Figure 3.
Schematic representation of how data are weighted according to an estimand. Suppose the original sample from the single-arm trial differs from the external controls in terms of patient severity, with 1 severe case over 4 in the trial compared with 3 over 4 in the external data. The objective is to modify the pooled data to obtain 2 groups where the proportion of severe cases is similar. Most methods are based on the PS, which is the probability of each patient being in the trial, conditional on their severity. In this setting, each severe case is given a PS of 1/4, whereas each nonsevere case is given a PS of 3/4. IPW consists of inversely weighting each individual in the original sample according to their probability of being in the original group, that is, for the treated, the individual contribution of each patient is divided by their PS (thus resulting in adding 1/3 of a fictive patient for each nonsevere patient and 3 fictive individuals for severe cases), while in the external group, this value is divided by 1 minus their PS (thus adding 1/3 of a fictive patient for each severe patient and 3 fictive individuals for each nonsevere case). This yields a weighted sample where the proportion of severe cases is similar in both groups (1/2) and differs from that in both original groups. ATT weights consist of using all individuals from the single-arm trial (weight of 1) and weighting each individual in the external sample by the odds of being in the trial. This results in odds of (1/4)/(3/4) = 1/3 in nonsevere cases and (3/4)/(1/4) = 3 in severe cases, reaching a ¼ prevalence of severe cases in the pooled weighted data set, that is, observed in the originally treated patients from the trial. ATC weights are conversely computed, with a weight of 1 for each patient from the external sample, whereas patients from the single-arm trial are given a weight of (3/4)/(1/4) (severe cases) or (1/4)/(3/4) (nonsevere cases). The resulting prevalence of severe cases is now that of the original external control group, that is, 3/4.

Schematic representation of how data are weighted according to an estimand. Suppose the original sample from the single-arm trial differs from the external controls in terms of patient severity, with 1 severe case over 4 in the trial compared with 3 over 4 in the external data. The objective is to modify the pooled data to obtain 2 groups where the proportion of severe cases is similar. Most methods are based on the PS, which is the probability of each patient being in the trial, conditional on their severity. In this setting, each severe case is given a PS of 1/4, whereas each nonsevere case is given a PS of 3/4. IPW consists of inversely weighting each individual in the original sample according to their probability of being in the original group, that is, for the treated, the individual contribution of each patient is divided by their PS (thus resulting in adding 1/3 of a fictive patient for each nonsevere patient and 3 fictive individuals for severe cases), while in the external group, this value is divided by 1 minus their PS (thus adding 1/3 of a fictive patient for each severe patient and 3 fictive individuals for each nonsevere case). This yields a weighted sample where the proportion of severe cases is similar in both groups (1/2) and differs from that in both original groups. ATT weights consist of using all individuals from the single-arm trial (weight of 1) and weighting each individual in the external sample by the odds of being in the trial. This results in odds of (1/4)/(3/4) = 1/3 in nonsevere cases and (3/4)/(1/4) = 3 in severe cases, reaching a ¼ prevalence of severe cases in the pooled weighted data set, that is, observed in the originally treated patients from the trial. ATC weights are conversely computed, with a weight of 1 for each patient from the external sample, whereas patients from the single-arm trial are given a weight of (3/4)/(1/4) (severe cases) or (1/4)/(3/4) (nonsevere cases). The resulting prevalence of severe cases is now that of the original external control group, that is, 3/4.

Close Modal
This Feature Is Available To Subscribers Only

or Create an Account

Close Modal
Close Modal