Y Sei1 sdSes

where Se(-) is the Kaplan-Meier estimator of the survival function 1 — Fe using the censored residuals {ei,, Si}.

3. Apply ordinary least squares (OLS) to {(¡S(Y°), Zi)}. Update Y = S Z.

4. Stop if Y converges or oscillates. Otherwise, return to step 2.

Incorporating PCR into the Buckley-James algorithm is straightforward, since the calculation of the principal components uses only the matrix of co-variates and is done before any regression models are estimated. A forward stepwise regression using Wald tests (Step-AFT) to enter new variables requires only parameter estimates and standard errors. As described below, we used a nonparametric bootstrap to estimate standard errors of regression parameters estimated using the Buckley-James algorithm. We did not incorporate a penalty term (e.g., AIC or BIC) in the stepwise regression since no theory has been worked out for these penalties in the AFT model.

Incorporating partial least squares into the AFT is more difficult. In [HH05], we have studied replacing step 3 in the algorithm with the partial least squares algorithm originally proposed by [Wol76], leading to an iterative partial least squares algorithm (BJ-PLS). The modified step 3 is:

3. Apply partial least squares with a fixed number K of latent variables on the transformed data {S>(Yio), Zi} with initial values Qo = Z and eo = S(Yo) — n-i11'S(Yo). For k = 1 to K, compute qk and tk. Update

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