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**M2 Medical Epidemiology**

Corrections for confounding. Effect Modification

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**Corrections for Confounding**

Adjusting measures of frequency for confounding Direct rate adjustment Indirect rate adjustment Adjusting measures of association for confounding By stratification Specific vs. Crude association measures Confounding vs. Effect modification Mantel-Haenszel confounder-adjusted odds ratio Fine stratification: matched pairs studies When to use or avoid mantel-Haenszel methods By multivariable statistical modeling Multiple regression models for continuous outcomes Multiple logistic regression models for dichotomous outcomes

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**Specific Vs. Crude Association Measures**

Crude rate, ratio, or proportion: calculated in an overall, heterogeneous population of interest. Specific rate, ratio, or proportion: calculated in a subgroup that shares specific values or levels of some characteristic(s), e.g. age, sex, age and sex. Crude odds ratio (OR) or relative risk (RR): calculated in an overall, heterogeneous population of interest, e.g. OR between smoking and lung cancer in CU. Specific odds ratio (OR) or relative risk (RR): calculated in a subgroup that shares specific values or levels of some characteristic(s), e.g. OR between smoking and lung cancer among CU men (sex-specific), CU year-old men (age by sex specific).

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**Confounding Vs. Effect Modification**

Effect Modifiers When the degree of association between an exposure variable E and a disease outcome D (as expressed by an odds ratio, relative risk or other appropriate parameter), changes according to the value or level of a third variable M, then M is called an “effect modifier” -- because M modifies the “effect” of E on D.

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**Confounding Vs. Effect Modification**

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**Confounding Vs. Effect Modification**

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**Confounding Vs. Effect Modification**

Gender is an effect modifier: it modifies the association between treatment and outcome.

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**Confounding vs. Effect Modification**

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**Confounding vs. Effect Modification**

Gender is an effect modifier: it modifies the relationship between exposure and disease.

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**Confounding vs. Effect Modification**

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**Confounding vs. Effect Modification**

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**Confounding Vs. Effect Modification**

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**Confounding Vs. Effect Modification**

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**Confounding Vs. Effect Modification**

What is effect modification? Different relationships between exposure and disease in subgroups of the population, i.e. different specific measures of association at different levels of a stratification variable. How do you look for it? Stratify the data and Compare stratum-specific association measures to one another What do you do about it? Report the stratum-specific association measures and ignore the crude association measure.

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**Confounding Vs. Effect Modification**

What is confounding? Distortion of an exposure disease relationship by failure to account for a third variable related to both. How do you look for it? Stratify the data and Compare stratum-specific association measures to the crude measure from the pooled data. What do you do about it? Adjust for it! HOW?

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**Mantel-Haenszel Confounder-adjusted Odds Ratio**

An adjusted odds-ratio (analogous to a directly-adjusted rate, but for representing association) Replaces the crude odds-ratio to correct for confounding (just as the adjusted rate replaces the crude rate under similar conditions) As the adjusted rate, is obtained by dividing data into subgroups, that is, by stratifying and reassembling data from the subgroups in a special way

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**Mantel-Haenszel Confounder-adjusted Odds Ratio**

Odds-ratio for a single table=ad/bc Consider stratified data etc.

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**Mantel-Haenszel Confounder-adjusted Odds Ratio**

etc. CRUDE odds-ratio=ad/bc = (ai)(di)/(bi)(ci), where the summations are over all strata. Mantel-Haenszel adjusted odds-ratio=(aidi/Ti)/( bici/Ti), where the summations are also over all strata.

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**Mantel-Haenszel Confounder-adjusted Odds Ratio**

Mantel-Haenszel adjusted odds-ratio=(aidi/Ti)/( bici/Ti), = (a1d1/T1)+ (a2d2/T2)+ (a3d3/T3) + etc divided by (b1c1/T1)+ (b2c2/T2)+ (b3c3/T3) + etc

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**Mantel-Haenszel Analysis**

Crude OR = (210 180)/(120 90) = 3.5

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**Mantel-Haenszel Analysis**

Mantel-Haenszel OR = 197x19/341+13x161/259 Divided by 77X48/341+43x42/259

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**Mantel-Haenszel Confounder-adjusted Odds Ratio**

197x19/341+13x161/259 77X48/341+43x42/259 = 3743/ /259 3696/ /259 = =19.1/18.0=1.06 Compare to Crude OR of 3.5

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**Mantel-Haenszel Analysis: Matched Studies**

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MH OR = 1x1/2 + 0x0/2 + 1x0/2 + 0x1/2 0x0/2 + 1x1/2 + 0x1/2 +1x0/2

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**Mantel-Haenszel Analysis: Matched Studies**

Four types of matched pairs:

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**Mantel-Haenszel Analysis: Matched Studies**

For concordant pairs ad=bc=0, so they contribute nothing to the Mantel-Haenszel odds ratio each count is equal to its expectation, so they contribute nothing to the Mantel-Haenszel test statistic For discordant pairs the Mantel-Haenszel odds ratio simplifies to Number of discordant pairs with case exposed/Number of discordant pairs with control exposed

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**Mantel-Haenszel Methods: When to Use**

When effect modification seems absent or minimal and confounding may be present. Then compare the adjusted OR to the crude OR. If different, confounding is present

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**Mantel-Haenszel Methods: When to Avoid**

Avoid the Mantel-Haenszel or any single summary of association when stratum-specific association measures differ substantially and sample sizes are moderate to large. Report the stratum-specific results. Especially when stratum-specific association measures are in opposite directions, e.g. OR or RR>1 in some strata and <1 in others. In this case, major effects may be missed because positive associations in some strata can be cancelled out by negative associations in other strata. Report the stratum-specific results, perform tests of statistical significance for the effect modification and, if these are positive, look for explanations.

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**Confounding Vs. Effect Modification**

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**Can You Have Both Confounding and Effect Modification?**

Yes. Difficult to see. But in extreme cases is easy to see. Example Crude RR=0.7 RR in men is 2.0 RR in women is 4.0 2 is different from 4, hence EM You are not allowed to use adjustment to summarize (average) the 2 and 4. But you know that the effect is RR >1 in both genders. So, gender has distorted the RR

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