In epidemics of infectious diseases such as influenza an individual may have one of four possible final states: prior immune escaped from infection infected with symptoms and infected asymptomatically. setting of an infectious disease transmitted in close contact groups. Assuming the independence between close contact groups we propose a hybrid EM-MCEM algorithm that applies the MCEM or the traditional EM algorithms to each close contact group depending on the dimension of missing data in that group and discuss the variance estimation for this practice. In addition we propose a bootstrap approach to assess the total Monte Carlo error and factor that error into the variance estimation. The proposed methods are evaluated using simulation studies. We use the hybrid EM-MCEM algorithm to analyze two influenza epidemics in the late 1970s to assess the effects of age and pre-season antibody levels on the transmissibility and pathogenicity of the viruses. households PKI-402 each of size = 1 … be the total number of people in the study. The transmission processes in different households are assumed to Rabbit Polyclonal to CSPG5. be independent. Let day be the stopping day of the epidemic. Let indicate the immune status of person = 1 … = 1 for immune and 0 for susceptible. The prior immunity could be due to either vaccination or previous infection. Let and be the binary indicators for the symptom and infection outcomes of individual during the epidemic season. We partition the study population into four possible final states at the end of the epidemic: (1) prior immunity (i.e. = 1 = 0 = 0) (2) susceptible but escaped infection (i.e. = 0 = 0 = 0) (3) symptomatic infection (i.e. = 0 = 1 = 1) and (4) asymptomatic infection (i.e. = 0 = 1 = 0). Individuals with the latter three states are susceptible to the influenza season prior. Let be the vector of covariates associated with individual on day is fully observed for all individuals. Let and be the infection infectiousness and day onset day of person and are not defined. For symptomatic infections we assume that the incubation period (the time from infection to symptom onset) and the latent PKI-402 period (the time from infection to infectiousness onset) are the same; is also the symptom onset day hence. We further assume that all infections whether symptomatic or asymptomatic share the same distributions of the latent period and infectious period and that these distributions are known from empirical studies. One more assumption is that given a fixed duration of the infectious period the infectiousness (i.e. infectivity) level is constant over the infectious period. Let days and longer is days or. Although not observed in general the infection time = (~ Bernolli(is the proportion of individuals with prior immunity and ~ Bernolli(is the probability of being symptomatic given infection. We assume the infection outcomes are generated by a chain binomial model (Yang Longini and Halloran 2007 Each susceptible individual is exposed to the risk of infection from casual contacts outside the household in addition to close contacts with infective household members. The casual contacts are generally not observed and are therefore modeled as exposure to an unknown infection source that is assumed to be identical across the study population. For a susceptible individual the daily unadjusted probability of infection by the unknown source is be the subset of (and on day by be the household of person and 1(is true 0 otherwise). Covariates can be adjusted for by the following logistic models: and PKI-402 are effective counterparts of and that are specific to each person or person-day and and are covariate effects. The probability of person escaping infection during and up to day are respectively = (1?(1? +1)) and is the infectiousness level of asymptomatic cases relative to symptomatic cases. We assume that is known to avoid non-identifiability for small numbers of outcomes. Let = {are fully observed the likelihood contributed by individual is given by = = and all elements of are observed and = = and some or all elements of are not observed. Let = {= 1 … = {= 1 … be the dimension of domain or equivalently the number of possible realizations of = 1 … for household = 1 … = 1 if is empty. For nonempty > 1. The exact scale of depends on the data. For example if of individual of household is the only unobserved quantity in PKI-402 that household then the range of is determined by 1 + ≤ ≤ and = ? here is the.