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The scenario is regarding treatment effect in an observational study (i.e. not randomised): those given the treatment would be more unwell at baseline.

A clinical trials statistician suggested adding in the baseline as a covariate in the regression model. I remember this being acceptable in randomised trials (RCT), but not observational studies (where propensity scores are commonly used).

Can someone please explain:

1) why adding baseline as covariate is not statistically acceptable in observational studies but is in RCTs

2) what other methods are there in addition to PS?

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    $\begingroup$ This linked paper provides both a theoretical explanation and empirical evidence as to how adding a baseline covariate can introduce bias in observational studies. $\endgroup$ – JWilliman Jun 14 '17 at 2:08
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Adding baseline as a covariate is statistically acceptable - or in fact advisable - in observational studies, as well as RCTs. It is typically just not sufficient to ensure valid inference, and adjustment/stratification for propensity scores (or some other methods that try to deal with the non-randomized nature of the comparison - e.g. structural equation models when the choice of treatment can be taken a several occasions) is usually done in addition.

However, there is no reason not to adjust for covariates in the analysis of observational studies and it is in general not an issue, if the baseline was also used in the construction of the propensity score. Adjusting for the baseline after the propensity score adjustment will not so much adjust for the baseline imbalance, but be more for reducing variability (in linear models) or reducing biased estimates of the individual level treatment effect (in generalized linear models with certain link functions).

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  • $\begingroup$ Thank you Bjorn. When you say it is "not sufficient to ensure valid inference," is there a more detailed explanation I can give to this statistician, who was insistent that it is sufficient? (as you can probably tell, I'm not a statistician) $\endgroup$ – bobmcpop Jan 8 '17 at 14:09
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    $\begingroup$ This issues is still controversial even in RCT. If you google "baseline as a covariate" in the first five hits you will find a document about using it in CLTs by the European regulatory authority and a powerpoint presentation by Stephen Senn (a British statistician). Senn has been critical about the use of baseline covariates in his publications (including his books) as well as this powerpoint tutorial $\endgroup$ – Michael R. Chernick Jan 8 '17 at 15:10
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    $\begingroup$ In RCTs randomization on average balances out measured and unmeasured covariates and (for linear models) covariate adjustment is about reducing variation between subjects that is explained by covariates. In observational studies a baseline covariate adjustment gets you at most to one covariate matching between groups in terms of the mean covariate value, but the groups may still differ in important ways that impact end of study outcomes. A more plausible idea is to put all possibly important available covariates in the model, but propensity score adjustments have a better reputation. $\endgroup$ – Björn Jan 8 '17 at 15:11
  • $\begingroup$ Thank you both. @Björn, I've seen people attempt to put all covariates in the model, by adding the propensity score as a covariate. (PS being derived from these covariates.) This model reduction, as I understand, is not how PS is meant to be used. One criticism sounds like it would apply to adding baseline as covariates? $\endgroup$ – bobmcpop Jan 8 '17 at 16:24
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    $\begingroup$ When the sample size allows stratifying (i.e. allowing the nuissance parameters incl. the model intercept to have separate values for each stratum) by e.g. deciles of propensity score is meant to be pretty sensible and one can imideately see how much stronger an assumption a linear propensity score in the model makes. However, adding the baseline to the model in addition to stratifying for the propensity score is entirely sensible and likely to increase power. $\endgroup$ – Björn Jan 8 '17 at 17:07

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