A Markov jump process approach to modeling blood donor status: Donor retention and attrition rates at a blood service center in Zimbabwe

Abstract

Background: Blood service agencies depend upon the availability of regular blood donors for sustainability. The knowledge and understanding of the stochastic behavior of donors is the first step toward sustaining the blood supply. Analyzing the changes in the donor status within the donor pool will help the blood service authorities to manage the blood donation process.

Objectives: The study presents a multistate Markov jump model in analyzing the changes in blood donor status during their blood donation career. Relevant covariates are used to aid in explaining the transitions.

Materials and methods: The status of a blood donor i that can be in one of four states S = {1; 2; 3; 4}. A new donor (s = 1), repeat/regular donor (s = 2), occasional donor (s = 3), and lapsed donor (s = 4). A Continuous-time Markov model was used to estimate blood donor progression during their blood donation career. Frequencies of blood donations made in a given time interval determines the state occupied.

Results: In the early years of blood donation career, first-time donors have a higher likelihood of becoming regular donors. Donor attrition increases with time whilst donor retention decreases with time. The results show that when the jump process is currently in an occasional state, the probability that it moves into lapsed state when it leaves the occasional state is given as 69.06%. Similarly, donors are forecasted to spend 21.193 months (1.8 years) in the occasional state before lapsing. Repeat donors can spend 39.342 months (3.3 years) in the regular state before the transition to other states. The study established that donor-specific demographic factors such as age and gender are critical in donor status transitions.

Conclusions: With the passage of time, donor status evolves, with trend inclined towards reduction in the frequency of blood donations as more donors become inactive or lapsed. The transition of donors in various states can be described by a time homogeneous Markov model.

Keywords: Kolmogorov's forward equations; Markov jump process; blood donor status; continuous‐time Markov model; multistate model; retention and attrition rates.