A Bernoulli Mixture Model to Understand and Predict Children Longitudinal Wheezing Patterns
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In this research, we estimate that around 27.99(±2.15)% of the population has experienced wheezing before turning 1 in the United Kingdom. Furthermore, the Bernoulli Mixture Model classification is found to work best with K=4 clusters in order to better balance the separability of the clusters with their explanatory nature, based on a cohort of N=1184. The probability of the group of parents in the jth cluster to say that their children have wheezed during the ith age is assumed P_ij∼Beta(1/2, 1/2), the probabilities of assignment to each cluster is R ∼Dirichlet_K(α), the assignment of the nth patient to each cluster is Z_n | R ∼Categorical(R), and the nth patient wheezed during the ith age is X_in | P_ij, Z_n ∼Bernoulli(P_i,Z_n); where i∈{1,...,6}, j∈{1,...,K}, and n∈{1,..., N}. The classification is then performed through the E-M optimization algorithm. We found that this clustering method groups efficiently the patients with late-childhood wheezing, persistent wheezing, early-childhood wheezing, and none or sporadic wheezing. Furthermore, we found that this method is not dependent on the data-set, and can include data-sets with missing entries.
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