ESTIMATING LIFETIME MALNOURISHED PERIOD: A MARKOV CHAIN WITH REWARD APPROACH

Abstract

Malnutrition among women has great consequences on achieving key global developmental targets. Height and age indices calculated as body mass index (BMI) are used to assess the various forms of malnutrition among adult individuals. This study introduces the concept of lifetime malnourished period (LMP), the expected number of years a woman would remain malnourished given that she is currently malnourished, and its measures of variation. The theory of Markov chains with rewards was used to obtain all the moments of the distribution of LMP based on age-speci c mortality rates and proportion of women of reproductive age that are either underweight or overweight using data from Nigeria and 11 neighboring African countries namely; Burkina Faso, Benin, Congo, Cote D'Ivoire, Ghana, Guinea, Liberia, Mali, Niger, Sierra Leone, Togo. The analysis treats malnutrition as a reward with probability equal to the proportion of malnourished women. In this model, the life cycle of an individual was considered to be an absorbing Markov chain with death representing the absorbing state. The individual moves among states ( age classes) with probability of transition (survival probability) pi from age class i to i +1 , and probability of transition qi from age class i to death. At each time the individual moves or remains in a state, a reward rij is accrued, and this reward represents the proportion of underweight or overweight women of reproductive age. The sensitivity and elasticity of all the statistics of LMP to mortality rate is presented. Findings indicate that in Nigeria, at age 15, an underweight woman would remain in that state for about 2.3 years but 5.8 years for overweight. At age 15, an underweight woman with no formal education would remain malnourished for about 3.4 years, higher than the national average, spending more time in her current state than a woman with formal education while an overweight woman with higher education would remain in that state for about 9.3 years. An underweight Nigerian women will remain in her current state longer than women from neighboring African countries considered. A proportional increase in mortality have little e ect on the mean and variance of LMP of Nigerian women. Findings from the study can guide in policy formulation aimed at tackling malnutrition.