Estimating Transition Probabilities Using Repeated Cross-sectional Data
28 Pages Posted: 24 Apr 2024
There are 2 versions of this paper
Estimating Transition Probabilities Using Repeated Cross-sectional Data
Estimating Transition Probabilities Using Repeated Cross-Sectional Data
Date Written: April 19, 2024
Abstract
Estimating transition probabilities using cross-sectional data is challenging due to the lack of state-to-state transitions over time for each observed individual. We propose a five-state Markov model (health, disabled, chronically ill, chronically ill and disabled, and dead) to calculate one-year transition probabilities using widely available general population mortality rates and annual prevalence rates derived from cross-sectional data. This results in an underdetermined system of transition probabilities which we solve by adding a set of mathematical relations between the unknown transition probabilities. We calculate annual prevalence rates and population mortality rates from five independent cross-sectional datasets from the Australian Survey of Disability, Ageing, and Carers (SDAC) and the Human Mortality Database, respectively. We use multinomial logistic regression to smooth the raw annual prevalence rates, accounting for age, gender, and time trends to remove noise. Finally, we graduate the estimated transition probabilities using the Whittaker-Henderson smoothing technique to remove the impact of data sampling fluctuations. The results show that the average occupancy probabilities across different states are highest between ages 65 − 74 and decline with advancing age for both genders. A healthy individual is more likely to transition to a chronic illness state than to become disabled. Conversely, a disabled individual is more likely to develop both chronic illness and disability than a chronically ill individual is to become disabled. A healthy individual is more likely to experience both chronic illness and disability than a disabled individual is to develop a chronic illness. Our proposed framework can enhance the development of longevity products in many countries because it relies on readily available population-level mortality and prevalence data to calculate transition probabilities.
Keywords: Disability, cross-sectional data, transition probabilities, prevalence rates, multiple-state model, long-term care, and longevity.
JEL Classification: C21
Suggested Citation: Suggested Citation