Bounds for a joint distribution function with fixed sub-distribution functions: Application to competing risks

AUTOR(ES)

Peterson, Arthur V.

RESUMO

This paper gives sharp bounds for the joint survival function G(t1, t2,...,tr) ≡ P(X1 > t1, X2 > t2,...,Xr > tr), and for the marginal survival functions Sj(t) ≡ P(Xj > t), j = 1,2,...,r, when the sub-survival functions Sj*(t) ≡ P(Xj > t, Xj = mink=1,2,...,rXk) are fixed. Theorem 1 gives the bounds for r = 2, and Theorem 2 gives the bounds for general r. Theorem 3 applies the result to the competing risks problem, and presents empirical bounds based on the observations. Finally, an example illustrates the bounds.

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