Performs hazard rate estimation over a grid of points using a kernel function.

Routine HAZST estimates the hazard function by use of the biweight kernel,

Because a “smoothed” estimate is computed, one generally would use either routine HAZRD or HAZEZ routine to obtain maximum (modified) likelihood estimates of the smoothing parameters α, β, and k. Maximum (modified) likelihood estimates of these parameters are not required, however. A user‑specified grid of points is generated. For each point, the hazard estimate is computed as

where n = NOBS, δi is the i‑th observation’s censoring code (0 = failed, 1 = censored), wi is the i‑th observation’s weight (either 1/(n ‑ i + 1) or ln(1 + 1/(n ‑ i + 1)) depending upon IWTO), and Ks(x ‑ x(i)), the “smoothed kernel”, is as follows:

Here, dik is the distance to the k‑th nearest failure from the i‑th observation. Because of the dik, HAZST requires the computation of matrix H, which contains constants needed to quickly compute dik. Often, H will have been computed in routine HAZRD or HAZEZ. In this case, the parameter IHCOMP should be set to zero and H should be input to HAZST. If H must be computed by HAZST, set IHCOMP = 1.

The following example is a continuation of the example from HAZRD. The data are from Stablein, Carter, and Novak (1981), and involve the survival times of individuals with nonresectable gastric carcinoma. Only those individuals treated with both radiation and chemotherapy are used.