Targeted Minimum Loss-Based Estimation of a Causal E ect Using Interval-Censored Time-to-Event Data - Interval-Censored-Time-to-Event Data: Methods and Applications - page 218

The minimizer a; m+2;n as the estimated coecient in a logistic re-
gression of binary outcome Y on covariate Q m+1

•

r=0 g rn (a) 1

with off-

Q a m+2;n , fitted on the subset of data for which A(m + 1) =

set logit

a 0;a (m + 1).

•The minimizer a;

k;n , for k 2f1; 2;:::;m + 1g, as the estimated coecient
in a logistic regression of outcome

k+1;n on covariate Q k1

Q a;

r=0 g rn (a) 1
with offset logit Q k;n , tted on the subset of data for which A(k 1) =
a 0;a (k 1).

The minimizer a; •

0;n as the estimated coecient in a logistic regression

of outcome Q a;

1;n on a constant predictor with offset logit Q 0;n , tted on
all available data.

The description of the asymptotic properties of the estimator described above

is identical to that provided for the estimator in Section 8.3. In particular,

confidence intervals may be constructed and tests of hypothesis conducted in

the same fashion as outlined therein.

8.5 Alternative Target Parameters

Thus far, we have been concerned with the estimation of a marginal causal

effect on survival until a fixed time-point. However, investigators may be in-

terested in understanding the causal effect of treatment within strata defined
by baseline covariates. For this purpose, a particularly common and useful

approach to summarizing covariate effects consists of employing a marginal

structural model. The methodology that has been used above may be extended

to produce targeted minimum loss-based estimators of such causal effects. We