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Glycyrrhizin for IFN-non responders 137
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APPENDIX
The method of G-estimation by J.M.Robins offers a solution to estimate the causal effect
of the time dependent glycyrrhizin-treatment on the development of HCC, in the presence
of a time-dependent covariate ALT that is both a confounder and an intermediate variable.
G-estimation of the parameter of a nested structural model estimates the expansion or
contraction parameter ψ of the time to event (HCC) due to the exposure to glycyrrhizin
treatment. If, for instance the exponent of -ψ (referred to as E in the text) = 1.20 the time
to HCC is expanded by 20%, corresponding with a benefi cial effect.
Fundamental for this approach is the assumption of no unmeasured confounders. This
means that all covariates infl uencing both the decision to use glycyrrhizin and the HCCfree
survival time should be measured. That means that given the covariates, the decision
to start treatment is independent of the patient’s (possibly counterfactual) HCC-free
survival time under any treatment regime.
A pooled logistic regression analysis over all visits was applied, with glycyrrhizin therapy
at visit k as outcome. This means that each subject contributed with multiple observations,
one for each visit, until development of HCC or censoring. Covariates considered
for inclusion in the model are baseline factors (age, sex, fi brosis stage, ALT and gamma
glutamyltransferase at the start of the study) and the covariate history before visit k
(ALT, glycyrrhizin treatment and concomitant medication at the two visits prior to visit k).
Furthermore the number of weeks since the prior visit and the number of weeks since
the start of the study were included in the model.
The parameter ψ is g-estimated by extending the logistic model with sets of imaginary
(counterfactual) HCC-free survival times, had glycyrrhizin-treatment never been given.
Weights have been calculated to adjust for patients who are lost to follow-up or who are
censored at a second interferon-based treatment.
Data description and annotation:
Ti = Observed failure time for subject i.