STATISTICS AND RESEARCH DESIGN
Case-control studies: Part 1 Nikolaos Pandis, Associate Editor of Statistics and Research Design Bern, Switzerland, and Corfu, Greece
I
n a case-control study, a group of subjects from a specified study population who have the outcome of interest (the cases)—eg, patients with temporomandibular joint (TMJ) pain—is identified, and a control group is then identified of those without the outcome of interest (the controls). Information is then collected from the cases and the controls on their past exposure or exposures. This information can be taken from sources such as interviews and medical records. Then the numbers of exposed and unexposed subjects within the cases and controls are compared; if there are important differences, then the exposure might be a risk factor for the disease. A diagrammatic representation of a case-control study is shown in the Figure. The case-control design and method of analysis were developed to investigate risk factors for diseases with long latent periods, when implementation of cohort studies is impractical. A classic example is the casecontrol study on the association between smoking and lung cancer. A relevant example could be the examination of the association between TMJ pain and trauma from a blow to the chin, or TMJ pain and orthodontic therapy. Cases and controls can be identified, and their exposure to trauma or orthodontic therapy ascertained. If the odds of exposure to trauma (or orthodontic therapy) are higher in the TMJ pain group, then an association between the exposure and the outcome might be implied. Tables I and II show the results of this hypothetical casecontrol study. Remember that the odds are defined as the number of exposed divided by the number of unexposed for the case and control groups. In these tables, we can see that the odds of exposure are 3 (600/200) among the cases and 1.125 (900/800) among the controls. The odds ratio is a measure of relative risk and is usually calculated by dividing the odds of exposure among the cases by the odds of exposure among the controls (3/ 1.125 5 2.67) or, less commonly, 1.125/3 5 0.375. At the end of Table I, a statistical test indicates that we
Am J Orthod Dentofacial Orthop 2014;146:266-7 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.05.021
266
have a statistically significant finding (c2 [1] 5 10.46 Pr . c2 5 0.001). However, whether trauma is a risk factor will depend on bias, the distribution of other factors (confounding), and whether the relationship is causal. Important measures should be taken during the identification and selection of the cases and especially the controls. The controls should be selected from the group of people who would have been considered for selection as cases if they had developed TMJ pain during the study period. In addition, the selection of controls should be unrelated to trauma (the exposure under investigation); this means that the controls should represent the exposure history of the population from which the cases are selected. Consider the following scenario in which patients with TMJ dysfunction are selected from a hospital in an affluent society and the controls are selected from “similar” patients from a hospital in a neighborhood of lower socioeconomic status. Now, the question is whether this control group would be appropriate for this study with the selected cases. Would the controls have been considered as study cases if they had developed TMJ dysfunction? Do the controls represent the population from which the cases came? The control group is not representative of the population from which the cases came, because patients in the low-income area might encounter more violence and chin trauma compared with patients from the high-income area clinic; therefore, the association between trauma and TMJ dysfunction would be underestimated. To clarify further, if the controls were selected from an area with a higher trauma prevalence, then the numbers exposed to trauma between the cases and the controls would be artificially diluted (underestimated). In case-control studies, the cases and the controls can differ appreciably in baseline characteristics and exposures other than the exposure of interest. To reduce the probability of an association between the exposure and the outcome of interest because of differences between the cases and controls in terms of baseline characteristics, multivariate analysis [at the analysis stage] and matching [at the design stage] are potential solutions. Matching could be applied at the group or individual level. Group matching means that the proportion of participants in terms of some important characteristics is
Statistics and research design
267
Fig. Diagrammatic presentation of a case-control study.
Table I. Distribution of exposed and unexposed subjects among the cases and controls
Table II. Calculation of the odds in exposed and unex-
posed subjects and odds ratio of exposed vs unexposed
Exposed to trauma TMJ syndrome Cases
Yes 600
No 200
Total 800
Controls Total
900 1500
800 1000
1700 2500
c2 (1) 5 10.46, Pr . c2 5 0.001.
similar between the cases and controls. For example, 60% of the cases and 60% of the controls are women, or 40% of the cases and 40% of the controls reside in a poor or an affluent neighborhood. In individual matching, each case is matched with at least 1 (usually up to 4) similar control in terms of some important outcome predictors. Up to 4 controls can be used per case to gain efficiency (study power). Selecting too many variables for matching is likely to make it difficult to recruit the required controls. Finally, the variables on which matching is performed cannot be assessed for association with the outcome, since we have produced artificially equal proportions of the matching characteristics between the cases and controls. Also, too many matching variables might result in overmatching, with no association
Odds Odds ratio
Exposed 600/200 5 3
Unexposed 900/800 5 1.125
Point estimates 3/1.125 5 2.67
between exposure and outcome. It is best to keep matching parameters to a minimum and confine them to parameters associated with the outcome for which there is no interest to further explore the association (between exposure and outcome).1 In the next article, I will discuss bias and the advantages and disadvantages of case-control studies. KEY POINTS
1. 2.
Case-control studies are easier to conduct compared with cohort studies. Selection of controls in case-control studies is difficult.
REFERENCE 1. Gordis L. Epidemiology. 4th ed. Philadelphia: Saunders Elsevier; 2009.
American Journal of Orthodontics and Dentofacial Orthopedics
August 2014 Vol 146 Issue 2
Case-control studies: Part 1 Nikolaos Pandis, Associate Editor of Statistics and Research Design Bern, Switzerland, and Corfu, Greece
I
n a case-control study, a group of subjects from a specified study population who have the outcome of interest (the cases)—eg, patients with temporomandibular joint (TMJ) pain—is identified, and a control group is then identified of those without the outcome of interest (the controls). Information is then collected from the cases and the controls on their past exposure or exposures. This information can be taken from sources such as interviews and medical records. Then the numbers of exposed and unexposed subjects within the cases and controls are compared; if there are important differences, then the exposure might be a risk factor for the disease. A diagrammatic representation of a case-control study is shown in the Figure. The case-control design and method of analysis were developed to investigate risk factors for diseases with long latent periods, when implementation of cohort studies is impractical. A classic example is the casecontrol study on the association between smoking and lung cancer. A relevant example could be the examination of the association between TMJ pain and trauma from a blow to the chin, or TMJ pain and orthodontic therapy. Cases and controls can be identified, and their exposure to trauma or orthodontic therapy ascertained. If the odds of exposure to trauma (or orthodontic therapy) are higher in the TMJ pain group, then an association between the exposure and the outcome might be implied. Tables I and II show the results of this hypothetical casecontrol study. Remember that the odds are defined as the number of exposed divided by the number of unexposed for the case and control groups. In these tables, we can see that the odds of exposure are 3 (600/200) among the cases and 1.125 (900/800) among the controls. The odds ratio is a measure of relative risk and is usually calculated by dividing the odds of exposure among the cases by the odds of exposure among the controls (3/ 1.125 5 2.67) or, less commonly, 1.125/3 5 0.375. At the end of Table I, a statistical test indicates that we
Am J Orthod Dentofacial Orthop 2014;146:266-7 0889-5406/$36.00 Copyright Ó 2014 by the American Association of Orthodontists. http://dx.doi.org/10.1016/j.ajodo.2014.05.021
266
have a statistically significant finding (c2 [1] 5 10.46 Pr . c2 5 0.001). However, whether trauma is a risk factor will depend on bias, the distribution of other factors (confounding), and whether the relationship is causal. Important measures should be taken during the identification and selection of the cases and especially the controls. The controls should be selected from the group of people who would have been considered for selection as cases if they had developed TMJ pain during the study period. In addition, the selection of controls should be unrelated to trauma (the exposure under investigation); this means that the controls should represent the exposure history of the population from which the cases are selected. Consider the following scenario in which patients with TMJ dysfunction are selected from a hospital in an affluent society and the controls are selected from “similar” patients from a hospital in a neighborhood of lower socioeconomic status. Now, the question is whether this control group would be appropriate for this study with the selected cases. Would the controls have been considered as study cases if they had developed TMJ dysfunction? Do the controls represent the population from which the cases came? The control group is not representative of the population from which the cases came, because patients in the low-income area might encounter more violence and chin trauma compared with patients from the high-income area clinic; therefore, the association between trauma and TMJ dysfunction would be underestimated. To clarify further, if the controls were selected from an area with a higher trauma prevalence, then the numbers exposed to trauma between the cases and the controls would be artificially diluted (underestimated). In case-control studies, the cases and the controls can differ appreciably in baseline characteristics and exposures other than the exposure of interest. To reduce the probability of an association between the exposure and the outcome of interest because of differences between the cases and controls in terms of baseline characteristics, multivariate analysis [at the analysis stage] and matching [at the design stage] are potential solutions. Matching could be applied at the group or individual level. Group matching means that the proportion of participants in terms of some important characteristics is
Statistics and research design
267
Fig. Diagrammatic presentation of a case-control study.
Table I. Distribution of exposed and unexposed subjects among the cases and controls
Table II. Calculation of the odds in exposed and unex-
posed subjects and odds ratio of exposed vs unexposed
Exposed to trauma TMJ syndrome Cases
Yes 600
No 200
Total 800
Controls Total
900 1500
800 1000
1700 2500
c2 (1) 5 10.46, Pr . c2 5 0.001.
similar between the cases and controls. For example, 60% of the cases and 60% of the controls are women, or 40% of the cases and 40% of the controls reside in a poor or an affluent neighborhood. In individual matching, each case is matched with at least 1 (usually up to 4) similar control in terms of some important outcome predictors. Up to 4 controls can be used per case to gain efficiency (study power). Selecting too many variables for matching is likely to make it difficult to recruit the required controls. Finally, the variables on which matching is performed cannot be assessed for association with the outcome, since we have produced artificially equal proportions of the matching characteristics between the cases and controls. Also, too many matching variables might result in overmatching, with no association
Odds Odds ratio
Exposed 600/200 5 3
Unexposed 900/800 5 1.125
Point estimates 3/1.125 5 2.67
between exposure and outcome. It is best to keep matching parameters to a minimum and confine them to parameters associated with the outcome for which there is no interest to further explore the association (between exposure and outcome).1 In the next article, I will discuss bias and the advantages and disadvantages of case-control studies. KEY POINTS
1. 2.
Case-control studies are easier to conduct compared with cohort studies. Selection of controls in case-control studies is difficult.
REFERENCE 1. Gordis L. Epidemiology. 4th ed. Philadelphia: Saunders Elsevier; 2009.
American Journal of Orthodontics and Dentofacial Orthopedics
August 2014 Vol 146 Issue 2
