Copyright ©2011 Brooks/Cole, Cengage Learning Relationships Between Categorical Variables – Risk Class 26 1

Homework Check Assignment: Chapter 4 – Exercise 4.1 and 4.7 Reading: Chapter 4 – p

Suggested Answer 3

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5 Use 2 Way table / Contingency table to calculate risk, relative risk, odds and odds ratios (Calculate the association between the 2 categorical variables)

Copyright ©2011 Brooks/Cole, Cengage Learning Risk, Relative Risk, and Misleading Statistics about Risk Number in category Total number in group Risk = Example: Within a group of 200 individuals, asthma affects 24 people. In this group the risk of asthma is 24/200 = 0.12 or 12%.

Copyright ©2011 Brooks/Cole, Cengage Learning 7 Risk in category 1 Risk in category 2 Relative Risk = Example: For those who drive under the influence of alcohol, the relative risk of an accident is 15  The risk of an accident for those who drive under the influence is 15 times the risk for those who don’t drive under the influence. Relative risk = 1  two risks are the same. Risk > 1  numerator category has higher risk. Risk in denominator often the baseline risk.

Use 2-way table to calculate risk and relative risk Copyright ©2011 Brooks/Cole, Cengage Learning 8

Use 2-way table to calculate risk and relative risk Copyright ©2011 Brooks/Cole, Cengage Learning 9

Use 2-way table to calculate risk and relative risk

Copyright ©2011 Brooks/Cole, Cengage Learning 12 Difference in risks Baseline risk Percent increase in risk Note: When risk is smaller than baseline risk, relative risk < 1 and the percent “increase” will actually be negative, so we say percent decrease in risk. = x 100% = (relative risk – 1) x 100%

Copyright ©2011 Brooks/Cole, Cengage Learning 13 Relative Risk of asthma = = 1.40 (boys compared to girls) Percent increase in risk = (1.40 – 1) x 100% = 40% Example 4.4 Sex and Risk of Asthma Interpretation:Boys under 18 have a risk of asthma that is 40% higher than the risk of asthma for girls. 15.7% 11.2% Based on 2006 National Heath Survey: Estimate 15.7% of boys and 11.2% of girls under 18 had at some point been diagnosed with asthma.

14 Does it mean the risk of for girls having asthma is 40% less than the boys? Interpretation: Boys under 18 have a risk of asthma that is 40% higher than the risk of asthma for girls.

15 Determine 1.the relative risk of ever having asthma for girls compared to boys. 2.the percent increase/decrease in risk. Quick Check

Copyright ©2011 Brooks/Cole, Cengage Learning 16 - Definition: The odds of an event compare the chance that the event happens to the chance that it does not. - Expressed as “a to b” - Example: 60% chance that it will rain tomorrow The odds that it will rain tomorrow = 60% / (1-60%) = 3 to 2 Odds

Copyright ©2011 Brooks/Cole, Cengage Learning 17 -Definition: Compares the odds of an event for two different categories. -= (odds in category 1) / (odds in category 2) -Features: Odds Ratio When odds are same  odds ratio = 1. When odds higher in numerator category  odds ratio > 1. When odds lower in numerator category  odds ratio < 1.

Odds ratio = = = 1.48 (boys vs. girls) Example 4.5 Odds Ratio for Sex and Asthma Interpretation:The odds of ever having had asthma for boys are 1.48 times the odds for girls. Odds for boys (15.7/84.3) Odds for girls (11.2/88.8) Based on 2006 National Heath Survey: Boys: Risk of asthma = 15.7%  Risk of no asthma = 100% – 15.7% = 84.3%, or 1 to 5.37 Girls:Risk of asthma = 11.2%  Risk of no asthma = 100% – 11.2% = 88.8%, or 1 to 7.93

Copyright ©2011 Brooks/Cole, Cengage Learning 19 Misleading Statistics About Risk Questions to Ask: What are the actual risk? What is the baseline risk? What is the population for which the reported risk or relative risk applies? What is the time period for this risk?

Copyright ©2011 Brooks/Cole, Cengage Learning 20 Example 4.7 Case Study 1.2 Revisited: Disaster in the Skies? Look at risk of controller error per flight: In 1998: 5.5 errors per million flights In 1997: 4.8 errors per million flights “Errors by air traffic controllers climbed from 746 in fiscal 1997 to 878 in fiscal 1998, an 18% increase.” USA Today Risk of error increased but the actual risk is very small.

Copyright ©2011 Brooks/Cole, Cengage Learning 21 Example 4.8 Dietary Fat and Breast Cancer Two reasons info is useless: 1.Don’t know how data collected nor what population the women represent. 2.Don’t know ages of women studied, so don’t know baseline rate. “Italian scientists report that a diet rich in animal protein and fat – cheeseburgers, french fries, and ice cream, for example – increases a woman’s risk of breast cancer threefold.” Prevention Magazine’s Giant Book of Health Facts (1991, p. 122).

Copyright ©2011 Brooks/Cole, Cengage Learning 22 Example 4.8 Dietary Fat and Breast Cancer (cont) Age is a critical factor. Accumulated lifetime risk of woman (currently 30) developing breast cancer by certain ages: By age 40: 1 in 227 By age 50: 1 in 54 By age 60: 1 in 24 By age 90: 1 in 8.2 Annual risk 1 in 3700 for women in early 30’s. If Italian study was on very young women, the threefold increase in risk represents a small increase.

Homework Assignment: Chapter 4 – Exercise 4.15, 4.17 and 4.29 Reading: Chapter 4 – p