Should you get rid of the nightlight in your child’s room? Quinn et al. 1999 Does the use of nightlights in children cause them to have myopia (nearsightedness)?

Should you get rid of the nightlight in your child’s room? Quinn et al. 1999 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 human subjects research –What is it? What does it do? »Positive and negative confounding –Use of counterfactuals to conceptualize origins of confounding –Definition of/criteria for a “confounder” »Historical -- narrative definitions »Modern -- directed acyclic graphs (DAGs) - “Common causes” are root source of confounding –Use of DAGs to: »Identify what to adjust for »Know what not to adjust for (“colliders”) »How to handle multiple causal pathways –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 research, confounding has 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.

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. 1999 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 the apparent effect of the night light on childhood myopia?

Positive or negative confounding? Child’s Myopia Night Light ? ? Parental Myopia 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: 0.26 - 1.4)

HIV acquisition AZT Use ? ? What is the most important confounder at play here? Age of provider - A Time of exposure - E Age of patient - C Sex of provider - BSeverity of exposure - D

AZT Use ? ? What is the most important confounder at play here? Age of provider - A Time of exposure - E Age of patient - C Sex of provider - B Severity of exposure - D Severity of Exposure HIV Acquisition

AZT Use ? ? Negative or positive confounding? Negative confounding - A Need more information - C Positive confounding - B Severity of Exposure HIV Acquisition

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 or sampling 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 Nights and Myopia  Because we cannot perform the counterfactual ideal (SAME population studied under 2 conditions), we must evaluate TWO distinct populations (exposed to night lights and unexposed) to study the problem Exposed to night lights Exposed to night lights Unexposed to night lights Unexposed to night lights time Other influences Other influences –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 other 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

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 & unexposed) to be “exchangeable” –i.e., identical in the other influences upon them  Whenever the TWO distinct populations are “non-exchangeable”, confounding will occur  Our strategies to manage confounding are attempts to make our populations exchangeable

Why Strive for the Counterfactual? Causal Inference  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 human subjects research  If a relationship is causal, interventions that change the exposure will change the outcome

Counterfactuals  Also known as “potential outcomes” –“Potential” refers to something that could happen (although actually never does)  Useful concept for understanding: –Origins of confounding –Advanced approaches to managing confounding »See BIOSTAT 215

Definition of/Criteria for a Confounder: A History The Narrative Era  Confounding occurs because of mixing between exposures of interest and unwanted extraneous factors. These extraneous factors are termed confounders.  Simplest Definition –A confounder is a variable which is associated with both exposure and disease.  Traditional Definition A confounding factor must: 1. Be associated with the exposure under study in the source population 2. Be a risk factor for the outcome 3. Not be affected by (caused by) the exposure or the outcome  Refined Definition 2. Factor must affect the outcome Sensitive but not fully specific Also not fully specific

The Modern Era: Graphical Confounding occurs if there is a factor C that is a “Common Cause” of both E and D Depicted in a Directed Acyclic Graph (DAG) The Modern Era: Graphical Confounding occurs if there is a factor C that is a “Common Cause” of both E and D Depicted in a Directed Acyclic Graph (DAG) C part of a “non-causal” (aka “biasing”, “backdoor”, “confounding”) path from E to D. D D E E ? ? C C Definition of/Criteria for Confounding: A History C1C1 C1C1 ? ? D D C2C2 C2C2 E E C2C2 C2C2 C1C1 C1C1 ? ? D D E E C3C3 C3C3

Y Y ? ? E E D D Directed Acyclic Graph (DAG) History  Humans have been drawing diagrams to depict relationships since they learned how to write.  Formal rules for such graphs started in the fields of engineering, computer science, & artificial intelligence  Adapted for epidemiology in 1990’s by computer scientist Judea Pearl (father of journalist Daniel Pearl) X X W W  Hashed edge with ? sometimes used to depict relationship under study (purpose of the study)  Other edges placed based on prior causal knowledge Basic Rules  Consist of nodes or vertices (variables) & edges (lines with arrowheads)  “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)

WARNING  S + N text does not follow contemporary rules of DAG depiction (requirement of uni- directional edges, etc.), but we will follow these rules in lecture and in problem sets  We don’t expect to see any two-headed edges (connections) in the problem sets

H H ? ? E E D D Directed Acyclic Graph (DAG) Some more terminology  All nodes immediately caused by another node are called “child” node; the proximal node is called the “parent” K K J J  All nodes along a path with edges in same direction are “descendants”; all proximal nodes are “ancestors” Parent of K and E Descendants of E A A B B C C F F G G L L

Connections Between Variables  Path – any series of edges, regardless of direction, between two nodes (e.g., between E and D) Types of Paths  Directed path – aka “causal” path  Series of edges are all going in the same direction  All edges have a head-to-tail sequence  “one way street”  Depicts a causal relationship  Undirected path – aka “non-causal” path  Any other series of edges between 2 nodes  “Backdoor path” – an undirected path where the initial edge points towards the initial node F F E E C C D D B B E E A A D D H H E E G G D D E E J J K K L L D D

How do we use DAGs? Major Use  For causal/etiologic research: Does E cause D?  Decide what factors to contend with in order to manage (i.e., eliminate or preclude) confounding when investigating the causal relationship between E and D Process  Establish exposure and outcome  Draw all non-causal paths between exposure and outcome  Via either study design and/or analysis, develop a plan that closes (“blocks”) all the non-causal paths  If there remains an association between E and D in your data, this suggests a causal relationship (although measurement error and chance are still possible explanations) ? ? E E D D C C

How do we use DAGs?  For causal/etiologic research: Does E cause D?  Smoking is a “common cause” of matches & lung cancer  Controlling for smoking blocks the non-causal (backdoor) path and unconfounds relationship ? ? Matches Lung Cancer Smoking

How do we use DAGs?  For causal/etiologic research: Does E cause D?  A genetic factor is a “common cause” of multivitamins use & birth defects  Controlling for history of birth defects blocks the non-causal (backdoor) path and unconfounds relationship ? ? Multivitamin Use Birth Defects Genetic Factor (not measured) History of birth defects

How do we use DAGs?  For causal/etiologic research: Does E cause D?  An unmeasured biologic factor is a “common cause” of sexual activity & mortality  Controlling for self-reported general health blocks the non-causal (backdoor) path and unconfounds relationship ? ? Sexual Activity Mortality Biologic Factors (not measured) General Health (self- reported)

Confounding is root source of one type of a non-causal path A Note on Terminology  C is the common cause, but A, B, X, and Z in addition to C are known as “confounders”  Adjusting (e.g., stratifying) for A, B, X, or Z (or C) will block this non-causal path and eliminate confounding  DAGs focus on the process of confounding (and how to eliminate) rather than on confounders per se ? ? E E D D C C A A B B Z Z X X

Attraction of DAGs for Management of Confounding  Abstract: The Traditional Criteria for Confounding 1. Be associated with the exposure under study in the source population 2. Be a risk factor for the outcome 3. Not be affected by (caused by) the exposure or the outcome  More tangible: DAGs –Draw the system –Look for “common causes” of exposure and disease, and their attendant non-causal paths –Control for something on the non-causal path ? ? Multivitamin Use Birth Defects Genetic Factor (not measured) History of birth defects

The Central Challenge in Confounding  DAGs provide the framework  However, to avoid confounding, you need to be a subject matter expert to draw the DAG –(in addition to being a methodologic expert)  Confounding is mainly a substantive rather than statistical issue  Advice: before planning a study, spend several weeks in the library to understand the surrounding system.

Confounding Paths are Not the Only Type of Non-Causal Paths Confounding Paths are Not the Only Type of Non-Causal Paths i.e., DAGs can tell us a lot more about bias

Birth Defects Folate Intake ? ? Should we control for (e.g., stratify) 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 (folate intake is protective against stillbirths)  Stillbirths are associated with birth detects: OR = 15.2  Stillbirths are not on the causal pathway between folate and birth defects  In the past, other investigators have commonly adjusted for stillbirths in analyses. 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 (folate intake is protective)  Stillbirths are associated with birth detects: OR = 15.2  Stillbirths are not on the causal pathway between folate and birth defects Should we adjust for (e.g., stratify) 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? DAGs Identify What Not to Control For Stillbirths are a “common effect” of both 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 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)

Colliders are the common effect of 2 parents Undirected edge (interpret as going either direction). D D E E ? ? M M Colliders are the Basis of the Other Type of Non-Causal Path Collider as part of a backdoor path A A B B ? ? D D E E M M Controlling for a collider induces a numerical relationship between the parents

Conditioning (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. Sum of A+BAB 716 725 734 743 752 761 Die A Sum of A and B ? ? Die B

Subject’s desire to participate in the research study ? ? Exposure Disease What does this DAG depict? Nuisance causal pathway - A Some other answer - E Selection Bias - C Confounding - BMediator variable - D

For Selection Bias to Occur  Need: A person’s selection/retention must be influenced by/associated with BOTH his/her exposure and outcome Selection/ retention Exposure Disease Selection/ retention Exposure Disease Other factors DiseaseExposure Selection/ retention Other factors Disease Selection/ retention Other factors Exposure From Selection Bias Lecture

For Selection Bias to Occur  Need: A person’s selection/retention must be influenced by/associated with BOTH his/her exposure and outcome Selection/ retention Exposure Disease From Selection Bias Lecture  When we analyze data from only subjects who are available to us (either via initial selection or subsequent retention), this is equivalent to conditioning upon their being available  When selection or subsequent retention are influenced by exposure & outcome, selection/retention is a collider  Selection bias comes from conditioning on a collider Conditioning on a Collider = Selection Bias

Conditioning on a Collider Scenarios  Intentional or unintentional activities related to which subjects are selected for or are in retained in a study – “classic selection bias” or  Inadvertent conditioning (via restriction, matching, stratification, etc) on a collider variable by investigator during design or analysis phase of a study –inappropriate management of confounding or  A few other scenarios (e.g., missing data)  Some researchers call anything that involves conditioning on a collider “selection bias” –Hernan et al. Epidemiology 2004 (Optional Reading)

To prevent confounding and selection bias Because DAGS encode both confounding and selection bias, the best advice is:  Keep the causal paths open (unblocked)  Close (i.e., block) the non-causal paths  If you do, all that will remain in your data is causal relationships (measurement error and chance notwithstanding)

Rules for Reading DAGs  A path between E and D is open (unblocked) if –There is no collider or any collider (“common effect”) is adjusted for (or a descendant of a collider is adjusted for). Adjusted for refers to stratification, regression or other techniques. and –all non-colliders are not adjusted for (i.e., left alone)  Open paths mean an association between E and D will be present –Open causal (directed) paths = true causation –Open non-causal (undirected) paths = bias Folate Birth defects Stillbirths ? ? Nightlights Child’s Myopia Parental Myopia ? ?

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

DAGs Force Investigators to First Conceptualize the System Sunlight exposure & melanoma  A college intern is given a dataset and asked to estimate the causal relationship between sunlight exposure and melanoma  He is told to make sure to adjust for everything he can to exclude the possibility of confounding  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 between sunlight exposure and melanoma Sunlight Exposure Melanoma ?

DAGs Force Investigators to First Conceptualize the System Sunlight exposure & melanoma  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 between sunlight exposure and melanoma Sunlight ExposureMelanoma ? Should we adjust for gum chewing in our final inference? Yes - A Need more information - C No - B

DAGs Force Investigators to First Conceptualize the System  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 not in your DAG, don’t control for it. Should we adjust for gum chewing in our final inference? Yes - A Need more information - C No - B

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

? ? E E D D I3I3 I3I3 What if there are many causal (directed) paths? Many different research questions:  What is the TOTAL effect of E on D? –through all causal paths  What is the DIRECT effect of E on D apart from its effect via I 1, I 2, and I 3 ? –discovery of new mechanisms  How much of the effect of E on D is mediated by I 1 (or I 2 ; or I 3 or any combination)? –“mediation analysis” I2I2 I2I2 I1I1 I1I1 I is a mediator (or intermediary) variable

? ? E E D D I3I3 I3I3 What if there are many causal (directed) paths? Many different research questions:  What is the TOTAL effect of E on D? –through all causal paths  Solution: Leave all above paths open and analyze association between E and D I2I2 I2I2 I1I1 I1I1

? ? E E D D I3I3 I3I3 What if there are many causal (directed) paths? Many different research questions:  What is the DIRECT effect of E on D apart from its effect via I 1, I 2, and I 3 ? –discovery of new mechanisms  Solution: Adjust for I 1, I 2, and I 3. –whatever association is leftover can be attributed to direct effect of E on D. I2I2 I2I2 I1I1 I1I1

? ? E E D D I3I3 I3I3 What if there are many causal (directed) paths? Many different research questions:  How much of the effect of E on D is mediated by I 1 (or I 2 ; or I 3 or any combination)? –“mediation analysis” –Solution: Compare total effect (adjust for none of the intermediaries) with effect when adjusting just for I 1 »Difference between analyses can be attributed to I 1 I2I2 I2I2 I1I1 I1I1

Hep B and C virus infection Hep B/C are not “common causes” but they do mediate a nuisance causal path from IDU to mortality Adjusting for Hep B/C blocks the nuisance path IDU 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

? ? E E D D I I What if we adjusted for I?  Adjustment for intermediaries on the causal path of interest will abolish the causal association  Basis for well known advice to not adjust for anything on the causal pathway C C ? ?

See Extra Slides  Example of how research question influences which causal paths to block –CCR5 and AIDS  How DAGs highlight problems that can occur when estimating DIRECT effects –Aspirin and heart disease

Two Reasons to Adjust to Minimize Bias 1. Close a non-causal path generated by a non- collider (confounding) Nightlights Child’s myopia Parental myopia ? ? Child’s Weight Child’s Diabetes Dad’s Income Participation in study Mom’s Education ? ? or by a conditioned-upon collider (selection bias)

Two Reasons to Adjust to Minimize Bias 1. Close a non-causal path generated by a non-collider (confounding) or by a conditioned upon collider (selection bias) Poverty Mortality Poor Diet ? ? 2. Close a direct path which is a nuisance –estimating “direct effect” of E on D, apart from its effect on I

Third Reason to Adjust – For Precision 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)

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 non-causal paths generated by confounding and selection bias –a sufficient number of factors that will enable to block all nuisance 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

Summary  Confounding occurs because we cannot study the counterfactual ideal  Confounding is the result of “common causes” of exposure and disease  DAGs: –best way to visualize/define confounding –also show selection bias –guide us what to control for –and what not to control for »colliders (if we can) »intermediaries of causal paths of interest »variables not on the DAG ! –guide how to handle multiple causal paths –identify potential effect modifiers (next week) –a concrete mechanism by which colleagues can communicate about a problem  Challenge of DAGs is whether we know system well enough to draw the right DAG –Before you start your project, spend a few weeks in the library

Methods to reduce confounding  During study design: »Randomization »Restriction »Matching »Instrumental variables  During study analysis: »Stratified analysis »Multivariable regression models »Propensity scores »Inverse probability weighting

Extra Slides Referred to in Lecture

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. & CHD But if –Assume common cause (e.g., genetic component) –Need other statistical methods, besides conditioning, to resolve (e.g., inverse weighting) Aspirin Coronary Heart Disease (CHD) Platelet Aggregation ? ? Aspirin Coronary Heart Disease Platelet Aggregation ? ? Genetic factors (not measured) Would be incorrect to stratify OR not to stratify for platelet aggregation Cole and Hernan IJE 2002 Ok to stratify for platelet agg.

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 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

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...

Should you get rid of the nightlight in your child’s room? Quinn et al. 1999 Does the use of nightlights in children cause them to have myopia (nearsightedness)?

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Should you get rid of the nightlight in your child’s room? Quinn et al. 1999 Does the use of nightlights in children cause them to have myopia (nearsightedness)?

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Presentation on theme: "Should you get rid of the nightlight in your child’s room? Quinn et al. 1999 Does the use of nightlights in children cause them to have myopia (nearsightedness)?"— Presentation transcript:

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