A Poisson geometric process approach for predicting drop-out and committed first-time blood donors

A Poisson geometric process (PGP) model is proposed to study individual blood donation patterns for a blood donor retention program. Extended from the geometric process (GP) model of Lam [16 Y. Lam, Geometric process and replacement problem, Acta Math. Appl. Sin. 4 (1988), pp. 366–377. doi: 10.1007/BF02007241[Crossref] , [Google Scholar]], the PGP model captures the rather pronounced trend patterns across clusters of donors via the ratio parameters in a mixture setting. Within the state-space modeling framework, it allows for overdispersion by equating the mean of the Poisson data distribution to a latent GP. Alternatively, by simply setting, the mean of the Poisson distribution to be the mean of a GP, it has equidispersion. With the group-specific mean and ratio functions, the mixture PGP model facilitates classification of donors into committed, drop-out and one-time groups. Based on only two years of observations, the PGP model nicely predicts donors’ future donations to foster timely recruitment decision. The model is implemented using a Bayesian approach via the user-friendly software WinBUGS.