Estimation of Dynamic Diarrhea Effects on Childhood Growth with Latent Subgroup

Childhood is a critical period for physical and cognitive development. Childhood diarrhea is not only associated with high mortality and morbidity rate, its complication can also lead to long term growth faltering.
Existing studies treat diarrhea effect on growth as constant over time, or assume diarrhea effect is the same across the population. Diarrhea episodes have different clinical severity, and the resulting growth shortfalls may not be the same. Under this rationale, we propose a semi-parametric model with latent subgroup to estimate the heterogeneous dynamic diarrhea effect. To accommodate subject differences, natural growth and diarrhea effect are treated as random effect curves and the mixture distributional assumption is adopted. The latent subgroup designation in the mixture model will help explain individual characteristics such as household socioeconomic status, hygiene level and other driving factors behind diarrhea. Parameter estimate and has been developed using the Expectation-Maximization algorithm. Asymptotic variance of the estimator is studied.
Simulation study shows that our model achieves simultaneous identification of subgroups in growth and diarrhea vulnerability and estimation of growth patterns and effect curves. The estimator variance is also validate by empirical coverage probability. The proposed models are applied to the data from NIH cohort study collected from children in Bangladesh. Results show that the diarrhea effect on children’s HAZ score peaks at around 400 days with a decrease of HAZ -0.12, and will leave long-term growth loss for 85% of the cohort. Overall, our model provides new statistical tools to quantify the dynamic pattern of childhood growth and diarrhea affects, which helps us make better health policy and conduct more efficient interventions.