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Lecture 9

# BIOS 1500 Lecture 9: Lecture_9.3_Case_Control_Design_2017

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School
Department
Biostatistics
Course
BIOS 1500
Professor
Kevin O'brien
Semester
Spring

Description
Case-Control Study Spring 2017 Case-Control Study The case-control study is implemented using samples based on the DEPENDENT variable. It has Backward directionality: Arguing from knowing the dependent variable (disease) to assessing the Independent (exposure status). The design consists of a sample of those with the disease (Cases) , and at least one other sample of those without the disease (Controls). Eg illness study). Case-Control Study The design fixes as known, the total sample size, and the marginal distribution for Disease: a+c, and b+d. Timing is retrospective, since both disease and exposure occurred in the past, prior to the study. The design is observational in that no interventions or randomization to treatments occurred Case-Control Study The design allows us to estimate: the Marginal distribution of Exposure The two Conditional distributions of exposure based on disease status. The design measures the prevalence of exposure in each group: Cases, and Controls. Case Control study The prevalence of disease cannot be estimated as the sampling design pre-determined how many diseased (Cases) and non-diseased (Controls) were to be studied. Case-Control Study The quantities known at the start are: a+c, b+d and the total sample size n. Conditional Distributions of Exposure Given a Disease Status Conditional Distribution of Exposure given disease present P(E|D) = a ÷(a+c) P(NE|D) = c ÷(a+c) Conditional Distribution of Exposure given not diseased P(E|ND) = b ÷(b+d) P(NE|ND) = d ÷(b+d) Measures of Association Exposure Difference Exposure Difference = P(E|D) – P(E|ND) If disease and exposure are not associated the difference will be close to zero. If the difference is positive the association is deemed positive (diseased have a higher proportion exposed) and if it is negative the association is negative: diseased have a lower prevalence of exposure. Again, a difference measure is mostly useful when the prevalence estimates of exposure are both say >0.20. Measure of Association Odds Ratio of Exposre Odds ratio of exposure given disease OR(E|D) = (a:c) ÷ (b:d) = (a÷c) ÷ (b÷d) = ad÷bc a:d => odds of exposure in diseased group. b:d => odds of exposure in non-diseased This is the preferred measure of association for this design Example: Case-Control Study The odds of a case having the exposure is estimated as Odds(Exp | D) = 33÷142 = 0.2324 The odds for a control having the exposure is estimated as Odds(Exp | ND) = 26÷197 = 0.1310 Case-Control Study The odds ratio is simply the ratio of the two odds just calculated. In this case: the odds of exposure if diseased divided by the odds of exposure if a control. Odds ratio = (33/142)÷(26/197) = (33x197)÷(26x142) = 1.75 Case-Control Study We interpret this by saying that the odds of exposur
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