Pairwise fitting of piecewise mixed models for the joint modeling of multivariate longitudinal outcomes, in a randomized crossover trial.

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 × $\times$ 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 et al. (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 2 × 2 $2\times 2$ 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 modeling framework.

Evaluation of a flexible piecewise linear mixed-effects model in the analysis of randomized cross-over trials.

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.

Food Insecurity and Not Dietary Diversity Is a Predictor of Nutrition Status in Children within Semiarid Agro-Ecological Zones in Eastern Kenya.

Machakos and Makueni counties in Kenya are associated with historical land degradation, climate change, and food insecurity. Both counties lie in lower midland (LM) lower humidity to semiarid (LM4), and semiarid (LM5) agroecological zones (AEZ). We assessed food security, dietary diversity, and nutritional status of children and women. Materials and Methods. A total of 277 woman-child pairs aged 15-46 years and 6-36 months respectively, were recruited from farmer households. Food security and dietary diversity were assessed using standard tools. Weight and height, or length in children, were used for computation of nutritional status. Findings. No significant difference (P > 0.05) was observed in food security and dietary diversity score (DDS) between LM4 and LM5. Stunting, wasting, and underweight levels among children in LM4 and LM5 were comparable as were BMI scores among women. However, significant associations (P = 0.023) were found between severe food insecurity and nutritional status of children but not of their caregivers. Stunting was significantly higher in older children (>2 years) and among children whose caregivers were older. Conclusion. Differences in AEZ may not affect dietary diversity and nutritional status of farmer households. Consequently use of DDS may lead to underestimation of food insecurity in semiarid settings.

Prevalence of metabolic syndrome among an urban population in Kenya.

OBJECTIVE: Developing countries are undergoing an epidemiologic transition accompanied by increasing burden of cardiovascular disease (CVD) linked to urbanization and lifestyle modifications. Metabolic syndrome is a cluster of CVD risk factors whose extent in Kenya remains unknown. The aim of this study was to determine the prevalence of metabolic syndrome and factors associated with its occurrence among an urban population in Kenya. RESEARCH DESIGN AND METHODS: This was a household cross-sectional survey comprising 539 adults (aged ≥18 years) living in Nairobi, drawn from 30 clusters across five socioeconomic classes. Measurements included waist circumference, HDL cholesterol, triacylglycerides (TAGs), fasting glucose, and blood pressure. RESULTS: The prevalence of metabolic syndrome was 34.6% and was higher in women than in men (40.2 vs. 29%; P < 0.001). The most frequently observed features were raised blood pressure, a higher waist circumference, and low HDL cholesterol (men: 96.2, 80.8, and 80%; women: 89.8, 97.2, and 96.3%, respectively), whereas raised fasting glucose and TAGs were observed less frequently (men: 26.9 and 63.3%; women: 26.9 and 30.6%, respectively). The main factors associated with the presence of metabolic syndrome were increasing age, socioeconomic status, and education. CONCLUSIONS: Metabolic syndrome is prevalent in this urban population, especially among women, but the incidence of individual factors suggests that poor glycemic control is not the major contributor. Longitudinal studies are required to establish true causes of metabolic syndrome in Kenya. The Kenyan government needs to create awareness, develop prevention strategies, and strengthen the health care system to accommodate screening and management of CVDs.