Copyright 2011 Brooks/Cole, Cengage Learning Relationships Between Categorical Variables Risk Class...

Copyright ©2011 Brooks/Cole, Cengage Learning

Relationships Between

Categorical Variables –

Risk

Class 26

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Homework Check• Assignment:• Chapter 4 – Exercise 4.1 and 4.7• Reading:• Chapter 4 – p. 113-118

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Suggested Answer

4

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• 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 6

4.2 Risk, Relative Risk, and Misleading Statistics about Risk

Number in categoryTotal 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%.


Risk in category 1Risk 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



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%


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.

1414

• 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.

1515

Determine 1. the relative risk of ever having asthma for

girls compared to boys.2. the percent increase/decrease in risk.

Quick Check


-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


- 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 5.37Girls: Risk of asthma = 11.2% Risk of no asthma = 100% – 11.2% = 88.8%, or 1 to 7.93


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?


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 flightsIn 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.


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).


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 227By age 50: 1 in 54By age 60: 1 in 24By 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. 118-122

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Copyright 2011 Brooks/Cole, Cengage Learning Relationships Between Categorical Variables Risk Class...

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