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This work aims to theoretically evaluate whether the number k of partitions of a discrete variable X affects the sensitivity Se(X) of a binary health outcome Y. The distribution of variable X was either unknown or the uniform. Thus, two discrete random variables Xk and Xk+1 with k and k+1 partitions, respectively, were considered. In addition, a random variable Y that indicates the actual health status of an individual was also considered. The case of the composite index Tkm which is formed by the sum of m variables Xk j , j = 1,2, . . . ,m either when the distribution of each variable Xk j is unknown or the uniform was also investigated. This work suggests that the sensitivity of an index is a non-decreasing function of the number of partitions, under certain conditions.

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