lecture 5 - Amazon Web Serviceslecturecontent.s3.amazonaws.com/pdf/15025.pdf · Lecture 5 . Section A Effect Modification: Introduction, with Some Examples . 3 Learning Objectives

Effect Modification (Interaction)

Lecture 5

Section A

Effect Modification: Introduction, with Some Examples

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Learning Objectives

n  Define the concept of effect modification, and explain how it is different than confounding

n  Gain exposure to two examples of investigating effect modification as a research question

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Confounding vs. Effect Modification

n  Confounding (Simpson’s paradox) -  The nature of an association can differ substantially in

magnitude (and even direction sometimes) for unadjusted and adjusted comparisons

-  This can occur when An association between an exposure X and a outcome Y can be confounded by another variable Z (or variable Z1, Z2…)

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Confounding vs. Effect Modification

n  Effect Modification -  The nature of an association can differ (sometimes

substantially) across different subpopulations from an overall populations

-  An association between an exposure X and an outcome Y can depend on another variable Z

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n  The relationship between Y and X depends on the value of a third variable Z; This will happen if Z is related the relationship between Y and X (Z may/may not be related directly to X and/or Y)

n  Ignoring a effect modifier can result in estimating one overall Y/X relationship for everyone when separate Y/X relationships for different values of Z better describe the phenomenon under study

X Y

Z

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n  Surgery works much better than drug therapy younger patients; surgery is notably worse than drug therapy for older patients

n  Women need a larger dose of the swine flu vaccine than men to get the same effect

n  An (attempted) picture

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Y

X

Z = 1

What’s Going On?

Y X

Z = 2

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What is the Solution for Effect Modification?

n  Actually, effect modification is not a problem per se: but in order to assess whether there is effect modification , one must look at Y/X associations separately for each level of Z and decide whether at least some of the associations differ . This can be done analytically by -  Stratified analyses -  Regression

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What is the Solution for Effect Modification?

n  Effect modification is a function of “nature” or “circumstance” or “setting”: It is not a function of study design per se, and as such can not be controlled by study design -  However, if you want to be able to estimate separate Y/X

relationship for differing values of Z as part of your initial research plans, may want to design study to be able to estimate these with some desired precision

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BTW…

n  Confounding is not necessary for effect modification to occur

n  Effect modification is not necessary for confounding to occur

n  Some studies will yield Y/X relationships that are not confounded or modified

n  Confounder and effect modification can both occur in a study; if so, interaction trumps confounding

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Example 1: PBC Trial

¢  Between January, 1974 and May, 1984 a double-blinded randomized trial on patients with primary biliary cirrhosis (PBC) of the liver was conducted at the Mayo clinic. A total of 312 patients were randomized to either receive the drug D-penicillamine (DPCA) or a placebo. The main research question was if there was a difference in the risk of death during the follow-up period in the two different treatment groups.

¢  Treatment assignment: randomized What does this mean about potential for :

- confounding by patient sex? - effect modification by patient sex?

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¢  Overall Analysis The relative risk of death for patients on DPCA compared to patients on placebo was 1.06 (0.80 – 1.40)

¢  Could this Y/X (death/treatment) association be confounded by sex?

Necessary Conditions: But (Hopefully) with Randomization

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¢  Overall Analysis The (crude) relative risk of death for patients on DPCA compared to patients on placebo was 1.06 (0.80 – 1.40) This was based on comparing the proportion who died in the DPCA group to the proportion dying in the placebo group.

However, numerator and denominator should be similar in terms of male/female composition, so this ratio should not be distorted by an imbalance

FMMMFFFFFFFFMMMFFFFFFF

==placebo died, proportion DPCAdied, proportion

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¢  Overall Analysis: The (crude) relative risk of death for patients on DPCA compared to patients on placebo was 1.06 (0.80 – 1.40)

¢  Adjusted Analysis: The sex-adjusted relative risk of death for patients on DPCA compared to patients on placebo was 1.05 (0.81 – 1.37 ) Conclusions, thus far: DPCA not associated with better/worse patient survival, and this estimated is not confounded by sex distribution differences in the DPCA/placebo groups (ie: randomization worked w/respect to sex, and hopefully many other questions)

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¢  Potential Nagging Question The relative risk of (RR) death for patients on DPCA compared to patients on placebo was 1.06 (0.80 – 1.40) : But should we estimate the same overall relationship between death and DPCA for men and women? Could the treatment could affect mortality differently for men and women? The question asked is about a possible interaction between sex and treatment.

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¢  Sex-specific (stratified) estimates of Y/X (death/DPCA) relationship

Females: RR 1.00 (0.73, 1.35) Males: RR 1.25 (0.71, 2.20)

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¢  Summary The (crude) relative risk of death for patients on DPCA compared to patients on placebo was 1.06 (0.80 – 1.40)

The sex-adjusted relative risk of death for patients on DPCA compared to patients on placebo was 1.05 (0.81 – 1.37)

Sex-specific (stratified) estimates of Y/X (death/DPCA) relationship

Females: RR 1.00 (0.73, 1.35) Males: RR 1.25 (0.71, 2.20)

¡  Conclusions?

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¢  Conclusions?

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Example 2: Tree Damage Data

n  Data on elevation and percentage of dead or badly damaged trees, from 64 Appalachian sites (reported by Committee on Monitoring and Assessment of Trends in Acid Deposition, 1986)

n  Eight of the 64 sites are in Southern states

n  Study Design?

n  Scatterplot of percent of damaged trees on elevation

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Tree Damage Data

n  Scatterplot of percent of damaged trees on elevation with trend (regression line: percent damage regressed on elevation)

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Tree Damage Data

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500 1000 1500 2000Elevation (Meters)

(unadjusted) slope =0.01 (-0.02, 0.03)

n  Scatterplot of damage by elevation with points labeled by region

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Tree Damage Data

n  Scatterplot of damage by elevation with points labeled by region

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Tree Damage Data

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Tree Damage Data

n  Southern region trees are at higher elevation

n  Southern region trees have less damage -  Damage related to elevation -  Damage related to region -  Elevation related to region

n  Possible diagram of scenario

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n  Scatterplot with unadjusted trend line (percent damage regressed on elevation) and trend line adjusted for region (plotted separately for N and S regions)

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Tree Damage Data

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n  Scatterplot with unadjusted trend line (percent damage regressed on elevation) and trend line adjusted for region (plotted separately for N and S regions)

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Tree Damage Data


(adjusted) slope =0.06 (0.03, 0.08)

(adjusted) slope =0.06 (0.03, 0.08)

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n  Does it make sense to estimate on overall Y/X Damage/elevation) relationship for N and S after adjusting for region?

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Tree Damage Data

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n  What if we separate estimate trend lines (percent damage on elevation) by region?

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Tree Damage Data

n  Unadjusted trend line and region-specific trend lines (percent damage on elevation)

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Tree Damage Data

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n  Unadjusted trend line and region-specific trend lines (percent damage on elevation)

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Tree Damage Data

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slope for Northern sites=0.09 (0.06, 0.12)

slope for Southern sites=-0.02 (-0.06, 0.02)

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Tree Damage Data: Recap, Conclusions

n  Overall (unadjusted) slope of damage on elevation with 95% CI 0.01 (-0.02, 0.03)

n  Region adjusted slope of damage on elevation with 95% CI 0.06 (0.03, 0.08)

n  Slopes of damage on elevation by region, with 95% CIs South: -0.02 (-0.06, 0.02)

North: 0.09 (0.06, 0.12)

n  Conclusions?

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Summary

n  Effect Modification (Interaction) occurs when the relationship between two variables, Y and X, depends on the level of a third variable Z

n  Effect modification can only be ascertained by looking a separate estimates (and CIs) for the Y/X relationship by different levels of Z

n  Comparing unadjusted and adjusted Y/X relationships, adjusted for Z, can be used to assess confounding, but not to assess effect modification

Section B

Effect Modification: More Examples of Investigating Effect Modification

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Learning Objectives

n  This lecture section will give more examples of effect modification and/or the processes used to investigate effect modification.

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Example 1: 2011 Article from AJE

n  Similar Relation of Age and Height to Lung Function Among Whites, African Americans, and Hispanics1

From Abstract:

Current guidelines recommend separate spirometry reference equations for whites, African Americans, and Mexican Americans, but the justification for this recommendation is controversial. The authors examined the statistical justification for race/ethnic-specific reference equations in adults in the Third National Health and Nutrition Examination Survey (1988–1994) and the Multi-Ethnic Study of Atherosclerosis Lung Study (2000–2006). Spirometry was measured following American Thoracic Society guidelines. “Statistical justification” was defined as the presence of effect modification by race/ethnicity among never-smoking participants without respiratory disease or symptoms and was tested with interaction terms for race/ethnicity (× age and height) in regression models.

1 Kiefer EM, Hankinson JL, Barr DL. Similar Relation of Age and Height to Lung Function Among Whites, African. Americans, and Hispanics. American Journal of Epidemiology 2011;173:376–387

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n  Similar Relation of Age and Height to Lung Function Among Whites, African From Abstract

There was no evidence of effect modification by race/ethnicity for forced expiratory volume in 1 second, forced vital capacity, or the forced expiratory volume in 1 second/forced vital capacity ratio among white, African-American, and Mexican-American men or women on an additive scale or a log scale. Interaction terms for race/ethnicity explained less than 1% of variability in lung function. The mean lung function for a given age, gender, and height was the same for whites and Mexican Americans but was lower for African Americans.

Study Design?

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Example 2: 2008 Article from NEJM

n  Rosuvastatin to Prevent Vascular Events in Men and Women with Elevated C-Reactive Protein2

The researchers randomized 17,800 healthy (without a history of cardiovascular disease) men and women with non-elevated LDL cholesterol levels to either 20 mg of statins daily, or placebo. Subjects were followed for up to 5 years. At the end of the follow-up period the study results include the following: Of the 8900 subjects randomized to the statins group, 142 developed cardiovascular disease. Of the 8900 subjects randomized to the placebo group, 251 developed cardiovascular disease.

2 Ridker P et al.. Rosuvastatin to Prevent Vascular Events in Men and Women with Elevated C-Reactive Protein. New England Journal of Medicine 2008;359 (21):2195 – 2207.

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n  Rosuvastatin to Prevent Vascular Events in Men and Women with Elevated C-Reactive Protein

Unadjusted Incidence Rate Ratio of CVD in follow-up period (statins to placebo)

95% CI (0.46 – 0.69)

n  Authors did not report adjusted incidence rate ratio despite other characteristics association with CVD: sex, age, smoking… WHY NOT?

56.0ˆ ≈RIR

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n  Nevertheless, the authors did investigate interactions between characteristics and statins

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n  Nevertheless, the authors did investigate interactions between characteristics and statins: from results:

The rates of the primary end point were 0.77 and 1.36 per 100 person-years of follow-up in the rosuvastatin and placebo groups, respectively (hazard ratio for rosuvastatin, 0.56; 95% confidence interval [CI], 0.46 to 0.69; P<0.00001)

Consistent effects were observed in all subgroups evaluated. The rosuvastatin (statins) group did not have a significant increase in myopathy or cancer but did have a higher incidence of physician-reported diabetes.

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n  Plasma Enterolignan Concentrations and Colorectal Cancer Risk in a Nested Case-Control Study3

“Enterolignans are biphenolic compounds that possess several biologic activities whereby they may influence carcinogenesis. The authors investigated the association between plasma enterolactone and enterodiol and colorectal ancer risk in a Dutch prospective study. Among more than 35,000 participants aged 20–59 years, 160 colorectal cancer cases were diagnosed after 7.5 years of follow-up (1987–2003). Cohort members who were frequency-matched to the cases on age, sex, and study center were selected as controls (n = 387).”

3 Anneleen K et al.. Plasma Enterolignan Concentrations and Colorectal Cancer Risk in a Nested Case-Control Study. American Journal of Epidemiology 2008;167 (6):734 -742

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n  Plasma Enterolignan Concentrations and Colorectal Cancer Risk in a Nested Case-Control Study

“Plasma enterodiol and enterolactone were not associated with risk of colorectal cancer after adjustment for known colorectalcancer risk factors (highest quartile vs. lowest: for enterodiol, ( odds ratio = 1.11, 95% confidence interval :0.56, 2.20 (p-trend = 0.75); for enterolactone, odds ratio = 1.70, 95% confidence interval: 0.88, 3.27 (p-trend 0.15)). However, sex (p-interaction = 0.06) and body mass index (p-interaction < 0.01) modified the relation between plasma enterolactone and colorectal cancer risk; increased risks were observed among women and subjects with a high body mass index.”

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Example 4: 2011 article from JAMA

n  Association of Race and Age With Survival Among Patients Undergoing Dialysis4

4 Kucircka K, et al. Association of Race and Age With Survival Among Patients Undergoing Dialysis. Journal of the American Medical Association. (2011) 306;6.

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Example 4

n  Methods Section Excerpts

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Example 4


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Example 4


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Example 4

n  Close-up of Table 2

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Summary

n  Effect modification occurs when the relationship between two quantities, Y and X, depends on the level of a third quantity, Z

n  Effect modification cannot be ascertained by comparing unadjusted (crude) and adjusted estimates

n  The investigation of effect modification requires the analyst to compared separate estimates of the Y/X association for different levels of the third quantity Z

Section C

Confounding versus Effect Modification: A Review

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Learning Objectives

n  This lecture section will reinforce the difference between confounding and effect modification in terms of: -  The phenomena -  How to investigate each -  Implications with regards to designing studies

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Confounding

n  Confounding is a possibility in non-randomized studies (and with small probability, in randomized studies)

n  Confounding of a two variable relationship (Y and X) can occur if a third factor Z (or factors Z1, Z2,..) are related to both Y and X

n  Confounding results in a distorted estimate (increased or decrease) of the Y/X relationship via the crude association

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Effect Modification

n  Effect Modification is a possibility regardless of the study design: the potential for effect modification is not minimized by randomization

n  Effect modification for two variable relationship (Y and X) can occur if a third factor Z is related to the association between Y and X

n  Ignoring/not investigating effect modification may result in estimating one overall Y/X association when separate, group specific estimates may be more appropriate

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Confounding: Assessment

n  Confounding can be controlled for in the estimation process: an adjusted Y/X association can be estimated, adjusted for a measured potential confounder(s): We will soon learn that multiple regression methods allow for adjustment.

n  Confounding can be assessed (as well as degree of confounding) by comparing the crude (unadjusted) Y/X association, and the resulting confidence interval, to the adjusted Y/X association and its confidence interval

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Effect Modification: Assessment

n  Effect modification can be investigated in the estimation process as well: separate Y/X associations can be estimated for separate values of a potential effect modifier. We will soon learn that multiple regression methods allow for this kind of analysis.

n  Effect modification can be assessed (as well as degree of effect modification ) by comparing the separate Y/X associations (and 95% CIs) across the values of a potential effect modifier; multiple regression will allow for a formal (hypothesis) test of interaction

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Confounding: Study Design Considerations

n  Certainly, the potential for confounding can be minimized by designing a randomized study

n  However, much research can only be done observationally: as such, confounding is a possibility

n  Potential confounders of the key relationships must be conceptualized before the start of the study, and must be measured as part of the study (this is ideal)…

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Confounding: Study Design Considerations

n  Associations can be adjusted for potential confounders that have been measured

n  An observational study can match exposed and unexposed subjects (for the exposure of primary interest) with similar potential (baseline) confounder values at the start of the study, as well

n  The difficulty with observational studies is that the only factors that can be adjusted for, are those that are measured as part of the study: there is always the nagging issue of “missed confounders”

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Effect Modification: Study Design Considerations

n  The potential for effect modification is not affected by study design

n  However, it is best to have a sense of any potential effect modifications of interest prior to designing a study. This will -  Limit the number of investigations done once the data is

collected (researchers will not “drive themselves crazy” looking at all possibilities

-  Allow for the study design to be powered to detect an effect modification of interest with a certain level of power

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Tree Damage and Elevation: Findings, n=64

n  Overall (unadjusted) slope of damage on elevation with 95% CI 0.01 (-0.02, 0.03)

n  Region adjusted slope of damage on elevation with 95% CI 0.06 (0.03, 0.08)

n  Slopes of damage on elevation by region, with 95% CIs South: -0.02 (-0.06, 0.02) (n=8)

North: 0.09 (0.06, 0.12) (n=56)

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Tree Damage and Elevation: Findings, n=64

n  This study was not designed to estimate precise damage/elevation estimates separately, by region

n  However, were another researcher interested in designing a follow-up study to better (more precisely) quantify regional differences in the Damage/Exposure association, he/she could design a study with enough observations from each region to detect a difference in the associations of a certain amount with high power

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lecture 5 - Amazon Web Serviceslecturecontent.s3.amazonaws.com/pdf/15025.pdf · Lecture 5 . Section A Effect Modification: Introduction, with Some Examples . 3 Learning Objectives