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A usual goal in health research is to examine the relationship between a specified disease outcome and exposure to a given agent or condition. In certain settings, however, the true exposure status for each individual may not be available. Instead, a Probability-Of-Exposure (POE) for each individual may be considered. This research introduces a modified logistic model (MLM) that can be used to estimate the exposure-disease (E-D) relationship when individual POE values are the only exposure data available. Various forms of the MLM are suggested, several of which allow for consideration of covariate information. Two alternative methods based on application of the usual logistic model to the data under certain exposure assumptions are also considered. Application of the MLM to three small samples of exploratory data shows that the parameter estimates are influenced by sampling error in the POE measure. In order to further investigate this finding and observe how the MLM and the alternative models perform in various analysis settings, the MLM, the two alternative models, and th