In the presence of competing risks, the WLW model models both the marginal hazard for death and the cause-specific hazard for recurrences [ 19].
The regression coefficient βtreat was set equal to 0.164156, 0.3945684, and 0.721035, to induce a marginal hazard ratio of 1.1, 1.25, and 1.5, respectively.
We examined the impact of four factors on the statistical power function: number of observed events, prevalence of treatment, the marginal hazard ratio, and the strength of the treatment-selection process.
But in randomized studies (where we assume ), when we model the marginal hazard as 12the interpretation of is the hazard ratio between and while c is marginalized.
To provide an understanding of the degree of confounding induced by the different treatment-selection models, we computed the relative bias in the crude estimate of the marginal hazard ratio in the observational data in each of the 9 scenarios with 5000 observed events.
Within each of the five figures there is one panel for each of the nine combinations of the true marginal hazard ratio (1.1 vs. 1.25 vs. 1.5) and the prevalence of treatment (10%% vs. 25%% vs. 50%%).
In Fig. 6 we report marginal (or average) estimates of statistical power across the different values of each of three factors (c-statistic, prevalence of treatment, and marginal hazard ratio).
When c is integrated out, the marginal hazards 2008 for and are not proportional over time, and the MLE of represents an average over time of the log marginal hazard ratios between and (Lin and Wei, 1989).
This process was used as we were unaware of a formula that relates the marginal hazard ratio to the conditional hazard ratio for treatment, characteristics of the distribution of the covariates in the population, and the hazard ratios relating the covariates to the hazard of the occurrence of the outcome.
Second, when the c-statistic was 0.8 and the marginal hazard ratio was low to moderate, then the power of the IPTW analysis tended to be less than that of the RCT design.
