This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: 10.7 Confidence interval for p 1 p 2 10.9 The odds ratio and relative risk Casecontrol studies Sections 10.7 and 10.9 Timothy Hanson Department of Statistics, University of South Carolina Stat 205: Elementary Statistics for the Biological and Life Sciences 1 / 23 10.7 Confidence interval for p 1 p 2 10.9 The odds ratio and relative risk Casecontrol studies 10.7 confidence interval for p 1 p 2 Recall, in population 1, we observe y 1 out of n 1 successes; in population 2 we observe y 2 out of n 2 successes, placed in a contingency table Group 1 2 Outcome Success y 1 y 2 Failure n 1 y 1 n 2 y 2 Total n 1 n 2 ˆ p 1 = y 1 / n 1 estimates p 1 & ˆ p 2 = y 2 / n 2 estimates p 2 . We want to compute a 95% confidence interval for p 1 p 2 . 2 / 23 10.7 Confidence interval for p 1 p 2 10.9 The odds ratio and relative risk Casecontrol studies Confidence interval for p 1 p 2 This interval is slightly different than your book’s. The estimate of p 1 p 2 is ˆ p 1 ˆ p 2 . The standard error is SE ˆ p 1 ˆ p 2 = s ˆ p 1 (1 ˆ p 1 ) n 1 + ˆ p 2 (1 ˆ p 2 ) n 2 . At 95% confidence interval for p 1 p 2 is ˆ p 1 ˆ p 2 ± 1 . 96 SE ˆ p 1 ˆ p 2 . This is given in R by prop.test(success,total) where success is a list of the number of successes in the two groups and total is a list of the total number sampled in each group. 3 / 23 10.7 Confidence interval for p 1 p 2 10.9 The odds ratio and relative risk Casecontrol studies Example 10.7.1 Migraine headache data Migraine headache patients took part in a doubleblind clinical trial to assess experimental surgery. 75 patients were assigned real surgery ( n 1 = 49) or sham surgery ( n 2 = 26) so total=c(49,26) . There were y 1 = 41 successes among real surgery and y 2 = 15 successes among sham so success=c(41,15) . ˆ p 1 = 41 / 49 = 83 . 7% & ˆ p 2 = 15 / 26 = 57 . 7% so ˆ p 1 ˆ p 2 = 0 . 260. The standard error of the difference is SE ˆ p 1 ˆ p 2 = r . 837(0 . 163) 49 + . 577(0 . 423) 26 = 0 . 110 . 95% confidence interval is . 260 ± 1 . 96(0 . 110) = (0 . 0444 , . 476). 4 / 23 10.7 Confidence interval for p 1 p 2 10.9 The odds ratio and relative risk Casecontrol studies R code for migraine headache data Use correct=FALSE to get “old fashioned” confidence interval. > total=c(49,26) > success=c(41,15) > prop.test(success,total,correct=FALSE) 2sample test for equality of proportions without continuity correction data: success out of total Xsquared = 6.0619, df = 1, pvalue = 0.01381 alternative hypothesis: two.sided 95 percent confidence interval: 0.04354173 0.47608150 sample estimates: prop 1 prop 2 0.8367347 0.5769231 We are 95% confident that real surgery reduces the probability of migraines by 4.3% to 47.6%....
View
Full
Document
This note was uploaded on 12/14/2011 for the course STAT 205 taught by Professor Hendrix during the Fall '09 term at South Carolina.
 Fall '09
 Hendrix
 Statistics

Click to edit the document details