To start with, the case of too many prescribed medicines is examined. Then, the repeated hospitalization due to non-adherence is examined. The contents of this article could be easily extended to other reasons of non-adherence as well. In the presence of a reason, there might exist a number of non-adherent X and a number of adherent, Y patients. Both X and Y is observable in a sample of size n1 with the presence of a reason and in another random sample of size n2 with the absence of a reason. The total sample size is n = n1 + n2. Let 0<Î¦<1 and 0<Ï<1 denote respectively the probability for a reason to exist in a patient and the probability for a patient to be non-adherent to the prescribed medicines. Of interest to the medical community is the trend of the sum, T = X+Y and Z = n-X-Y denoting respectively the total number of non-adherent and adherent patients irrespective of a reason. Hence, this article constructs a bivariate probability distribution for T and Z utilize it to explain several non-trivialities. To illustrate, non-adherence patientsâ€™ data in the literature are considered. Because the bivariate probability distribution is not seen in the literature, it is named as non-adherent bivariate distribution. Various statistical properties of the non-adherent bivariate distribution are identified and explained. An information based hypothesis testing procedure is devised to check whether an estimate of the parameter, Ï is significant. Two closely connected factors for the patients not adhering to the prescribed medicines are examined. The first is a precursor and it is that too many medicines are prescribed to take. In an illustration for the first reason, the probability for a patient not to adhere the medicines is estimated to be 0.78 which is statistically significant. The second is the post cursor and it is that the patients not-adhering to the medicines are more often hospitalized again. In an illustration of the second factor, the probability for the diabetic patients not to adhere the medicines is estimated to be 0.44 which is significant. The statistical power of accepting the true non-adherence probability by our methodology is excellent in both illustrations. A few comments are made about the future research work. Other reasons for the patientsâ€™ non-adherence might exist and they should also be examined. A regression type prediction model can be constructed if additional data on covariates are available. A principal component analysis might reveal clusters of reasons along with the grouping of illnesses if such multivariate data become available. The usual principal component analysis requires bivariate normally distributed data. For the data governed by the non-adherent bivariate distribution, a new principal component methodology needs to be devised and it will be done in a future research article. The contents of this article is the conceptual foundation for such future research work.

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