Validation for the Cox Model. Terry M. Therneau Mayo Foundation. Breslow estimates. Exact partial likelihood, страница 7

Score residuals at β = 0 are

SAS returns the unweighted residuals as given above; it is the weighted sum of residuals that totals zero, = 0, likewise for the score and Schoenfeld residuals evaluated at β^ˆ. S also returns unweighted residuals by default, with an option to return the weighted version. Whether the weighted or the unweighted form is more useful depends on the intended application, neither is more “correct” than the other. S does differ for the dfbeta residuals, for which the default is to return weighted values. For the third observation in this data set, for instance, the unweighted dfbeta is an approximation to the change in β^ˆ that will occur if the case weight is changed from 2 to 3, corresponding to deletion of one of the three “subjects” that this observation represents, and the weighted form approximates a change in the case weight from 0 to 3, i.e., deletion of the entire observation.

The increments of the Nelson-Aalen estimate of the hazard are shown in the rightmost column of table 3. The hazard estimate for a hypothetical subject with covariate X^† is Λ_i(t) = exp(X^†β)Λ₀(t) and the survival estimate is S_i(t) = exp(−Λ_i(t)). The two term of the variance, for X^† = 0, are Term1 + d⁰V d:

For β = log(2) and X^† = 0, where k ≡ the variance of β^ˆ = 1/2.153895 this reduces to