The RMSTREG Procedure
Inverse Probability Censoring Weighting Estimation
Suppose you can observe the quantities 
, where T is the event time, C is the censoring time, and 
is a p-dimensional vector of covariates. For the ith subject, 
, let 
, 
, and 
be the observed time, event indicator, and covariate vector, respectively.
Assume that 
is a prespecified time point of interest and 
. Let
where 
is the Kaplan-Meier estimate (alternatively, the Breslow estimate) of the survival function of the censoring variable, which is calculated using 
.
Suppose that the following relationship holds for the RMST,
where 
is a smooth and strictly increasing function. Note that another column can be added to 
for an intercept effect.
Under suitable regularity conditions, the regression coefficients 
are estimated by solving the following score function (Tian, Zhao, and Wei 2014):
Let
The sandwich variance estimate of 
is
where 
is the empirical variance-covariance matrix of 
that is given by
where
Estimation with Stratified Weights
Assuming that you have K strata, within each stratum the censoring distribution is homogeneous. For the ith subject, let 
be the stratum indicator. It is more appropriate to use stratum-specific weights in the estimation. For the kth stratum, you compute the Kaplan-Meier estimate 
for the censoring variable by using 
.
For the ith subject, the weight is computed as
The following quantities are also adjusted accordingly in the estimation:
