In a case/control study, the investigators examined the medical records of the last 100 consecutive patients who had been treated for colon cancer. A control group of 100 patients from the same hospital who had been treated for abdominal hernias was used for controls. Information on current smoking status was obtained from the medical records. Of the 100 cases, 45 were current smokers and 55 were not. Of the 100 controls, 26 were current smokers and 74 were not.
(a) Compute the odds ratio of having colon cancer based on smoking status.
(b) Multiply the number of controls by 2, so there are 200 controls, 52 of whom smoke and 148 who do not smoke. Compute the same odds ratio as in (a).
(c) Compute chi-square and test that the proportion of smokers is the same among cases and controls for (a) and (b). Is the chi-square the same if the number of controls is doubled?