An evaluation of inverse probability weighting using the propensity score for baseline covariate adjustment in smaller population randomised controlled trials with a continuous outcome

Abstract

Background: It is important to estimate the treatment effect of interest accurately and precisely within the analysis of randomised controlled trials. One way to increase precision in the estimate and thus improve the power for randomised trials with continuous outcomes is through adjustment for pre-specified prognostic baseline covariates. Typically covariate adjustment is conducted using regression analysis, however recently, Inverse Probability of Treatment Weighting (IPTW) using the propensity score has been proposed as an alternative method. For a continuous outcome it has been shown that the IPTW estimator has the same large sample statistical properties as that obtained via analysis of covariance. However the performance of IPTW has not been explored for smaller population trials (< 100 participants), where precise estimation of the treatment effect has potential for greater impact than in larger samples.

Methods: In this paper we explore the performance of the baseline adjusted treatment effect estimated using IPTW in smaller population trial settings. To do so we present a simulation study including a number of different trial scenarios with sample sizes ranging from 40 to 200 and adjustment for up to 6 covariates. We also re-analyse a paediatric eczema trial that includes 60 children.

Results: In the simulation study the performance of the IPTW variance estimator was sub-optimal with smaller sample sizes. The coverage of 95% CI's was marginally below 95% for sample sizes < 150 and ≥ 100. For sample sizes < 100 the coverage of 95% CI's was always significantly below 95% for all covariate settings. The minimum coverage obtained with IPTW was 89% with n = 40. In comparison, regression adjustment always resulted in 95% coverage. The analysis of the eczema trial confirmed discrepancies between the IPTW and regression estimators in a real life small population setting.

Conclusions: The IPTW variance estimator does not perform so well with small samples. Thus we caution against the use of IPTW in small sample settings when the sample size is less than 150 and particularly when sample size < 100.

Keywords: Covariate adjustment; Inverse probability weighting; Propensity score; Randomised controlled trial; Small population; Small sample size.

Fig. 1

Mean treatment effect estimates in adjusted analysis performed by multiple linear regression and IPTW. True treatment effect = 5. In most cases the difference between the IPTW and regression estimate is negligible, therefore the lines are coinciding

Fig. 2

Mean estimated standard error versus empirical standard error of estimated treatment effects in adjusted analysis

Fig. 3

Coverage rates of 95% confidence intervals in adjusted analysis

Fig. 4

Mean bootstrap standard error versus empirical standard error of estimated treatment effects in adjusted analysis

Fig. 5

Propensity score distributions by treatment arm for the ADAPT case study