How do we understand residual bias in propensity score analysis

[Dennisky]

Dear all, 

When using propensity score analysis methods, how do we understand residual bias, and what are the differences between residual bias and residual confounding?  

Thanks!

[sbxkoenk]

Bias refers to systematic error in how we measure or report data,

while confounding refers to real but misleading associations.
It's very helpful to (be able to) distinguish between biasing and confounding factors in evaluating the true impact of a program or initiative on the desired outcome.

Residual bias occurs when you don't mitigate the bias (in your data) properly. You should try to mitigate information bias, observer bias, losses to follow-up bias, recall bias, sample selection bias.

Residual confounding occurs when a confounder has not been adequately adjusted for in the analysis, for example by using too large age groups in an epidemiological study.

I don't want to get philosophical but confounding is also a form a bias. Confounding is a bias because it can result in a distortion in the measure of association between an exposure and health outcome.

In Causal Inference there can be biasing and confounding factors of course , but don't forget about Treatment , Outcome , Mediators and Colliders.

Ciao, Koen

[Season]

I searched on the web and did not find literature on propensity score matching using the term "residual bias". But there is a bias when using this method. You are highly unlikely to put all factors in the model that creates the propensity score because you may not have the data on every factor you wish to put in the model. So there is a gap between the so-called randomization based on propensity score matching and real randomization that is applied in randomized clinical trials, where every observed and unobserved confounder is balanced between (or among) groups. I think this gap is the residual bias that you referred to.

[Dennisky]

Thank you for your help. In a propensity score-related paper I read before, the concept of residual bias was mentioned.

We once thought this was a term coined by the author, of course, it might also be due to our limited knowledge.

Schuster NA, Rijnhart JJM, Bosman LC, Twisk JWR, Klausch T, Heymans MW. Misspecification of confounder-exposure and confounder-outcome associations leads to bias in effect estimates. BMC Med Res Methodol. 2023 Jan 12;23(1):11. 

[Season · Accepted solution]

I skimmed the article you mentioned for the keyword "residual confounding" and found that it was stated in the context of multivariable regression where one fails to take nonlinear association between the confounder and the outcome into account. This concept was not related to propensity score analysis. Actually, when I first saw your questions, I thought your question regarding "residual confounding" was a bit strange as, to the best of my knowledge, this problem arises in regression instead of propensity score matching. Now that I have seen a clearer explanation, I am more confident on my a priori assessment of where this problem might occur.

As for "residual bias", the article did not provide a clear-cut definition of this concept. I think it might be the bias I mentioned in my earlier post. If you are still unclear or not sure of what this concept means, I think you can contact the corresponding author of this article.

By the way, I searched in the list of references of the article you mentioned and found two research papers that might be helpful:

Adjustment for continuous confounders: an example of how to prevent residual confounding - PubMed

The concept of residual confounding in regression models and some applications - PubMed

[Dennisky]

Thank you for your continuous attention and patient responses

In the following paragraph of the article, we want to explore whether the term 'residual bias' refers to a formal concept or is merely an offhand remark by the author.

“Propensity score matching is not a magic bullet. Whereas RCTs involve actual random treatment assignment, which theoretically should balance all possible pretreatment char- acteristics, even the unmeasured ones, propensity score matching works only with the variables that are collected. Unfortunately, the collected variables are rarely the only variables that could affect treatment assignment, which leaves residual bias. ”    https://www.jtcvs.org/article/S0022-5223(16)00300-7/fulltext 

[Season]

Never mind. I was once in your shoes when I was trying to find answers to my problems and was offered helping hands by others in this Community. I have just won the badge of two years of membership in this Community a couple of minutes ago, reminding me of the time and feelings when I first raised my question in this Community. If you are interested, you can look at my first post in this Community that was about the selection of an optimal tuning parameter in generalized additive models. I spent months on searching for a solution to this problem but ended up in failure on reaching a definite conclusion. I posted my questions here and was informed that there was not a universal solution to the problem I encountered, dismissing the need of any further attempt to conduct more extensive search for it on the Internet. I therefore felt obliged to help others in need when I am the one that can be of some help.

As for your very specific question of whether "residual bias" is an acknowledged and widely used term or not, I am sorry to say that I do not have the expertise to make this judgement because my past research experience did not necessitate the use of this method. I have therefore known only the basics of this method, including its general and superficial rationale and some of its limitations, including the one I mentioned in my earliest reply to this question. Unlike other statistical methods like logistic regression and multiple imputation, I have not yet read a single monograph on this topic and cannot be sure whether it is a term or not. I therefore do not have the expertise to make this judgement. I think you can wait in the Community to see if anybody who knows more on this method than I do answer your question. But it is also likely that you may never get a reply. I suggest that you read some monographs or reviews on this method to see if experts on this topic use the term "residual bias" while waiting for a reply on this Community. I found a few books, you may also look for them by yourself:

Propensity Score Analysis: Statistical Methods and Applications (Advanced Quantitative Techniques in...

Amazon.com: Practical Propensity Score Methods Using R: 9781452288888: Leite, Walter L.: Books

Amazon.com: Propensity Score Analysis: Statistics Methods and Applications (Chinese Edition): 978756...