Biostat Methods STAT 5820/6910 Handout #4: Chi-square, Fisher s, and McNemar s Tests

Transcription

1 Biostat Methods STAT 5820/6910 Handout #4: Chi-square, Fisher s, and McNemar s Tests Example 1: 152 patients were randomly assigned to 4 dose groups in a clinical study. During the course of the study, some patients dropped out. Is there a difference in dropout rates among dose groups? Dropout Yes No Dose data a1 input dose dropout $ cards 10 yes 5 10 no yes 6 20 no yes no yes no 27 proc freq data=a1 tables dose*dropout / chisq nopercent norow title1 'Testing equal rates in all doses' /* No evidence of a general association, but evidence of a dose-response trend. Could investigate linear trend using Cochran-Armitage test */ 1

2 Testing equal rates in all doses The FREQ Procedure Frequency Col Pct Table of dose by dropout dose dropout no yes Total Total Statistics for Table of dose by dropout Statistic DF Value Prob Chi-Square Likelihood Ratio Chi-Square Mantel-Haenszel Chi-Square Phi Coefficient Contingency Coefficient Cramer's V

3 /* Any different inference in exact test? */ proc freq data=a1 tables dose*dropout / fisher title1 'Fishers exact test' Fishers exact test Fisher's Exact Test Table Probability (P) Pr <= P Example 2: Bilirubin data 86 patients treated with experimental drug for 3 months pre- and post-study bilirubin levels were recorded. Many patients exhibited abnormally high bilirubin levels. Posttest Level Normal High Normal High Pre two representations Pretest Normal Post Level High 6 6 Is there evidence of a change in pre- to post-treatment rates of abnormalities? χ 2 =2.46, P-value= But are treatment groups independent? Also what is the true sample size? /* What if we assumed independence of treatment groups? */ data temp input trt $ bilirubin $ count cards pre normal 74 pre high 12 post normal 66 post high 20 3

4 proc freq data=temp tables trt*bilirubin / chisq title1 'Assume Independence' Assume Independence Frequency Row Pct Col Pct Table of trt by bilirubin trt bilirubin high normal Total post pre Total Statistics for Table of trt by bilirubin Statistic DF Value Prob Chi-Square Likelihood Ratio Chi-Square Continuity Adj. Chi-Square Mantel-Haenszel Chi-Square Phi Coefficient Contingency Coefficient Cramer's V

5 /* An alternative representation of the data */ data a2w input pretrt $ posttrt $ count cards normal normal 60 normal high 14 high normal 6 high high 6 /* Is there evidence of a change in pre- to post-treatment rates of abnormalities? */ proc freq data=a2w tables pretrt*posttrt / agree norow nocol title1 'McNemars test' Frequency Percent McNemars test The FREQ Procedure Table of pretrt by posttrt pretrt posttrt high normal Total high normal Total Statistics for Table of pretrt by posttrt McNemar's Test Statistic (S) DF 1 Pr > S Simple Kappa Coefficient Kappa ASE % Lower Conf Limit % Upper Conf Limit Sample Size = 86 5

6 /* Get equivalent results using patient-level data: pre = 1 iff abnormally high pre-test post = 1 iff abnormally high post-test */ data a2 input pre cards proc freq data=a2 tables pre*post / agree norow nocol title1 'McNemars test, again' 6

7 Example 3: Two tests are being considered (call them Method A and Method B) to check blood samples and diagnose whether or not a patient has a particular condition. 100 patients provide blood samples, and each sample is run through both methods. We are interested in whether there is a difference in the two methods' diagnostic abilities. /* Compare McNemar and Fishers */ /* Define data */ data a1 input methoda $ methodb $ count cards Y Y 18 N Y 27 Y N 35 N N 20 /* Check McNemar's and Fishers */ proc freq data=a1 tables methoda*methodb / agree chisq fisher nopercent nocol norow title1 'McNemar and Fishers Tests' McNemar and Fishers Tests Fisher's Exact Test Cell (1,1) Frequency (F) 20 Left-sided Pr <= F Right-sided Pr >= F McNemar's Test Statistic (S) DF 1 Table Probability (P) Pr > S Two-sided Pr <= P

8 /* Define re-configured data based on column and row sums */ data a2 input method $ diagnosis $ count cards A Y 53 A N 47 B Y 45 B N 55 /* Check McNemar's and Fishers */ proc freq data=a2 tables method*diagnosis / agree chisq fisher nopercent nocol norow title1 'McNemar and Fishers Tests' title2 'Reconfigured Data' McNemar and Fishers Tests Reconfigured Data Fisher's Exact Test Cell (1,1) Frequency (F) 47 Left-sided Pr <= F Right-sided Pr >= F McNemar's Test Statistic (S) DF 1 Pr > S Table Probability (P) Two-sided Pr <= P