fit model was determined using the Log likelihood ratio test. Inclusion of direct maternal genetic covariance increased the variance components estimates dramatically which resulted in a corresponding increase in the direct and maternal heritability estimates. The best fitted model (Model 4) had direct and maternal genetic effects as the only random effects with a non-zero direct-maternal genetic covariance. The direct heritability, maternal heritability and direct-maternal genetic correlation estimate of the best model was 0.57, 0.16 and -0.78, respectively. Our result suggests the problem of (co)sampling variation in the partitioning of additive genetic effect into direct and maternal components.