Skin prick test (SPT) response is often the main outcome used to summarize sensitization to allergens in childhood atopic epidemiological studies. The first study objective was to characterize the development of atopy from patterns of SPT responses using Item Response Theory (IRT) models. In the IRT framework, the latent variable was assumed to be the underlying atopic state, where atopic state refers to the familially related trait of hypersensitivity to environmental allergens and is therefore not directly measured. The Cincinnati Childhood Allergy and Air Pollution Study (CCAAPS), a prospective birth cohort study, provides an ideal population in which to examine longitudinal SPT results. SPTs were performed using a panel of 15 aeroallergens and two foods including: two grass pollens: Timothy and fescue; four tree pollens: white oak, maple mix, American elm, and red cedar; short ragweed; four mold spore extracts: Alternaria alternata, Aspergillus fumigatus, Penicillium mix, and Cladosporium herbarum; four indoor aeroallergens: house dust mite mixture of Dermaphagoids (D.) farinae and D. pterynissinus, German cockroach, cat dander, dog dander; and two foods: milk and egg. A total of 537 children had SPT results available at ages one, two, three, and four, and were included in this analysis. Using IRT modeling, at age one, the highest associations between SPT positivity and atopy were found for indoor allergens, whereas, at age four, the highest associations between SPT positivity and atopy were observed for outdoor allergens. Atopy scores were obtained using the posterior distribution of the latent variable and were used to predict age four allergic symptoms. Atopy scores computed at ages one through four were associated with year four allergic symptoms. This novel modeling approach provides a unique way of assessing atopy based on SPT responses.
The second study objective was to apply two types of transition Markov models, marginalized transition models (MTM) and continuous time Markov models (CTMM), to describe SPT responses during the first four years of life. These models showed the serial dependence of the current outcome on previous outcomes. The estimated first-order coefficient was statistically significant for Alternaria alternata, Cladosporium herbarum, Penicillium mix, dust mite, German cockroach, meadow fescue, red cedar, American elm, maple mix, white oak, and milk. Second-order MTM models were fit for cat, dog, Timothy, and egg based on the score test for a second-order parameter. In these models, both the first-order and second-order coefficients were significant. The MTM models showed no sign of SPT stabilization for all 17 allergens over the four years. The comparison of the MTM and CTMM estimates showed similar results. The CTMM was expanded to include a multivariate response and a simulation experiment was conducted to assess the model. The simulation revealed that the multivariate model did well at capturing the true parameters when the transition probabilities were high. However, the model fails to capture the true correlation between processes when the transition probabilities are low. This study provides a first step in defining a multivariate transition model that is relatively simple to apply using standard statistical software.