Inferences About Exposure-Disease Associations Using Probability-of-Exposure Information

Unconditional and conditional likelihood methods are proposed for modeling odds and odds ratios relating a binary disease variable and an exposure variable that is only known probabilistically (e.g., via measurement of a Surrogate exposure variable), while adjusting appropriately for a vector of covariables. Assuming nondifferential errors, a probabilistic structure is developed that permits analysis of the marginal relation between disease and the Surrogate while maintaining important properties of the marginal relation between disease and true exposure. In particular, analyses conditioned on marginal totals in surrogate–disease tables remove the same nuisance Parameters as are removed in a conditional analysis of true exposure-disease tables. In addition, a relation between the probability of exposure (POE) in the disease and disease-free groups is derived, permitting the use of information about exposure from populations with structure different from the study population. Examples are presented illustrating methods appropriate when the POE values are known or when they must be estimated using partial information on true exposure; in this latter case, the exposure data may be considered to be missing at random.