3.5: Case Control Studies
- Page ID
- 58978
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Many observational studies are based on looking at the current conditions of a population, and tracing back possible causes in the past. For example, a researcher might hypothesize that children who are exposed to domestic violence at home are more likely to be incarcerated later in life. The researcher is interested in comparing the outcomes of children who were not exposed to domestic violence, the control group, to children who were, the treatment group. One way to do this study would be to survey individuals who had been exposed to domestic violence and a similar number of individuals who had not been exposed to domestic violence in their childhood. While this is a perfectly valid method for conducting such a study, there is a practical problem: The percentage of incarcerated individuals is generally quite small, and therefore it is unlikely that any incarcerated individuals will be observed in the study, regardless of whether they were exposed to domestic violence. Hence, the comparison between the two groups would not be useful. One way to solve this problem is to simply observe as many people as is possible. The practical problem with this solution is the expense and time involved. A much better approach is to design the study so that incarcerated individuals are forced to be observed.
For this second approach the researchers could decide to simply interview many individuals who have been incarcerated and several individuals who have not. The researchers could then compare the rate at which individuals who were incarcerated were exposed to domestic violence compared to those individuals who were not incarcerated. In this version of the study, things have been turned around. Instead of comparing rates of incarceration for those who were exposed to domestic violence against those who were not, the researchers would be comparing the rates of domestic violence for those who were incarcerated against those who were not, even though the researchers are still interested in whether exposure to domestic violence affects incarceration rates. This type of study is known as a case-control study.
A case control study is an observational study that observes data about past differences between two groups.
A case control study gathers evidence about the differences between two groups, but in a less direct way than a controlled experiment. Because the assignment of groups is not controlled by the researcher, and the study is therefore observational, the interpretation of case-control studies is less straightforward than a designed experiment (Shadish et al. 2002). Potential confounding factors can present real challenges when interpreting the results of case-control studies. In the example of studying the effect of exposure to domestic violence, the observation that more of the individuals who were incarcerated were exposed to domestic violence could be caused by some other factor associated with both outcomes. For example, it could be the case that children in households that were more exposed to criminal activity are also more likely to experience domestic violence. In this case it could be argued that the exposure to criminal activity early in life could be the cause of higher incarceration rates, and not the exposure to domestic violence. In this case the exposure to domestic violence would also be the result of exposure to criminal activity.