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Observational studies are often used to understand relationships betweenexposures and outcomes. They do not, however, allow conclusions about causalrelationships to be drawn unless statistical techniques are used to account forthe imbalance of confounders across exposure groups. Propensity score andbalance weighting (PSBW) are useful techniques that aim to reduce theimbalances between exposure groups by weighting the groups to look alike on theobserved confounders. Despite the plethora of available methods to estimatePSBW, there is little guidance on what one defines as adequate balance, andunbiased and robust estimation of the causal treatment effect is not guaranteedunless several conditions hold. Accurate inference requires that 1. thetreatment allocation mechanism is known, 2. the relationship between thebaseline covariates and the outcome is known, 3. adequate balance of baselinecovariates is achieved post-weighting, 4. a proper set of covariates to controlfor confounding bias is known, and 5. a large enough sample size is available.In this article, we use simulated data of various sizes to investigate theinfluence of these five factors on statistical inference. Our findings provideevidence that the maximum Kolmogorov- Smirnov statistic is the properstatistical measure to assess balance on the baseline covariates, in contrastto the mean standardised mean difference used in many applications, and 0.1 isa suitable threshold to consider as acceptable balance. Finally, we recommendthat 60-80 observations, per confounder per treatment group, are required toobtain a reliable and unbiased estimation of the causal treatment effect.

How balance and sample size impact bias in the estimation of causal treatment effects: A simulation study