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March 30

March 30. More examples of case-control studies General I x J table Chi-square tests. Exam Question. p = proportion who smoke cigarettes n = 10 x = 3 report smoking p = 3/10 = 0.30 is estimate of p SE(p) = = 0.14. 95% CI for p: 0.30 ± 1.96 (0.14) 0.30 ± 0.28 or (0.02 – 0.58).

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March 30

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  1. March 30 • More examples of case-control studies • General I x J table Chi-square tests

  2. Exam Question • p = proportion who smoke cigarettes • n = 10 • x = 3 report smoking • p = 3/10 = 0.30 is estimate of p SE(p) = = 0.14 95% CI for p: 0.30 ± 1.96 (0.14) 0.30 ± 0.28 or (0.02 – 0.58)

  3. HRT Use and Colonic Polyps • Case-control study conducted at Digestive Healthcare (DH) in Minneapolis (1990-1995) • Patients underwent colonoscopy • Cases were patients with adenomatous polyps • Controls were patients without polyps • Questionnaires completed • Use of hormone replacement therapy ascertained • Published CEBP 1996 (Potter et al) • Since patients undergoing colonoscopy were not a random sample RR of polyps cannot be estimated

  4. HRT Use and Polyps Case (Polyps) Control (No Polyps) HRT Use 247 No HRT Use 216 174 289 463 RO HRT Use (Case v Control) RO = 72/102 175/114 c2 = ( 463 ) (RO)2 ( 174) (289) (247) (216) = 0.46 =16.04

  5. USING SAS DATA hrt; INFILE DATALINES; INPUT hrt ccstatus count; DATALINES; 1 1 72 1 2 175 2 1 102 2 2 114 ; PROCFREQDATA=hrt; TABLES hrt*ccstatus/CHISQRELRISK; WEIGHT count; RUN; ccstatus =1 is case ccstatus = 2 is control

  6. hrt ccstatus Frequency| Percent | Row Pct | Col Pct | 1| 2| Total ---------+--------+--------+ 1 | 72 | 175 | 247 | 15.55 | 37.80 | 53.35 | 29.15 | 70.85 | | 41.38 | 60.55 | ---------+--------+--------+ 2 | 102 | 114 | 216 | 22.03 | 24.62 | 46.65 | 47.22 | 52.78 | | 58.62 | 39.45 | ---------+--------+--------+ Total 174 289 463 37.58 62.42 100.00 Estimates of the Relative Risk (Row1/Row2) Type of Study Value 95% Confidence Limits ----------------------------------------------------------------- Case-Control (Odds Ratio) 0.4598 0.3135 0.6744 Cohort (Col1 Risk) 0.6173 0.4855 0.7849 Cohort (Col2 Risk) 1.3424 1.1562 1.5587

  7. Interpretation (RO = 0.46) • Women who use HRT are at a 54% decreased risk of developing polyps compared to women who do not use HRT. • The odds of developing polyps is 54% lower in women who use HRT compared to women who do not use HRT.

  8. Analyses of I x J Tables • Two factors, one with I levels, second with J levels • I rows, J columns • General hypothesis: • Are rows independent of columns? • Ho: p1 = p2 = p3 (when J=2) • Chi-square (c2) test with (I-1 x J-1 df): Sum over all cells (IxJ)

  9. Example TOMHS • Rows – 6 treatment groups • Columns – 4 levels of side-effect • 1 = none; 2=mild, 3=moderate, 4=severe • Do side effect distribution depend on group? • Group 1 = diuretic • Group 2 = ACE • Group 3 = placebo • Side effects: 1=none, 2=mild, 3 = moderate/severe • Look at cough

  10. Cough None Mild Mod/Sev Diuretic 133 133 ACE Placebo 232 359 109 30 498 Expected Frequencies if Ho is true: Cell (1,1) = 359*133/498 = 95.9 Cell (1,2) = 109*133/498 = 29.1 Compute for all 9 cells

  11. Cough- Expected Frequencies None Mild Mod/Sev Diuretic 133 133 ACE Placebo 232 359 109 30 c2(4DF) = (99-95.9)2 /95.9 + (28-29.1)2 /29.1 + … + (13-14)2/14 = 5.41 P = 0.25

  12. USING SAS DATA cough; INPUT group cough count; DATALINES; 1 1 99 1 2 28 1 3 6 2 1 86 2 2 36 2 3 11 3 1 174 3 2 45 3 3 13 ; PROCFREQDATA=hrt; TABLES group*cough/CHISQCMH; WEIGHT count; RUN; cough =1 (none) cough = 2 (mild) cough = 3 (mod/severe)

  13. GROUP cough Frequency| Expected | Percent | Row Pct | Col Pct | 1| 2| 3| Total ---------+--------+--------+--------+ 3 | 99 | 28 | 6 | 133 | 95.878 | 29.11 | 8.012 | | 19.88 | 5.62 | 1.20 | 26.71 | 74.44 | 21.05 | 4.51 | | 27.58 | 25.69 | 20.00 | ---------+--------+--------+--------+ 5 | 86 | 36 | 11 | 133 | 95.878 | 29.11 | 8.012 | | 17.27 | 7.23 | 2.21 | 26.71 | 64.66 | 27.07 | 8.27 | | 23.96 | 33.03 | 36.67 | ---------+--------+--------+--------+ 6 | 174 | 45 | 13 | 232 | 167.24 | 50.779 | 13.976 | | 34.94 | 9.04 | 2.61 | 46.59 | 75.00 | 19.40 | 5.60 | | 48.47 | 41.28 | 43.33 | ---------+--------+--------+--------+ Total 359 109 30 498 72.09 21.89 6.02 100.00

  14. Statistic DF Value Prob ------------------------------------------------------ Chi-Square 4 5.4105 0.2477 Likelihood Ratio Chi-Square 4 5.2873 0.2591 Mantel-Haenszel Chi-Square 1 0.0245 0.8756 Phi Coefficient 0.1042 Contingency Coefficient 0.1037 Cramer's V 0.0737 Effective Sample Size = 498 Frequency Missing = 7 Cochran-Mantel-Haenszel Statistics (Based on Table Scores) Statistic Alternative Hypothesis DF Value Prob --------------------------------------------------------------- 1 Nonzero Correlation 1 0.0245 0.8756 2 Row Mean Scores Differ 2 4.9233 0.0853 3 General Association 4 5.3996 0.2487 Takes into account the ordering of the row categories

  15. 1-Sample Z-Test: Matched Pair Data Control Positive Control Negative Pos Case Neg Analyses is done on discordant pairs b and c Called McNemar’s chi-square Ho: p = 0.5 where n=b+c and x=b Z = (b/(b+c) – 0.5)/sqrt(.5*.5/(b+c)) Z = (b-c)/sqrt(b+c) c2 = (b-c)2/(b+c)

  16. Example – Vitamin Use/Disease(440 Pairs) Control Vitamin + Control Vitamin - Vit + Case Vit - Ho: p = 0.5 where n=140 and b = 50 c2 = (50-90)2/(50+90) = 11.43 (p=.0007)

  17. Example of Matched Case-control Study DATA vitamin; INFILE DATALINES; INPUT v_case $ v_cont $ count; LABEL v_case = 'Case Use of Vitamins'; LABEL v_cont = 'Control Use of Vitamins'; DATALINES; 1-YES 1-YES 100 1-YES 2-NO 50 2-NO 1-YES 90 2-NO 2-NO 200 ; 100 pairs where both case and control took vitamins

  18. PROCFREQDATA=vitamin; TABLES v_case*v_cont/AGREE; WEIGHT COUNT; TITLE'Matched Case-control Study'; RUN;

  19. v_case(Case Use of Vitamins) v_cont(Control Use of Vitamins) Frequency| Percent | Row Pct | Col Pct |1-YES |2-NO | Total ---------+--------+--------+ 1-YES | 100 | 50 | 150 | 22.73 | 11.36 | 34.09 | 66.67 | 33.33 | | 52.63 | 20.00 | ---------+--------+--------+ 2-NO | 90 | 200 | 290 | 20.45 | 45.45 | 65.91 | 31.03 | 68.97 | | 47.37 | 80.00 | ---------+--------+--------+ Total 190 250 440 43.18 56.82 100.00 Only the off diagonals give information Table gives evidence that vitamins were protective.

  20. v_case(Case Use of Vitamins) v_cont(Control Use of Vitamins) Frequency| Percent | Row Pct | Col Pct |1-YES |2-NO | Total ---------+--------+--------+ 1-YES | 100 | 50 | 150 | 22.73 | 11.36 | 34.09 | 66.67 | 33.33 | | 52.63 | 20.00 | ---------+--------+--------+ 2-NO | 90 | 200 | 290 | 20.45 | 45.45 | 65.91 | 31.03 | 68.97 | | 47.37 | 80.00 | ---------+--------+--------+ Total 190 250 440 43.18 56.82 100.00 Statistics for Table of v_case by v_cont McNemar's Test ------------------------ Statistic (S) 11.4286 DF 1 Pr > S 0.0007 c2 = (50-90)2/(50+90) = 11.43 Obtained with AGREE Option

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