When predictive covariates for a dichotomous outcome dependent variable are undetectable or unmeasurable for some subjects, a fact in itself that may be of considerable prognostic importance, traditionally such subjects' data are dropped from multiple logistic regression analyses. An alternative analytical algorithm is offered here for such situations. First, a series of multiple logistic regressions are applied to the complete data where covariates are initially coded as dichotomous, e.g., detectable or nondetectable. Then, a second series of logistic regressions are fitted for those subjects for whom a covariate is detectable and measurable with the fully resolved measure as the covariate. Ultimately, all individual model-specific predicted probabilities of the outcome for a subject are combined into a single probability through the proposed "Composite Probability Modelling of Increased Resolution" (CPMIR). When such an analysis was applied to discriminate 133 patients with acoustic tumours from a sample of 133 patients with cochlear disease, using a latency measure of the auditory brainstem response evoked potential as the predictive covariate, CPMIR yielded a superior model chi square to any component model, used the full cohort of patients, and produced the largest area under the ROC curve. This algorithm is offered as a general statistical modelling device.