Should you get rid of the nightlight in your child’s room? Quinn et al Does the use of nightlights in children cause them to have myopia (nearsightedness)? Prevalence ratio = Yes, get rid of nightlight - A Need more information - C No, keep nightlight - B

Confounding and Interaction I  Confounding: one of the central problems in observational clinical research –What is it? What does it do? »positive and negative confounding –Use of counterfactuals to conceptualize origins of confounding –Use of causal diagrams (directed acyclic graphs; DAGs) to guide us regarding what to adjust for »“Common causes” are confounders »Which variables are not confounders? (colliders and mediator variables)? »Emphasis on specifying the research question and understanding the underlying biological/clinical/behavioral system »Confounding is a substantive, not statistical issue

Matches and Lung Cancer  A tobacco company researcher believes that exposure to matches is a cause of lung cancer  He conducts a large case-control study to test this hypothesis  Exposure odds ratio = (820/180) / (340/660) = disease odds ratio  OR = 8.8  95% CI (7.2, 10.9)  Should we remove matches from the environment as a means of preventing lung cancer?

Smoking, Matches, and Lung Cancer Stratified Crude Non-SmokersSmokers OR crude OR CF+ = OR smokers OR CF- = OR non - smokers  Stratification produces two 2-by-2 tables  In each stratum, all subjects are homogeneous with respect to smoking  We have stratified, adjusted, controlled, or conditioned for smoking  OR crude = 8.8 (7.2, 10.9)  OR smokers = 1.0 (0.6, 1.5)  OR non-smoker = 1.0 (0.5, 2.0)  OR adjusted = 1.0 (0.5, 2.0)

Confounding: Smoking, Matches, and Lung Cancer  Illustrates how confounding can create an apparent effect even when there is no actual true effect –Can also be opposite: confounding can mask an effect when one is truly present  Proper terminology –In the relationship between matches and lung cancer, smoking is a confounding factor or a confounder –Smoking confounds the relationship between matches and lung cancer  In clinical research, confounding has a very specific meaning

Estes continues to be confounding puzzle Ray RATTO Ray RATTO SHAWN ESTES seemed loath to analyze his own performance last night, for fear that people would see the first three innings and use them to obscure the last four. But that's what made his outing so perfectly Estes-like -- an ongoing argument with himself that he eventually won. Well, an argument in which he held his own and his teammates won for him in the bottom of the ninth. Ramon Martinez lined a game-tying single with two outs, and Jeff Kent followed two batters later with a bases- loaded walk off Juan Acevedo to give the Giants a 2-1 victory against Colorado and move them to within 4 1/2 games of division leader Arizona. It was in many ways an eye-opening victory for a team that hadn't had one of this type for a while.

Submission to NEJM  Finding: “After an initial course of post-exposure prophylactic (PEP) medication following a sexual exposure to HIV infection, gay men reported a decrease in the practice of high-risk behavior over the following year.”  Reviewer: “Perhaps the men simply withheld the real amount of high-risk behavior they had in order to be eligible for future courses of PEP. How do you account for this confounding?”

Stratified Crude Matches Absent Matches Present OR crude OR CF+ = OR matches OR CF+ = OR no matches  OR crude = 21.0 (16.4, 26.9)  OR matches = 21.0 (10.7, 41.3)  OR no matches = 21.0 (13.1, 33.6)  The study is not over!  To be complete, you decide to examine the relationship between smoking and lung cancer independent from the use of matches.

Confounding: Smoking, Matches, and Lung Cancer  What is the effect of matches on the relationship between smoking and lung cancer? Matches have no effect on the relationship  Effect of matches could have been predicted based on the “matches — lung cancer” relationship –Illustrates one important component in the requirements of a confounder (aka a confounding factor) - A confounder must be causally related to the outcome

Confounding: Examples of Magnitude and Direction Stratified (adjusted) Crude (unadjusted) Potential Confounder Absent Potential Confounder Present OR crude OR CF+ OR CF-

Nightlights Let there be light!

Nightlights and Myopia  Quinn et al. Nature 1999  Prevalence Ratio =

 Insert picture with nightlight off Lights are off and the stumbling around begins.

Should you get rid of the nightlight in your child’s room? Quinn et al Prevalence ratio = Yes, get rid of nightlight - A Need more information - C No, keep nightlight - B

Should you get rid of the nightlight in your child’s room? Quinn et al Prevalence ratio = Yes, get rid of nightlight - A Need more information - C No, keep nightlight - B

Nightlights and Myopia  Two subsequent studies found no association and explained the prior result by confounding –Zadnik et al. and Gwiazda et al. Nature, 2000

Child’s Myopia Night Light ? ? How might confounding account for this finding?

Child’s Myopia Night Light Parental Myopia X X Positive or negative confounding? Positive

 Insert picture with nightlight on again Let there be light (again)!

AZT to Prevent HIV After Needlesticks  Case-control study of whether post-exposure AZT use can prevent HIV seroconversion after needlestick (NEJM 1997) Crude OR crude = 0.61 (95% CI: )

AZT to Prevent HIV After Needlesticks Crude OR crude = 0.61 (95% CI: ) Should health care workers take AZT after a needlestick from an HIV-infected patient? Yes - A Need more information - C No - B

HIV AZT Use ? ? What is the confounder? Age - A None of the above - E Experience of provider - C Gender - BRegion of the U.S. - D

HIV AZT Use ? ? What is the confounder? Age - A None of the above - E Experience of provider - C Gender - BRegion of the U.S. - D

HIV AZT Use Severity of Exposure ? ?

HIV AZT Use Severity of Exposure ? ? Negative or positive confounding? Negative - A Positive - B

HIV AZT Use Severity of Exposure ? ? Negative or positive confounding? Negative - A Positive - B

Adjustment for Confounder  Potential confounder: severity of exposure Minor Severity Major Severity Crude Stratified OR crude =0.61 OR adjusted = 0.30 (95% CI: 0.12 – 0.79) Negative Confounding “Confounding by Indication”

Counterfactuals: Conceptualizing Why Confounding Occurs Night lights and myopia  Ideal study: evaluate children exposed to night lights for several years and directly compare them to the SAME children not exposed to night lights –Result (e.g., risk ratio) is called the “causal effect measure” of night lights –Assuming no measurement error, the “causal effect measure” must be true.  However, since time has passed and children are older it is impossible to assess them without night lights  Hence, the ideal is “counterfactual” – contrary to the fact. It is unobservable. It cannot happen. Exposed to night lights Exposed to night lights Unexposed to night lights Unexposed to night lights time Go back in time

Counterfactuals: Conceptualizing Why Confounding Occurs Gender and heart disease  Ideal study: evaluate men for several years for occurrence of heart disease; compare them directly to SAME individuals who are now women  However, you cannot change a man into a woman and you cannot go back in time  The “causal effect measure” is preposterous to consider. It cannot be observed. It is counterfactual. men women time

Counterfactuals: Conceptualizing Why Confounding Occurs Nights and Myopia  Because we cannot perform the counterfactual ideal (SAME population studied under 2 conditions), we must evaluate TWO distinct populations (exposed to a night light and unexposed) to study the problem –Result (e.g. risk ratio): a “measure of association”  The TWO distinct populations may be subject to different influences OTHER than just the night light  If these influences cause the disease under study, any difference in the risk ratio between the SAME population study (effect measure) and the TWO population study (measure of association) is what is known as confounding  Confounding occurs because of these other influences, a mixing of effects Exposed to night lights Exposed to night lights Unexposed to night lights Unexposed to night lights time Other influences Other influences

Striving for the Counterfactual In the real (observable) world  All of our strategies in analytic studies are striving to simulate the counterfactual  We strive for our TWO distinct populations (exposed and unexposed) to be “exchangeable” –i.e., identical in the other influences upon them  Whenever the TWO distinct populations are “non- exchangeable”, confounding will be present  Our strategies to manage confounding are attempts to make our populations exchangeable

Why Strive for the Counterfactual?  Counterfactual ideal would allow certainty in knowing whether a numerical/statistical association between an exposure and outcome is causal  Knowing whether a relationship is causal is the “holy grail” in clinical research  If a relationship is causal, interventions that change the exposure will change the outcome

Back to the Observable (Factual) World: Criteria for Confounding  Confounding occurs because of mixing between exposures of interest and unwanted extraneous factors  Extraneous factors are termed confounders  Classical criteria for a confounder –Must be causally associated with the outcome, or be a surrogate for a causally related variable –Must be associated with the exposure under study, but cannot be caused by the exposure –Must not be on the causal pathway under study (i.e., must not be an intermediary variable)

Y Y ? ? E E D D Causal Diagrams -- DAGs  DAGs = directed acyclic graphs; aka chain graphs  Consist of nodes (variables) and edges (lines or arrows)  “Directed”: all edges have one-way direction which depict causal relationships  “Acyclic”: there is never a complete circle around any node (i.e. no factor can cause itself) X X Z Z W W Research Question: Does E cause D?  Hashed edge with ? sometimes used to depict relationship under study  Other edges drawn based on prior causal knowledge of system  All nodes immediately caused by another node called “child” node; the proximal node is “parent”  All nodes along a path with edges in same direction are “descendants”; all proximal nodes are “ancestors”

Causal Diagrams -- DAGs  Better than the classical criteria for confounding when planning studies and analyses  Frontier of epidemiologic theory  Forces investigator to conceptualize system –Forces the issue about what is known vs unknown  Identifies pitfalls of adjusting and not adjusting for certain variables  WARNING: S + N text does not strictly follow contemporary rules of DAG depiction (requirement of uni-directional edges, etc.), but we will in class and in problem sets

C C ? ? E E D D Confounding in a DAG Confounding occurs if there is a factor C that is a “Common Cause” of both E and D  C is part of a “backdoor path” from E to D  Adjusting/controlling for C closes the backdoor path; eliminates confounding

C C ? ? E E D D Backdoor Paths in a DAG Starting at E, find any edge directed at E and then head away from E. If a series of edges, regardless of direction, lead to D, it is called a backdoor path.

Lung Cancer Matches Smoking ? ? Smoking is a “common cause” of matches and lung cancer. It therefore confounds the relationship (positive CF) Controlling for smoking blocks the backdoor path and unconfounds relationship Smoking is a “common cause” of matches and lung cancer. It therefore confounds the relationship (positive CF) Controlling for smoking blocks the backdoor path and unconfounds relationship RQ: Do matches cause lung cancer?

Birth Defects Multi- vitamin Use History of birth defects ? ? Genetic factor is the “common cause” but cannot be measured or adjusted for Genetic Factor (not measured) Adjusting for history of birth defects, which can be measured, blocks the path between genetic factor and MVI use, and prevents confounding Threat: negative confounding Hernan AJE 2002

Serious Head Injury Use of Helmets in Motorcyclists Safety- oriented Personality (not measured) ? ? Safe Driving Practices Threat: positive confounding Adjusting for safe driving practices, which can (theoretically) be measured, blocks path from safety- oriented personality to head injury

Attraction of DAGs  Abstract: The Classical Criteria for Confounding –Must be causally associated with the outcome, or be a surrogate for a causally related variable –Must be associated with the exposure under study, but cannot be caused by the exposure –Must not be on the causal pathway under study (i.e. must not be a mediator variable)  More tangible: DAGs –Draw the system –Look for “common causes” of exposure and disease Birth Defects Multi- vitamin Use ? ? Genetic Factor (not measured) History of birth defects

The Central Challenge in Confounding  DAGs provide the framework  However, to identify the confounders, you need to be a subject matter expert  Confounding is a substantive rather than statistical issue  Advice: before planning a study, spend several weeks in the library

Sexual Activity ? Mortality RQ: Does sexual activity cause longer lifespan?

Self- reported General Health Unknown biologic factor(s) (not measured) Sexual Activity ? Mortality RQ: Does sexual activity cause greater lifespan?

Ca channel Blockers GI Bleeding ? RQ: Do calcium channel blockers cause GI bleeding?

Coronary Artery Disease Other Meds (e.g., aspirin) Ca channel Blockers GI Bleeding ? RQ: Do calcium channel blockers cause GI bleeding?

Birth Defects Folate Intake ? ? What should we do with stillbirths (spontaneous abortions)? RQ: Does lack of folate cause birth defects?  Stillbirths are associated with folate intake, even among infants without birth defects: OR = 0.50 (protective)  Stillbirths are associated with birth detects: OR =  Stillbirths are not on the causal pathway between folate and birth defects  In the past, other investigators have commonly adjusted for stillbirths in analyses, or have limited analyses to live births. Slone Epidemiology Unit Birth Defects Study Hernan AJE 2002

Birth Defects Folate Intake ? ? RQ: Does lack of folate cause birth defects?  Stillbirths are associated with folate intake, even among infants without birth defects: OR = 0.50 (protective)  Stillbirths are associated with birth detects: OR =  Stillbirths are not on the causal pathway between folate and birth defects Should we adjust for stillbirths? Hernan AJE 2002 Yes - A Need more information - C No - B

Birth Defects Folate Intake ? ? RQ: Does lack of folate cause birth defects?  Stillbirths are associated with folate intake, even among infants without birth defects: OR = 0.50 (protective)  Stillbirths are associated with birth detects: OR =  Stillbirths are not on the causal pathway between folate and birth defects Should we adjust for stillbirths? Hernan AJE 2002 Yes - A Need more information - C No - B

Adjustment for Stillbirths Stillbirth No stillbirth Crude Stratified OR crude = 0.65 (95% CI 0.45 – 0.95) OR adjusted = 0.80 (95% CI: 0.53 – 1.2) Apparent positive confounding Public health implication: No reason for women to supplement diet with folate Slone Epidemiology Unit Birth Defects Study Hernan AJE 2002

Birth Defects Folate Intake Stillbirths ? ? RQ: Does lack of folate intake cause birth defects? Use of DAGs to Identify What is Not Confounding Stillbirths are a “common effect” of both te exposure & disease – not a common cause. Common effects are called “colliders” Adjusting for colliders OPENS paths. Will actually result in bias. It is harmful. Stillbirths are a “common effect” of both te exposure & disease – not a common cause. Common effects are called “colliders” Adjusting for colliders OPENS paths. Will actually result in bias. It is harmful. Hernan AJE 2002 Undirected edge (interpret as going either direction)

Stratifying upon a Collider  A pair of dice (die A and die B)  We know they are independent  What if we stratify upon the sum of the dice?  This is stratifying for a collider –e.g., in stratum where sum = 7  Now, if you know A, you know B  Stratifying has induced a relationship between A and B that otherwise does not exist. Die A Die B Sum of A and B ? ? Sum of A+BAB

Birth Defects Multi- vitamin use Maternal Weight Gain ? ? No common causes for exposure and disease DAGs to Identify What is Not Confounding Maternal weight gain is a collider Adjusting for colliders will OPEN the path. Will actually result in bias. It is harmful. Maternal weight gain is a collider Adjusting for colliders will OPEN the path. Will actually result in bias. It is harmful. Behavioral factors (not measured) Genetic Factor (not measured) Hernan AJE 2002

DAGs Force Investigators to First Conceptualize the System Sunlight exposure & melanoma  A college intern is given a large dataset and asked to estimate relationship between sunlight exposure and melanoma – and he is told to adjust for “everything that is significant”  He analyzes the data and finds that gum chewing is significantly associated with melanoma and significantly associated with sunlight exposure  After adjusting for gum chewing there is an appreciable difference between the crude and adjusted measure of association Sunlight Exposure Melanoma ?

DAGs Force Investigators to First Conceptualize the System Sunlight exposure & melanoma  A college intern is given a large dataset and asked to estimate relationship between sunlight exposure and melanoma – and he is told to adjust for “everything that is significant”  He analyzes the data and finds that gum chewing is significantly associated with melanoma and significantly associated with sunlight exposure  After adjusting for gum chewing there is an appreciable difference between the crude and adjusted measure of association Sunlight Exposure Melanoma ? Should we adjust for gum chewing? Yes - A Need more information - C No - B

DAGs Force Investigators to First Conceptualize the System Sunlight Exposure Melanoma ? Should we adjust for gum chewing?  No.  Based on our a priori understanding of the role of gum chewing (in melanoma), it is more likely that chance – as opposed to truth -- is causing appearance of confounding  Controlling for a variable should only be done if there is a strong a priori subject matter evidence.  i.e., If it is not in your DAG, don’t control for it. Yes - A Need more information - C No - B

Sunlight Exposure Melanoma ? Should we adjust for gum chewing? Gum chewing Outdoor- loving Personality DAG’s make the philosophy of adjusting for “everything” or for “everything that is statistically significant” illogical

Rules for Reading DAGs  A path between E and D is blocked if –a collider (“common effect”) is present, which has not been adjusted for (by stratification, mathematical regression or other techniques) Or –a non-collider is adjusted for  To prevent confounding, block all backdoor paths that are generated from common causes Folate Birth defects Stillbirths ? ? Nightlights Child’s Myopia Parental Myopia ? ?

Rules for Reading DAGs  A path between E and D is open if –A collider (“common effect”) is adjusted for Or –all non-colliders are not adjusted for  Open paths -- aside from those directly under study -- produce bias Folate Birth defects Stillbirths ? ? Nightlights Child’s Myopia Parental Myopia ? ?

What other variables are NOT Confounders?  “Must not be on the causal pathway under study (i.e. must not be a mediator variable)”  A variable that you are conceiving as an intermediate step in the causal path under study between the exposure in question and the disease is not a confounding variable. E E D D factor I Despite being associated with both exposure and outcome, Factor I is not a confounder It is on the pathway under study. I mediates the effect of E on D. I is a mediator (or intermediary) variable Despite being associated with both exposure and outcome, Factor I is not a confounder It is on the pathway under study. I mediates the effect of E on D. I is a mediator (or intermediary) variable

What if we adjusted for I?  Any association between E and D would be blocked E E D D I I

CCR5 and HIV Disease Progression CCR5 (receptor) defect AIDS CD4 count  How should CD4 count be handled in assessing the association between CCR5 defect status and progression in HIV disease to AIDS?  CCR5: the human cellular receptor for HIV –found on CD4 cells  Genetic defects in CCR5 now described - Are genetic defects in CCR5 associated with slower progression to AIDS?  CD4 count potent predictor of time-to-AIDS  CCR5: the human cellular receptor for HIV –found on CD4 cells  Genetic defects in CCR5 now described - Are genetic defects in CCR5 associated with slower progression to AIDS?  CD4 count potent predictor of time-to-AIDS ? ?

CCR5 and HIV Disease Progression CCR5 (receptor) defect AIDS  How should CD4 count be handled in assessing the association between CCR5 defect status and progression in HIV disease to AIDS? ? ? CD4 count

Forces us to specify the research question CCR5 defect Other mechanisms CD4 count; Other mechanisms CD4 count; Other mechanisms AIDS #1: Do CCR5 defects reduce progression to AIDS, irrespective of mechanism? CCR5 defect Low CD4 count AIDS Do not adjust for CD4 count ! High CD4 count CD4 count Do Adjust ! #2: Do CCR5 defects reduce progression to AIDS, independent of their effect on CD4 count? ? ? ? ?

Taylor et al. JAIDS 2003 CCR5 defect Other mechanism #2 ? ? CD4 count AIDS #1 CCR5 defect ? ? AIDS CD4 not adjusted for CD4 count CD4 adjusted for Crude (unadjusted) association: - rate ratio: 0.71 Crude (unadjusted) association: - rate ratio: 0.71 Stratified (adjusted) by CD4 count -rate ratio: 0.93; -Conclude: no mechanism other than via CD4 Stratified (adjusted) by CD4 count -rate ratio: 0.93; -Conclude: no mechanism other than via CD4

Hep B and C virus infection Hep B/C are not “common causes” but they do mediate an extraneous causal path from IDU to mortality; adjusting for Hep B/C blocks the path IDU Early Mortality ? [via bacterial infections] RQ: Does injection drug use (IDU) cause earlier mortality independent of its effect on hepatitis infections? Estimating the “direct effect” of IDU, apart from its effect on hepatitis virus infections

Poor Diet Poverty Mortality ? [access to care] RQ: Does poverty cause early mortality independent of effects on diet? Adjust for diet to remove the extraneous causal pathway

Two Reasons to Adjust 1. Close a backdoor path generated by a non-collider which is a “common cause” (a confounder) 2. Close a direct path which is a nuisance/extraneous –estimating “direct effect” of E, apart from its effect on X (e.g., poor diet) Nightlights Child’s myopia Parental myopia ? ? Poverty Mortality Poor Diet ? ?

Third Reason to Adjust To enhance statistical precision, but only when X is a strong determinant of D E E D D X X ? ? Whether to adjust depends upon the adjustment technique (e.g., regression model)

DAGs point out special issue when estimating direct effects  RQ: Does aspirin prevent CHD in a pathway other than through platelet aggregation –Assumes no common cause of platelet agg. and D Would be correct to adjust But if –Assume common cause (e.g., genetic component) –Need other statistical methods to resolve Aspirin Coronary Heart Disease Platelet Aggregation ? ? Aspirin Coronary Heart Disease Platelet Aggregation ? ? Genetic factors (not measured) Would be incorrect to adjust OR not to adjust for platelet aggregation Cole and Hernan IJE 2002

Practical Implications for Research: When Designing a Study, What Should You Plan to Measure?  Draw the DAG for the system  Measure: –a sufficient number of factors that will enable to block all backdoor paths generated by confounders (“sufficient set of confounders”) –a sufficient number of factors that will enable to block all extraneous direct paths –all known strong determinants of the outcome  If you don’t measure it, you may regret it later  Confounding can be dealt with in the analysis phase of a study but NOT if the factor is not measured

Seeking cause of high Marin cancer rates activists canvass residents to search for trends Thousands of volunteers scattered across Marin County under baleful skies Saturday in an unprecedented grassroots campaign against the region's soaring cancer rate. Armed with surveys, some 2,000 volunteers went door to door in every neighborhood in the county.... The volunteers hope to collect enough money to hire an epidemiologist...

Practical Implications for Research: When Analyzing Data, What Should You Adjust for?  Draw the DAG for the system  Adjust for: –a sufficient number of factors that will enable to block all backdoor paths generated by confounders (“sufficient set of confounders”) –a sufficient number of factors that will enable to block all extraneous direct paths –depending upon the adjustment technique, all known strong determinants of the outcome  Know why you are adjusting for any variable

Methods to reduce confounding  During study design: »Randomization »Restriction »Matching  During study analysis: »Stratified analysis »Multivariable regression models