Calculation of prevalence estimates through differential equations: application to stroke-related disability.

BACKGROUND: Neurological diseases now make up 6.3% of the global burden of disease mainly because they cause disability. To assess disability, prevalence estimates are needed. The objective of this study is to apply a method based on differential equations to calculate the prevalence of stroke-related disability. METHODS: On the basis of a flow diagram, a set of differential equations for each age group was constructed. The linear system was solved analytically and numerically. The parameters of the system were obtained from the literature. The model was validated and calibrated by comparison with previous results. RESULTS: The stroke prevalence rate per 100,000 men was 828, and the rate for stroke-related disability was 331. The rates steadily rose with age, but the group between the ages of 65 and 74 years had the highest total number of individuals. DISCUSSION: Differential equations are useful to represent the natural history of neurological diseases and to make possible the calculation of the prevalence for the various states of disability. In our experience, when compared with the results obtained by Markov models, the benefit of the continuous use of time outweighs the mathematical requirements of our model.

Calculation of prevalence with Markov models: budget impact analysis of thrombolysis for stroke.

OBJECTIVES: The objective is to develop a method for calculating the prevalence of stroke based on Markov models and to apply it to the assessment of the budget impact analysis of thrombolytic treatment. METHODS: A Markov model was used to reproduce the natural history of stroke. The first step was to run the model to build the sojourn matrix from the initial population vector. The second step was to ascertain the number of individuals in the origin of each annual cohort. Finally, prevalence figures were obtained, validated, and used to calculate the impact of treatment with thrombolysis in 10% of patients with stroke in the Basque Country as if thrombolysis had begun in 2000 and would continue to 2015. RESULTS: Stroke prevalence rates per 100,000 for the entire population are 898 for men and 686 for women, with a combined rate of 774 for men and women. Rates for stroke-related disability are 358 per 100,000 for men, 275 for women, and 309 for men and women combined. If 10% of the stroke patients would have received thrombolytic treatment from 2000 to 2015, the number of disabled in 2015 would be reduced by 328, and the net savings for the Basque society (2,100,000 inhabitants) would be 1.7 million euro. CONCLUSIONS: The budget impact analysis of thrombolysis for stroke starting in 2000 shows a positive impact on the health budget because it saves costs after 2006 and produces a net benefit in health from the beginning of treatment.