Confounding: Difference between revisions

{{short description|Variable or factor in statisticscausal inference}}

[[File:comparison_confounder_mediatorcomparison confounder mediator.svg|thumb|upright=1.3|Whereas a mediator is a factor in the causal chain (above), a confounder is a spurious factor incorrectly implying causation (bottom)]]

In statistics[[causal inference]], a '''confounder''' (also '''confounding variable''', '''confounding factor''', '''extraneous determinant''' or '''lurking variable''') is a variable that influences both the [[dependent and independent variables|dependent variable and independent variable]], causing a [[Spurious relationship|spurious association]]. Confounding is a [[Causality|causal]] concept, and as such, cannot be described in terms of correlations or associations.<ref name="Pearl 2009">Pearl, J., (2009). [[Simpson's Paradox]], Confounding, and Collapsibility In ''Causality: Models, Reasoning and Inference'' (2nd ed.). New York : Cambridge University Press.</ref><ref>{{cite journal | last1 = VanderWeele | first1 = T.J. | last2 = Shpitser | first2 = I. | year = 2013 | title = On the definition of a confounder | journal = Annals of Statistics | volume = 41 | issue = 1| pages = 196–220 | doi=10.1214/12-aos1058| pmid = 25544784 | pmc = 4276366 | arxiv = 1304.0564 }}</ref><ref name="Greenland Pearl Robbins 1999">{{cite journal | last1 = Greenland | first1 = S. | last2 = Robins | first2 = J. M. | last3 = Pearl | first3 = J. | year = 1999 | title = Confounding and Collapsibility in Causal Inference | doi = 10.1214/ss/1009211805 | journal = Statistical Science | volume = 14 | issue = 1| pages = 29–46 | doi-access = free }}</ref> The existence of confounders is an important quantitative explanation why [[correlation does not imply causation]]. Some [[Causal notation|notations]] are explicitly designed to identify the existence, possible existence, or non-existence of confounders in causal relationships between elements of a system.

because the observational quantity contains information about the correlation between ''X'' and ''Z'', and the interventional quantity does not (since ''X'' is not correlated with ''Z'' in a randomized experiment). It can be shown <ref name="Pearl 1993">Pearl, J., (1993). "Aspects of Graphical Models Connected With Causality,", ''In Proceedings of the 49th Session of the International Statistical Science Institute,'' pp. 391–401.</ref> that, in cases where only observational data areis available, an unbiased estimate of the desired quantity <math>P(y \mid \text{do}(x))</math>, can

which gives an unbiased estimate for the causal effect of ''X'' on ''Y''. The same adjustment formula works when there are multiple confounders except, in this case, the choice of a set ''Z'' of variables that would guarantee unbiased estimates must be done with caution. The criterion for a proper choice of variables is called the Back-Door <ref name="Pearl 1993"></ref><ref name="pearl09-causal-diagrams">Pearl, J. (2009). Causal Diagrams and the Identification of Causal Effects In ''Causality: Models, Reasoning and Inference'' (2nd ed.). New York, NY, USAUS: Cambridge University Press.</ref> and requires that the chosen set ''Z'' "blocks" (or intercepts) every path between ''X'' and ''Y'' that contains an arrow into X. Such sets are called "Back-Door admissible" and may include variables which are not common causes of ''X'' and ''Y'', but merely proxies thereof.

Contrary to common beliefs, adding covariates to the adjustment set ''Z'' can introduce bias.<ref>{{cite web |last1=Cinelli |first1=C.|last2=Forney |first2=A.|last3=Pearl |first3=J.|title=A Crash Course in Good and Bad Controls |url=http://ftp.cs.ucla.edu/pub/stat_ser/r493.pdf |website=UCLA Cognitive Systems Laboratory, Technical Report (R-493) |date=March 2022}}</ref> A typical counterexample occurs when ''Z'' is a common effect of ''X'' and ''Y'',<ref>{{cite journal |last=Lee |first=P. H. |title=Should We Adjust for a Confounder if Empirical and Theoretical Criteria Yield Contradictory Results? A Simulation Study |journal=[[Scientific Reports|Sci Rep]] |year=2014 |volume=4 |pages=6085 |doi=10.1038/srep06085 |pmid=25124526 |bibcode=2014NatSR...4E6085L |pmc=5381407 }}</ref> a case in which ''Z'' is not a confounder (i.e., the null set is Back-door admissible) and adjusting for ''Z'' would create bias known as "[[Collider (epidemiology)|collider]] bias" or "[[Berkson's paradox]]." Controls that are not good confounders are sometimes called [[bad control]]s.

In general, confounding can be controlled by adjustment if and only if there is a set of observed covariates that satisfies the Back-Door condition. Moreover, if ''Z'' is such a set, then the adjustment formula of Eq. (3) is valid.<ref name="Pearl 1993"></ref><ref name="pearl09-causal-diagrams">Pearl, J. (2009). Causal Diagrams and the Identification of Causal Effects In ''Causality: Models, Reasoning and Inference'' (2nd ed.). New York, NY, USAUS: Cambridge University Press.</ref> Pearl's do-calculus provides all possible conditions under which <math>P(y \mid \text{do}(x))</math> can be estimated, not necessarily by adjustment.<ref>{{cite journal | last1 = Shpitser | first1 = I. | last2 = Pearl | first2 = J. | year = 2008 | title = Complete identification methods for the causal hierarchy | journal = The Journal of Machine Learning Research | volume = 9 | pages = 1941–1979 }}</ref>

According to Morabia (2011),<ref>{{cite journal | last1 = Morabia | first1 = A | year = 2011 | title = History of the modern epidemiological concept of confounding | url =http://jech.bmj.com/content/jech/65/4/297.full.pdf | journal = Journal of Epidemiology and Community Health | volume = 65 | issue = 4| pages = 297–300 | doi=10.1136/jech.2010.112565| pmid = 20696848 | s2cid = 9068532 | doi-access = free }}</ref> the word ''confounding'' derives from the [[Medieval Latin]] verb "confudereconfundere", which meant "mixing", and was probably chosen to represent the confusion (from Latin: con=with + fusus=mix or fuse together) between the cause one wishes to assess and other causes that may affect the outcome and thus confuse, or stand in the way of the desired assessment. [[Ronald Fisher|Fisher]] used the word "confounding" in his 1935 book "The Design of Experiments"<ref>FisherGreenland, R.Robins A.and (1935). The design of experiments (pp. 114–145).Pearl</ref> toname="Greenland denoteRobins anyPearl source of error in his ideal of randomized experiment. According to Vandenbroucke (2004)<ref1999">{{cite journal | last1 = VandenbrouckeGreenland | first1 = J. PS. | yearlast2 = 2004Robins | titlefirst2 = TheJ. history of confoundingM. | journallast3 = Soz PraventivmedPearl | volumefirst3 = 47 | issue = 4| pages = 216–224 | doi = 10J.1007/BF01326402 | pmidyear = 124159251999 | s2cidtitle = 198174446Confounding }}</ref>and itCollapsibility wasin [[LeslieCausal Kish|Kish]]<ref>{{cite journalInference | last1doi = Kish | first1 = L | year = 1959 | title = Some statistical problems in research design10.1214/ss/1009211805 | journal = AmStatistical SociolScience | volume = 2614 | issue = 31| pagespage = 328–33831 | doi-access = 10.2307/2089381 | jstor = 2089381free }}</ref> whonote usedan theearly word "confounding" in the modern senseuse of the word, to meanterm "incomparabilityconfounding" ofin twocausal orinference moreby groupsJohn (e.g.,Stuart exposed and unexposed)Mill in an observational study1843.

* An '''operational confounding''' can occur in both [[experiment]]al and non-experimental research designs. This type of confounding occurs when a measure designed to assess a particular construct inadvertently measures something else as well.<ref name=Pelham>{{cite book |last=Pelham |first=Brett |year=2006 |title=Conducting Research in Psychology |location=Belmont |publisher=Wadsworth |isbn=978-0-534-53294-9 }}</ref>

* A '''procedural confounding''' can occur in a laboratory experiment or a [[quasi-experiment]]. This type of confound occurs when the researcher mistakenly allows another variable to change along with the manipulated independent variable.<ref name=Pelham/>

* A '''person confounding''' occurs when two or more groups of units are analyzed together (e.g., workers from different occupations), despite varying according to one or more other (observed or unobserved) characteristics (e.g., gender).<ref>{{cite book |last1=Steg |first1=L. |last2=Buunk |first2=A. P. |last3=Rothengatter |first3=T. |year=2008 |title=Applied Social Psychology: Understanding and managing social problems |location=Cambridge, UK |publisher=Cambridge University Press |chapter=Chapter 4 }}</ref>

Say one is studying the relation between birth order (1st child, 2nd child, etc.) and the presence of [[Down Syndrome]] in the child. In this scenario, maternal age would be a confounding variable:{{cn|date=April 2024}}

Artifacts are variables that should have been systematically varied, either within or across studies, but that waswere accidentally held constant. Artifacts are thus threats to [[external validity]]. Artifacts are factors that covary with the treatment and the outcome. Campbell and Stanley<ref name=C&S2006>{{cite book|last1=Campbell|first1=D. T.|last2=Stanley|first2=J. C.|year=1966|title=Experimental and quasi-experimental designs for research|location=Chicago|publisher=Rand McNally}}</ref> identify several artifacts. The major threats to internal validity are history, maturation, testing, instrumentation, [[Regression analysis|statistical regression]], selection, experimental mortality, and selection-history interactions.

|publisher=[[Cambridge University Press]]}}|isbn=9780521551281

{{Selfref|These sites contain descriptions or examples of confounding variables:.}}