M-2 Epidemiology



M-2 Epidemiology

Understanding Confounding and Effect Modification

1. In the text Chapter 1 question 4 is a bad question for which there is no definite answer.

2. Recap Confidence Intervals

If a 95% CI does not include the null then all the following are true

■ The p-value is less than 0.05.

■ The data are not compatible with the null hypothesis at the 0.05 level of significance.

■ The null hypothesis is rejected.

■ The results are statistically significant at the 5% level.

If a 95% CI does include the null then all the following are true

■ The CI includes the possibility of NO EFFECT (i.e. Null)

■ The data are compatible with the null hypothesis at the 0.05 level of significance.

■ The null hypothesis is not rejected.

■ The results are not statistically significant at the 5% level.

■ The p-value is more than 0.05.

Note :

■ The null value is 1 for RR, OR, or Hazard Ratio, but zero for AR or differences between means),

■ The 99% CI is wider than the 95% CI.

■ If the 95% CI includes the null then the 99% CI will definitely include it.

■ If the results are significant at the 1% level then they are also significant at the 2%, 5% etc.

■ If the results are significant at the 5% level they might not be significant at the 1% level.

■ If the 95% CI for RR does not include 1.0, the 99% might.

Determinants of power

Before conducting a study, we can predict its power for detecting clinical important effects. We do this by

■ Estimating baseline probability. That is the probability of the event in the control group.

■ Determining an effect size that’s important to detect and realistic.

■ Choosing a standard of evidence-alpha.

■ Estimating biological and measurement variability from existing relevant literature and/or preliminary studies.

■ Specifying the sample size.

■ Choosing a tentative statistical analysis plan.

3. Definition of confounder

A confounder is:

1. Associated with the exposure

2. Statistically associated with outcome (risk factor) independent of the exposure

3. Not necessarily a cause of the outcome

4. Not a result of the exposure. Example: Moderate alcohol consumption protects from coronary disease (OR =0.56). It is well established that moderate alcohol consumption CAUSES an increase in HDL and that increased HDL protects from CAD. HDL is NOT a confounder.

So what to do if a factor is associated with the outcome but IS a RESULT of the exposure? Should we ever adjust for it?

Even though you know that HDL is not a confounder you can still intentionally “adjust” for it, for a very specific reason - to find out if alcohol’s protective effect is “totally’ mediated through HDL. If it is, the association between alcohol and CAD will disappear. (That does not mean that HDL was a confounder or that you should adjust for it when assessing alcohol’s effect on CAD risk.) If the association between alcohol and CAD is not totally mediated through HDL then some of the association will remain after adjusting for HDL

You may read something that looks like this:

“It has been postulated that alcohol’s coronary protective effect is mediated by raising HDL. When the association between alcohol and CAD was adjusted for HDL level the OR for moderate drinking increased from 0.56 to 0.77 but remained significant.”

Interpretation:

HDL explains some but not all of alcohol’s coronary protective effect.

Some of the protective effect of alcohol (23% reduction in CAD [OR of 0.77]) is independent of its effect on HDL.

Alcohol offers more protection (total OR 0.56 meaning 44% protection) through its effect on raising HDL.

Some of the protective effect is mediated (not confounded) by HDL

Both HDL and alcohol are truly and independently associated with decreased coronary events.

4. Effect Modification versus confounding

When the degree of association between an exposure variable E and a disease outcome D

(as expressed by an odds ratio, relative risk etc.), 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.

What is effect modification?

Different relationships between exposure and disease in subgroups of the population. For example: Hypertension increases risk for stroke. But the increase is more in the black versus white population. Thrombolytics decrease risk of death in someone with an acute MI who does not have a brain hemorrhage, but increases risk of death in someone with an acute MI who also has a brain hemorrhage. Thus all “contraindications” of a drug are effect modifiers because the drug is good for you if you don’t have a contraindication, but bad for you if you do. In clinical trials “subgroup analysis” looks at subgroups to see if the drug works better (or not as good, or is harmful) in subgroups according to variables like age, sex, coexisting disease. If there is a difference by sex, that is to say the drug works better in men or in women then sex is an effect modifier. In regression analysis the term for effect modification is “interaction” .

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. Effect modification is not an artifact of the data or a fluke of your study. It is a fact of nature and needs no “adjustment” or “correction”. It needs to be reported as such.

If there is no effect modification the stratum specific OR’s will be similar to each other. If they are different than the crude OR then there is confounding. That is to say the crude OR is distorted by that variable. As we did in age adjustment, we would like to summarize all these strata OR’s into one OR that is not distorted

5. The Mantel-Haenszel adjusted odds-ratio

Is used to summarize the stratum specific OR’s to correct for confounding (when there is no effect modification). (If there is EM we do not summarize the strata. We keep the strata separate.)

CRUDE odds-ratio = ad/bc

Mantel-Haenszel adjusted odds-ratio= numerator/denominator

Numerator = a1d1/t1 + a2d2/t2 + etc

Denominator = b1c1/t1 + b2c2/t2 + etc

6. Regression

Is the most commonly used tool to deal with confounders and effect modifiers. Multiple linear regression is used when the outcome is continuous (example blood pressure). Multiple logistic regression is used when the outcome is dichotomous (life versus death, disease versus no disease). (Most of our class so far dealt with the dichotomous type outcomes.) In regression the variable you are interested in and all other variables associated with the outcome are entered into the equation. Thus each is adjusted for all the others. This way, none of those variables will be able to distort (confound) the others. There is no difference between how the primary exposure that you are interested in and any of the other factors are treated in regression. Usually the factors are added into the equation one at a time. Each time a variable is added the ( (coefficient) for all the others may change. Whenever a ( of a variable gets close to zero that variable is taken out. That means this factor is not truly independently associated with the outcome. Whatever association there seemed to be was caused by a confounder. You may see something that reads like this: “There were 10 factors significantly associated with the outcome in univariate analysis. In multivariate analysis only factors 1-5 remained significant.”

Interpretation:

■ Factors 1-5 are truly associated with the outcome.

■ Factors 6-10 are not independently associated with the outcome.

■ Factors 6-10 were confounded by factors 1-5.

■ ( for factors 6-10 became 0 after adjustment for factors 1-5.

How does regression deal with effect modification?

Let’s go back to the first example. Hypertension increases risk for stroke. But the increase is more in the black versus white population. Race itself is associated with the risk of stroke. Blacks have a higher risk. But that difference in risk between races is more pronounced in individuals with hypertension. That is to say both of these factors- race and hypertension- increase the risk of stroke. But, when they occur together there is an interaction that causes their effect to be more than would be expected if there were no interaction. In a regression equation both factors will show up individually, but there will also be an “interaction” term that predicts what happens when they occur together.

Multiple Logistic Regression

You have seen how multiple linear regression predicts your blood pressure if you provide values for all the variables that are known to affect your blood pressure. Multiple logistic regression predicts a dichotomous outcome if you provide values for all the variables that are known to affect the risk for that outcome. But what exactly does it predict? It predicts the natural log of the odds of that outcome. Not the probability and not even the odds but the natural log of the odds. If the exposure is also dichotomous (like exposed versus unexposed) then the ( for that factor is the natural log of the odds ratio.

7. Propensity Scores

Regression deals with confounders by including all factors associated with the outcome. But to determine if a factor is associated with an outcome we need enough outcomes in those exposed and those unexposed. If there are not enough “events” regression cannot be used. If you remember, a confounder has to be associated with both the exposure and the outcome. We can look for confounders by looking at variables associated with the exposure. A typical example is in non randomized assessment of a drug. The exposure is the drug versus no drug and the outcome is mortality. The possible confounders are all factors associated with the use of the drug and also associated with mortality. Age may be associated with the use of the drug. (For example, if it is used long term to deal with a risk factor like cholesterol, it is likely it will not be used much in very old people.) And age is obviously associated with mortality. So we definitely want to adjust for age. Typically we use regression to determine if age is associated with the outcome. If the outcome is rare we cannot use regression. We can instead look to see if there is an association between age and the exposure (the use of the drug). We can repeat this for other factors until we find all the factors associated with the use of the drug. These factors are then used to classify patients according to probability (propensity) of receiving the drug. The patients are grouped by quintile of increasing probability (propensity) of receiving the drug, the 1st quintile least likely, the 5th most likely. Patients within each quintile will be similar in their likelihood to receive the drug. So, they are similar to each other with regard to all the confounding variables. Within each quintile we compare those who received the drug to those who did not with regard to the outcome.

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