Case Control Studies ERIC Notebook

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Johns Hopkins University *

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PH.340.601

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Oct 30, 2023

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ERIC at the UNC CH Department of Epidemiology Medical Center Case-Control Studies E R I C N O T E B O O K S E R I E S Case-control studies are used to determine if there is an association between an exposure and a specific health outcome. These studies proceed from effect (e.g. health outcome, condition, disease) to cause (exposure). Case-control studies assess whether exposure is disproportionately distributed between the cases and controls, which may indicate that the exposure is a risk factor for the health outcome under study. Case- control studies are frequently used for studying rare health outcomes or diseases. Unlike cohort or cross-sectional studies, subjects in case-control studies are selected because they have the health outcome of interest (cases). Selection is not based on exposure status. Controls, persons who are free of the health outcome under study, are randomly selected from the population out of which the cases arose. The case-control study aims to achieve the same goals (comparison of exposed and unexposed) as a cohort study but does so more efficiently, by the use of sampling. After cases and controls have been identified, the investigator determines the proportion of cases and the proportion of controls that have been Second Edition Authors: Lorraine K. Alexander, DrPH Brettania Lopes, MPH Kristen Ricchetti-Masterson, MSPH Karin B. Yeatts, PhD, MS ERIC Notebook Second Edition At baseline:  ·Selection of cases and controls based on health outcome or disease status  Exposure status is unknown *Exposure at some specified point before disease onset

ERIC at the UNC CH Department of Epidemiology Medical Center exposed to the exposure of interest. Thus, the denominators obtained in a case-control study do not represent the total number of exposed and non-exposed persons in the source population. After the investigator determines the exposure, a table can be formed from the study data. Measures of incidence in case-control studies In case-control studies the proportion of cases in the entire population-at-risk is unknown, therefore one cannot measure incidence of the health outcome or disease. The controls are representative of the population-at-risk, but are only a sample of that population, therefore the denominator for a risk measure, the population- at-risk, is unknown. We decide on the number of diseased people (cases) and non-diseased people (controls) when we design our study, so the ratios of controls to cases is not biologically or substantively meaningful. However, we can obtain a valid estimate of the risk ratio or rate ratio by using the exposure odds ratio (OR).* Diseased person-years RR = (a/n1)/(c/n2) Case-Control Study OR = (a/c)/(b/d) = (a/b)/(c/d) = (axd)/(cxb) If b and d (from the case-control study) are sampled from the source population, n1 + n2, then b will represent the n1 component of the cohort and d will represent the n2 component, and (a/n1)/(c/n2) will be estimated by (a/b)/ (c/d). Interpreting the odds ratio The odds ratio is interpreted the same way as other ratio measures (risk ratio, rate ratio, etc.). For example, investigators conducted a case-control study to determine if there is an association between colon cancer and a high fat diet. Cases were all confirmed colon cancer cases in North Carolina in 2010. Controls were a sample of North Carolina residents without colon cancer. The odds ratio was 4.0. This odds ratio tells us that individuals who consumed a high fat diet have four times the odds of colon cancer than do individuals who do not consume a high-fat diet. In another study of colon cancer and coffee consumption, the OR was 0.60. Thus, the odds of colon cancer among coffee drinkers is only 0.60 times the odds among individuals who do not consume coffee. This OR tells us that coffee consumption seems to be protective against colon cancer. Types of case-control studies Case-control studies can be categorized into different groups based on when the cases develop the health outcome and based on how controls are sampled. Some ERIC NOTEBOOK PAGE 2 Cases Controls Exposed a b Unexposed c d Odds of exposure among cases = a/c Odds of exposure among controls = b/d Disease No Disease Exposed a n 1 Unexposed c n 2 Cases Controls Exposed a b Unexposed c d OR = 1 Odds of disease is the same for exposed and unexposed OR > 1 Exposure increases odds of disease OR < 1 Exposure reduces odds of disease *Note: Under some conditions, the odds ratio approxi- mates a risk ratio or rate ratio. However, this is not always the case, and care should be taken to interpret odds ratios appropriately. In case-control studies the proportion of cases in the entire population-at-risk is unknown, therefore one cannot measure incidence of the health outcome or disease. The controls are representative of the population-at-risk, but are only a sample of that population, therefore the denominator for a risk measure, the population- at-risk, is unknown. We decide on the number of diseased people (cases) and non-diseased people (controls) when we design our study, so the ratios of controls to cases is not biologically or substantively meaningful. However, we can obtain a valid estimate of the risk ratio or rate ratio by using the exposure odds ratio (OR).* Odds of exposure among cases = a divided by c Odds of exposure among controls = b divided by d RR = (a divided by n1) divided by (c divided by n2) OR = (a divided by c) divided by (b divided by d) = (a divided by b) divided by(c divided by d) = (axd) divided by (cxb) The odds ratio is interpreted the same way as other ratio measures (risk ratio, rate ratio, etc.). OR = 1 Odds of disease is the same for exposed and unexposed OR > 1 Exposure increases odds of disease OR < 1 Exposure reduces odds of disease For example, investigators conducted a case-control study to determine if there is an association between colon cancer and a high fat diet. Cases were all confirmed colon cancer cases in North Carolina in 2010. Controls were a sample of North Carolina residents without colon cancer. The odds ratio was 4.0. This odds ratio tells us that individuals who consumed a high fat diet have four times the odds of colon cancer than do individuals who do not consume a high-fat diet. In another study of colon cancer and coffee consumption, the OR was 0.60. Thus, the odds of colon cancer among coffee drinkers is only 0.60 times the odds among individuals who do not consume coffee. This OR tells us that coffee consumption seems to be protective against colon cancer.

ERIC at the UNC CH Department of Epidemiology Medical Center remained free of the health outcome at the end of follow- up then we call the sampling cumulative density sampling or survivor sampling. Controls cannot ever have the outcome (become cases) when using this type of sampling. In these case-control studies, the odds ratio estimates the rate ratio only if the health outcome is rare, i.e. if the proportion of those with the health outcome among each exposure group is less than 10% (requires the rare disease assumption). Incidence density sampling or risk set sampling When cases are incident cases and when controls are selected from the at-risk source population at the same time as cases occur (controls must be eligible to become a case if the health outcome develops in the control at a later time during the period of observation) then we call this type of sampling incidence density sampling or risk set sampling. The control series provides an estimate of the proportion of the total person-time for exposed and unexposed cohorts in the source population. In these case -control studies, the odds ratio estimates the rate ratio of cohort studies, without assuming that the disease is rare in the source population. Note that it is possible, albeit rare, that a control selected at a later time point could become a case during the remaining time that the study is running. This differs from case-control studies that use cumulative density sampling or survivor sampling, which select their controls after the conclusion of the study from among those individuals remaining at risk. Selecting controls in a risk set sampling or incidence density sampling manner provides two advantages: 1. A direct estimate of the rate ratio is possible. 2. The estimates are not biased by differential loss to follow up among the exposed vs. unexposed controls. For example, if a large number of smokers left the source population after a certain time point, they would not be available for selection at the end of the study – when controls would be selected in a study that uses cumulative density sampling or survivor sampling. This would give the case-control studies use prevalent cases while other case- control studies use incident cases. There are also different ways that cases can be identified, such as using population-based cases or hospital-based cases. Types of cases used in case control studies Prevalent cases are all persons who were existing cases of the health outcome or disease during the observation period. These studies yield a prevalence odds ratio, which will be influenced by the incidence rate and survival or migration out of the prevalence pool of cases, and thus does not estimate the rate ratio. Case control studies can also use incident cases, which are persons who newly develop the health outcome or disease during the observation period. Recall that prevalence is influenced by both incidence and duration. Researchers that study causes of disease typically prefer incident cases because they are usually interested in factors that lead up to the development of disease rather than factors that affect duration. Selecting controls Selection of controls is usually the most difficult part of conducting a case-control study. We will discuss 3 possible ways to select controls: 1. Base or case-base sampling 2. Cumulative density or survivor sampling 3. Incidence density or risk set sampling Base sampling or case-base sampling This sampling involves using controls selected from the source population such that every person has the same chance of being included as a control. This type of sampling only works with a previously defined cohort. In these case-control studies, the odds ratio provides a valid estimate of the risk ratio without assuming that the disease is rare in the source population. Cumulative density sampling or survivor sampling When controls are sampled from those people who ERIC NOTEBOOK PAGE 3

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