Portnoy (2003) proposes the use of weighted quantile regression to sequentially estimate along the equally spaced grid . You can request this method by specifying the METHOD=KM option in the PROC QUANTLIFE statement. The grid points are equally spaced with specified by the INITTAU= option and the step between adjacent grid points specified by the GRIDSIZE=option.
This method uses a weight function for each censored observation. The weight function is constructed as follows: Let be the first grid point at which and ; otherwise let . When computing the th quantile, assign weight to the censored observation if ; otherwise assign . The algorithm for computing is as follows:
Compute by using the standard quantile regression method.
For , obtain sequentially by minimizing the following weighted quantile regression objective function:

where is the weight for the rightcensored observation at computing , and the complementary weight are for , a large constant that is greater than all .
The weighted quantile regression method is similar to Efron’s redistributionofmass idea (Efron, 1967) for the KaplanMeier estimator.
Note that if all observations are uncensored, is the same as the standard quantile regression estimator.