Download Calculating Risk Differences, Ratios, and Odds: An Example in Biostatistics and more Study notes Mathematical Methods in PDF only on Docsity! 1 Applied Biostatistics Proportions, risk ratios and odds ratios Martin Bland Professor of Health Statistics University of York http://www-users.york.ac.uk/~mb55/ Risk difference Cough during the day or at night at age 14 and bronchitis before age 5 Cough at Bronchitis before age 5 Total age 14 Yes No Yes 26 9.5% 44 4.2% 70 No 247 90.5% 1002 95.8% 1249 Total 273 100.0% 1046 100.0% 1319 Want an estimate of the size of the bronchitis effect. Difference between proportions: 0.095 – 0.042 = 0.053 or 9.5% – 4.2% = 5.3 percentage points. Standard error for difference = 0.019, 95% CI: 0.053 – 1.96 × 0.019 to 0.053 + 1.96 × 0.019 = 0.016 to 0.090. Risk difference Cough during the day or at night at age 14 and bronchitis before age 5 Cough at Bronchitis before age 5 Total age 14 Yes No Yes 26 9.5% 44 4.2% 70 No 247 90.5% 1002 95.8% 1249 Total 273 100.0% 1046 100.0% 1319 Want an estimate of the size of the bronchitis effect. Difference between proportions: 0.095 – 0.042 = 0.053 or 9.5% – 4.2% = 5.3 percentage points. Proportion who cough is called the risk of cough for that population. Difference is absolute risk difference. 2 Risk ratio Cough during the day or at night at age 14 and bronchitis before age 5 Cough at Bronchitis before age 5 Total age 14 Yes No Yes 26 9.5% 44 4.2% 70 No 247 90.5% 1002 95.8% 1249 Total 273 100.0% 1046 100.0% 1319 Want an estimate of the size of the bronchitis effect. Proportion who cough is called the risk of cough for that population. Difference is absolute risk difference. Risk ratio = 0.095/0.042 = 2.26. Also called relative risk, RR. Risk ratio Cough during the day or at night at age 14 and bronchitis before age 5 Cough at Bronchitis before age 5 Total age 14 Yes No Yes 26 9.5% 44 4.2% 70 No 247 90.5% 1002 95.8% 1249 Total 273 100.0% 1046 100.0% 1319 Risk ratio = 0.095/0.042 = 2.26. Because risk ratio is a ratio, it has a very awkward distribution. If we take the log of the risk ratio, we have something which is found by adding and subtracting log frequencies. The distribution becomes approximately Normal. Provided frequencies are not small, simple standard error. Risk ratio Cough during the day or at night at age 14 and bronchitis before age 5 Cough at Bronchitis before age 5 Total age 14 Yes No Yes 26 9.5% 44 4.2% 70 No 247 90.5% 1002 95.8% 1249 Total 273 100.0% 1046 100.0% 1319 Risk ratio = 0.095/0.042 = 2.26. loge(RR) = 0.817. SE for loge(RR) = 0.238. 95% CI for loge(RR) = 0.817 – 1.96× 0.238 to 0.817 + 1.96 × 0.238 = 0.351 to 3.607. 95% CI for RR = exp(0.351) to exp(1.283) = 1.42 to 3.61.
