S160 #15. Comparing Two Proportions, Part 3 Odds Ratio. JC Wang. March 15, 2016

Transcription

1 S60 #5 Comparing Two Proportions, Part 3 JC Wang March 5, 206

2 Outline Odds Odds 2 JC Wang WMU) S60 #5 S60, Lecture 5 2 /

3 The odds that an event occurs is Odds = Odds Probability that event occurs Probability that event does not occur = p p Probability Odds 0.0 /9 = /4 = / = / = / = 9.00 JC Wang WMU) S60 #5 S60, Lecture 5 3 /

4 iclicker Question 5. A clinical trial was conducted to study the efficacy of a new drug intended to lower the LDL low-density lipoprotein, a.k.a., bad cholesterol). All study subjects showed high LDL level at the baseline. Of the 00 treated subjects, 80 of them showed reduction to normal LDL level two weeks after treatment. What is the odds that a treated subject having reduction in LDL to normal level after two weeks? A B. 4 C. 80 D. 20 E. cannot determine JC Wang WMU) S60 #5 S60, Lecture 5 4 /

5 Outline Odds Odds 2 JC Wang WMU) S60 #5 S60, Lecture 5 5 /

6 When comparing two groups, the odds ratio is = Odds of group Odds of group 2 It is easier to interpret an OR when it s greater than and hence, when OR <, exchange the roles of the groups above to get an OR >. JC Wang WMU) S60 #5 S60, Lecture 5 6 /

7 Hepatits E Vaccine Example, revisited Hepatitis E Yes No Total Placebo Vaccine If we consider the placebo i.e., unvaccinated) group as group, then OddsHepatits Placebo) = OddsHepatits Vaccine) = = = = = = OddsHepatits Placebo) OddsHepatits Vaccine) = = 23.7 So, the odds of getting hepatitis is about 24 times greater if you remain unvaccinated. JC Wang WMU) S60 #5 S60, Lecture 5 7 /

8 Consider Disease Yes No Total Group a b a + b Group 2 c d c + d The odds ratio is then OR = a d b c = successes failures 2 failures successes 2 = successes ) /failures successes 2 /failures 2 where successes = # of successes yes s) in group and failures = # of failures no s) in group ; successes 2 = # of successes yes s) in group 2 and failures 2 = # of failures no s) in group 2. Note: assume OR >. If OR < then switch the rows above and then the new OR is the reciprocal of the old one. JC Wang WMU) S60 #5 S60, Lecture 5 8 /

9 iclicker Question 5.2 A clinical trial was conducted to study the efficacy of a new drug intended to lower the LDL low-density lipoprotein, a.k.a., bad cholesterol). All study subjects showed high LDL level at the baseline. Of the 00 treated subjects, 80 of them showed reduction to normal LDL level two weeks after treatment. On the other hand, of the 00 subjects who received placebo, only 0 showed reduction to normal LDL level after two weeks. What is the odds ratio of the treatment group versus the placebo group? A. 36 B. 4 C. 9 D. 8 E. cannot determine JC Wang WMU) S60 #5 S60, Lecture 5 9 /

10 A 95% Confidence Interval for Calculate a 95% confidence interval for the log odds ratio calculate log odds ratio [ ] ad lnor) = ln bc calculate the standard error of lnodds ratio) SE = a + b + c + d a 95% c.i. for lnor): lnor).96se, lnor) +.96SE ) 2 A 95% confidence interval for OR is e lnor).96se, e lnor)+.96se) JC Wang WMU) S60 #5 S60, Lecture 5 0 /

11 A 95% Confidence Interval for Calculate a 95% confidence interval for the log odds ratio calculate log odds ratio [ ] ad lnor) = ln bc calculate the standard error of lnodds ratio) SE = a + b + c + d a 95% c.i. for lnor): lnor).96se, lnor) +.96SE ) 2 A 95% confidence interval for OR is e lnor).96se, e lnor)+.96se) JC Wang WMU) S60 #5 S60, Lecture 5 0 /

12 A 95% Confidence Interval for Calculate a 95% confidence interval for the log odds ratio calculate log odds ratio [ ] ad lnor) = ln bc calculate the standard error of lnodds ratio) SE = a + b + c + d a 95% c.i. for lnor): lnor).96se, lnor) +.96SE ) 2 A 95% confidence interval for OR is e lnor).96se, e lnor)+.96se) JC Wang WMU) S60 #5 S60, Lecture 5 0 /

13 A 95% Confidence Interval for Calculate a 95% confidence interval for the log odds ratio calculate log odds ratio [ ] ad lnor) = ln bc calculate the standard error of lnodds ratio) SE = a + b + c + d a 95% c.i. for lnor): lnor).96se, lnor) +.96SE ) 2 A 95% confidence interval for OR is e lnor).96se, e lnor)+.96se) JC Wang WMU) S60 #5 S60, Lecture 5 0 /

14 A 95% Confidence Interval for Calculate a 95% confidence interval for the log odds ratio calculate log odds ratio [ ] ad lnor) = ln bc calculate the standard error of lnodds ratio) SE = a + b + c + d a 95% c.i. for lnor): lnor).96se, lnor) +.96SE ) 2 A 95% confidence interval for OR is e lnor).96se, e lnor)+.96se) JC Wang WMU) S60 #5 S60, Lecture 5 0 /

15 A 95% Confidence Interval for Calculate a 95% confidence interval for the log odds ratio calculate log odds ratio [ ] ad lnor) = ln bc calculate the standard error of lnodds ratio) SE = a + b + c + d a 95% c.i. for lnor): lnor).96se, lnor) +.96SE ) 2 A 95% confidence interval for OR is e lnor).96se, e lnor)+.96se) JC Wang WMU) S60 #5 S60, Lecture 5 0 /

16 Hepatits E Vaccine Example, revisited Recall that the odds ratio of placebo subjects getting hepatitis against that of vaccinated subjects is OR = = 23.7 and hence 95% c.i. for lnor): lnor) = ln23.7) = 3.65 SElnOR)) = a 95% c.i. for lnor) is given by = [ ], [ ]) = 2.004, 4.326) }{{}}{{} =.6 =.6 2 Hence, a 95% c.i. for OR is e 2.004, e 4.326) = 7.4, 75.6) So, with 95% confidence, the odds of unvaccinated subjects getting hepatitis is approximately between 7 and 76 times greater than that of vaccinated subjects. JC Wang WMU) S60 #5 S60, Lecture 5 /

17 Hepatits E Vaccine Example, revisited Recall that the odds ratio of placebo subjects getting hepatitis against that of vaccinated subjects is OR = = 23.7 and hence 95% c.i. for lnor): lnor) = ln23.7) = 3.65 SElnOR)) = a 95% c.i. for lnor) is given by = [ ], [ ]) = 2.004, 4.326) }{{}}{{} =.6 =.6 2 Hence, a 95% c.i. for OR is e 2.004, e 4.326) = 7.4, 75.6) So, with 95% confidence, the odds of unvaccinated subjects getting hepatitis is approximately between 7 and 76 times greater than that of vaccinated subjects. JC Wang WMU) S60 #5 S60, Lecture 5 /

18 Hepatits E Vaccine Example, revisited Recall that the odds ratio of placebo subjects getting hepatitis against that of vaccinated subjects is OR = = 23.7 and hence 95% c.i. for lnor): lnor) = ln23.7) = 3.65 SElnOR)) = a 95% c.i. for lnor) is given by = [ ], [ ]) = 2.004, 4.326) }{{}}{{} =.6 =.6 2 Hence, a 95% c.i. for OR is e 2.004, e 4.326) = 7.4, 75.6) So, with 95% confidence, the odds of unvaccinated subjects getting hepatitis is approximately between 7 and 76 times greater than that of vaccinated subjects. JC Wang WMU) S60 #5 S60, Lecture 5 /

19 Hepatits E Vaccine Example, revisited Recall that the odds ratio of placebo subjects getting hepatitis against that of vaccinated subjects is OR = = 23.7 and hence 95% c.i. for lnor): lnor) = ln23.7) = 3.65 SElnOR)) = a 95% c.i. for lnor) is given by = [ ], [ ]) = 2.004, 4.326) }{{}}{{} =.6 =.6 2 Hence, a 95% c.i. for OR is e 2.004, e 4.326) = 7.4, 75.6) So, with 95% confidence, the odds of unvaccinated subjects getting hepatitis is approximately between 7 and 76 times greater than that of vaccinated subjects. JC Wang WMU) S60 #5 S60, Lecture 5 /

20 Hepatits E Vaccine Example, revisited Recall that the odds ratio of placebo subjects getting hepatitis against that of vaccinated subjects is OR = = 23.7 and hence 95% c.i. for lnor): lnor) = ln23.7) = 3.65 SElnOR)) = a 95% c.i. for lnor) is given by = [ ], [ ]) = 2.004, 4.326) }{{}}{{} =.6 =.6 2 Hence, a 95% c.i. for OR is e 2.004, e 4.326) = 7.4, 75.6) So, with 95% confidence, the odds of unvaccinated subjects getting hepatitis is approximately between 7 and 76 times greater than that of vaccinated subjects. JC Wang WMU) S60 #5 S60, Lecture 5 /

21 Hepatits E Vaccine Example, revisited Recall that the odds ratio of placebo subjects getting hepatitis against that of vaccinated subjects is OR = = 23.7 and hence 95% c.i. for lnor): lnor) = ln23.7) = 3.65 SElnOR)) = a 95% c.i. for lnor) is given by = [ ], [ ]) = 2.004, 4.326) }{{}}{{} =.6 =.6 2 Hence, a 95% c.i. for OR is e 2.004, e 4.326) = 7.4, 75.6) So, with 95% confidence, the odds of unvaccinated subjects getting hepatitis is approximately between 7 and 76 times greater than that of vaccinated subjects. JC Wang WMU) S60 #5 S60, Lecture 5 /