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Matching in Case-Control Designs EPID 712 Lecture 13 02/23/00 Megan O’Brien

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Objectives Discuss methods of matching in case-control studies Discuss advantages and disadvantages of matching in case-control studies Discuss methods of analyzing matched case- control data

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Recommended reading: Szklo and Nieto pgs: 40-48 277 314-317 328-331 Further reading: See Rothman and Greenland. Modern Epidemiology

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What is matching? The process of making a study group and a comparison group comparable with respect to extraneous factors (Last JM. A Dictionary of Epidemiology. 3rd Ed. New York, NY: Oxford University Press; 1995) In case-control studies, we match to make cases and controls as similar as possible with regard to potentially important confounding factors

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Types of matching Individual (paired) matching: for each case, one (or more) controls with the relevant characteristics matching the case are chosen –For continuous variables such as age or weight, controls may be selected if they are within a specified range of the control value Example: Age ± 2 years Example: Weight ± 5 pounds

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When matching on a variety of characteristics, including continuous variables, it may be very difficult to individually match on all characteristics Minimum Euclidean distance: identify the individual who is the closest match with regard to all of the variables. –We usually do this using mathematical modeling techniques

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Frequency matching: Controls are selected such that the distribution of the relevant characteristic in the controls is similar to the distribution in the cases Example: If 30% of cases are smokers, then select a control group in such a way that 30% of controls are smokers

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Advantages of Matching May be the best way to control for a strong confounder when there is little overlap of the confounder between the cases and controls –Example: If the cases tend to be older (CHD, prostate cancer) and a random sample of controls would result in a much younger control group, then there may not be much overlap of age between cases and controls –This lack of overlap makes adjustment for confounding difficult. Why? When the confounder is strong, matching increases the efficiency of the study (by decreasing the width of the confidence intervals around an estimate)

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Matching can be a useful method of sampling controls when cases and controls are identified from a reference population for which there is no available sampling frame (list). –Example: Reference population is patients at a clinic or hospital

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Disadvantages of Matching It may difficult (and expensive) to identify a matched control When you match on a characteristic, you create an equal distribution in the cases and controls. Therefore, you cannot examine the association between the matched characteristic and the outcome

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You cannot assess additive interaction between the matching variable and the exposure of interest You must account for matching in the data analysis You may create groups that are no longer representative of the reference population, thus decreasing your ability to generalize your findings

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If you match on a characteristic that is a weak confounder, you may decrease the statistical power of your study If you match on a characteristic that is strongly correlated with the exposure of interest, you may overmatch If you categorize continous variables too broadly, you may still have residual confounding

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Overmatching Overmatching occurs when you match on a variable that is strongly correlated with the exposure of interest By setting the distribution of the matching variable to be equal between cases and controls, you are effectively setting the distribution of the exposure variable to be equal between cases and controls In doing so, you will be unable to detect a difference in exposure between cases and controls

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Residual confounding Occurs when you categorize continuous variables Ex. Create age categories for matching 20-25 25-30 30-35 For each case between 20 and 25, select a control who is also between 20 and 25 Now your cases and controls are comparable with respect to age right?

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Are these two groups really comparable?

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Analysis of matched data Mantel-Haenszel OR (pg. 277) –If we pair-match cases and controls, we keep them in pairs for the calculation of the odds ratio –What combinations will be possible with regard to exposure?

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Concordant pairs: Both case and control are exposed Neither case nor control are exposed Discordant pairs Case is exposed, control is not Control is exposed, case is not What do the concordant pairs tell us? –Nothing We are interested in the discordant pairs

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Note that each cell contains pairs. So the OR is a ratio of the discordant pairs. See pg. 280 for the derivation of this formula. How do you interpret the MH OR? Just as usual.

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Cases are 6.76 times more likely to be exposed than controls.

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Multivariate analysis of matched data Conditional logistic regression (pg. 314) –Use when you have individual matching –Analogous to logistic regression, but the model takes into account the pairing of cases and controls Logistic regression –Use when you have frequency matching –Simply include the matching variables in the model

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