Chapter 03
Nonparametric Estimation
Define treatment effects through restricted win ratios, average win time, and while-alive loss.
Chapter overview · Full exposition to follow
3.1 Restricted Win Ratio
A restricted win ratio defines win and loss probabilities at a prespecified time horizon, τ. The comparison asks what would happen if each patient’s outcome history were available through that horizon.
\[ \mathrm{WR}(\tau) = \frac{w_{1,0}(\tau)}{w_{0,1}(\tau)} \]
Defining the target at τ does not itself solve censoring. The slides discuss estimation through inverse-probability-of-censoring weighting or imputation, under the assumptions required by those approaches.
3.2 Average Win Time
Rather than summarize only which patient wins at one time, consider the time a patient spends in a more favorable state than a patient from the other group. Integrating that comparison up to τ and taking a population average leads to restricted mean time in favor of treatment (RMT-IF).
The net average win time is the treatment group’s average win time minus the control group’s average win time. It is measured in units of time and can be decomposed by outcome state. For a life–death outcome alone, it reduces to the difference in restricted mean survival time.
3.3 While-Alive Weighted Loss
Death limits the opportunity to accumulate nonfatal events. While-alive methods address this by relating outcome burden to time alive, with the precise estimand depending on the specified loss process and weighting.
The course introduces general while-alive estimands and nonparametric estimation, followed by an HF-ACTION analysis using WA::LRfit(). The interpretation of component weights and the role of survival are essential parts of that analysis.