Application of inverse probability weights in survival analysis

Suppose that a researcher is interested in comparing two ‘‘treatments’’—A and B—and how the treatment affects an outcome of interest. The ideal study design would be to conduct a randomized trial where treatment assignment is randomly assigned. The random treatment assignment aims to make the subjects between the two treatments similar, i.e., it aims to balance any differences in baseline characteristics, so that any differences in outcome may be attributed to the treatment. The challenge with randomized trials is that they are typically costly and sometimes impractical. Observational studies are less costly and more practical for researchers. However, even with a well-designed observational study, subjects in different treatment groups are not likely to be comparable with respect to their baseline characteristics. For instance, consider the study discussed in the paper by Farzaneh-Far et al published in this issue comparing the prognostic value of using two different agents in myocardial perfusion imaging. 1 In this case, the two ‘‘treatments’’ of interest are the agents (regadenoson vs adenosine) used to determine the values of summed stress scores (SSS) and the summed difference scores (SDS). It is of interest to test whether the predictive ability of SSS and SDS on the composite outcome of time to cardiovascular death or myocardial infarction will depend on what agent is used. Some of the baseline characteristics in the adenosine group are not similar to those in the regadenoson group, e.g., there is significantly lower percentage of women and higher percentage of smokers and diabetics in the adenosine group. This issue of imbalance if not addressed in the analyses may result in misleading conclusions about the treatment effect due to potential selection bias and possible confounding variables. How then can the data be used to enable a direct, meaningful, and valid comparison between the two treatments when subjects in the two groups are dissimilar? The more traditional method is to include the baseline variables showing significant differences between the treatment groups as covariates in the multivariable regression model that investigates the treatment effect. When a fitted univariate regression model with only treatment as the variable in the model shows significant treatment effect and, after adjusting for the baseline characteristics in a multivariate model, the treatment effect is still significant, then one has stronger evidence to conclude that there is a significant treatment effect. However, in studies where sample sizes may be small relative to the number of unbalanced variables, this method may not work, or worse, may not be appropriate. An alternative method of addressing the issue of imbalance is the use of propensity scores which can overcome some of the shortcomings of the aforementioned method of adjusting using covariates in a regression model. 2,3 Propensity score is defined as the probability of an individual being assigned to one of two treatments given all information (e.g., baseline characteristics) available before assignment. 4 These scores are estimated based on the data collected such that individuals with similar baseline covariates would have similar scores, and vice versa. Thus, individuals with similar propensity scores are comparable except for the treatment assignment. Propensity scores are used in the analyses in different ways: for matching to identify similar subjects between treatment groups; for defining strata based on the scores where one may perform stratified analysis; as a covariate in a regression model; and being used to obtain the inverse probability weights (IPW). The use of IPW in regression modeling, in particular to survival