• Multivariate mixed-effects models/ Joint modeling of mixed outcomes

• Mixed models / random-effects models / multilevel models

• Marginalized multilevel models

• Overdispersion/ zero-inflation/ marginalized zero-inflated models

• Generalized linear models

• Bayesian, pseudo-likelihood and maximum likelihood estimation methodology

• Modeling long-term evolution of neurodegenerative diseases (Alzheimer's and Parkinson's)

• Infectious disease modeling

(A) Model development and long-term predictions of neurological disease outcomes using short-term data

Multivariate models for several longitudinal outcomes, which use random effects to account for both within and between outcome associations, permit a straightforward prediction of the individual-level profile for subjects in the dataset used in fitting the original models. For completely new subjects, prediction of future trajectories with baseline data or some run-in data is quite challenging since estimates of these subjects' random effects are not available. Very limited work has been done to address this for the multivariate models for multiple longitudinal outcomes. Iddi et al (2019) proposed that such individuals' baseline data are included in the original dataset involving other subjects with longitudinal measures and the model is refitted to estimate random intercepts and slopes for the new subjects. Although their approach led to small mean absolute and mean weighted errors, the procedure was found to be cumbersome as it was computationally very expensive and may not be useful for clinical practice particularly when the time is of the essence. An important area of application is the estimation of individual trajectories of Alzheimer's disease individuals at varying stages of the disease progression spectrum.

In this research, we consider two methods for estimating random-effects for a new subject based on multiple outcome measures reliably assessed at baseline. These random-effects estimates are combined with the systematic part of the specified diseased progression models to make individualized future predictions. The multivariate mixed-effects model for longitudinal data is used to assess the impact of risk factors on outcomes and predict the course of the disease.

(B) Power and Sample Size for Longitudinal Models in R -- The longpower Package and Shiny App.

Longitudinal studies are ubiquitous in medical and clinical research. Sample size computations are critical to ensure that these studies are sufficiently powered to provide reliable and valid inferences. There are several methodologies for calculating sample sizes for longitudinal studies that depend on many considerations including the study design features, outcome type, and distribution, and proposed analytical methods.

In this research, we shall review the current state-of-the-art sample size formulas for continuous longitudinal data, develop an R package that implements these methods to examples that compare treatment versus control groups in randomized trials assessing treatment effect on clinical outcomes. A Shiny app will be developed to assist researchers in obtaining required sample sizes for longitudinal studies by allowing users to enter required pilot estimates. For Alzheimer's studies, the app will estimate required pilot parameters using data from the Alzheimer’s Disease Neuroimaging Initiative (ADNI). Illustrative examples will be used to demonstrate how the app can be used to generate sample size and power curves. The ease and flexibility in the use of the app will significantly aid researchers to optimally perform power analysis for Alzheimer's clinical trials and other related research studies.

(C) A time homogenous multi-state model for modeling transitions in child anthropometric classifications.

Malnutrition among children predisposes them to non-communicable diseases, overweight, and obesity throughout their life course. Anthropometry measures such as Weight-for-Age, Height-for-Age, and Weight-for-Height Z-scores are useful in studying childhood physical development. Monitoring trends of these anthropometry outcomes and assessing risk factors are critical in understanding childhood development. To understand how children transition between different stages or classification of the three anthropometric measures, the continuous outcomes will be classified into four stages, normal, marginal, moderate, and severe, based on the Z-scores. By leveraging on the longitudinal profiles of children's anthropometric outcomes, a time-homogeneous multi-state transition model will be developed to assess the effect of child, mother, and household-level factors on transitions between the stages using data from the Nairobi Health and Demographic Surveillance System (NUHDSS). The novel application of the methodology will enable researchers to establish the important determinants of child growth and nutritional status and develop policies and programs to improve child health and growth in slum settings.