Utts Ch 12

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Utts Ch 12

• Relationships between
• categorical variables

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Contingency tables
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Construct a contingency table

• A study was conducted to see if drinking alcohol
  affected the relapse rate for smoking.
• Of the 177 people enrolled in the study, 20
  people who consumed alcohol relapsed, and 48 of
  the 144 people who did not consume alcohol
  relapsed.
• Data for a study of alcohol and smoking (based on
  Schiffman, 1982)

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Contingency table for Relapsed x Consumption
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Conditional percentages
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Percent, proportion, probability, and odds

• age with the trait with trait/ total 100
• Prop with trait with trait/ total
• Probability of having trait w trait/ total
• Risk of having the trait w trait/ total
• Odds of having it with/ without to 1

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Percent, proportion, and probability

• 25 of the US population has HPV
• The proportion of people in the population with
  HPV is .25
• The probability that a someone has HPV is 1/4 or
  .25.
• The risk of having HPV is .25

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Percent, proportion, and probability AND ODDS

• 25 of the US population has HPV
• The proportion of people in the population with
  HPV is .25
• The probability that a someone has HPV is 1/4 or
  .25.
• The risk of having HPV is .25
• The ODDS of having HPV is 1 in 3, or 1/3 to 1.

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Odds Proportion

• p proportion who have the trait, then the odds
  of having it are p/(1-p) to 1
• If the odds of having the trait are a to b, the
  proportion who have it is a/(ab)

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Odds ratio
Odds for drinkers 20/13 to 1Odds for
nondrinkers 48/96 to 1Odds ratio (20/13
)/(48/96) (1.5/.5) 3 OR ad/bc
(2096)/(4813) 1920/624 3. There is a three
fold greater odds for people who consume alcohol
to relapse.
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Risk

• Baseline - risk w/o treatment or behavior
• Relative risk (RR) - ratio of the risks for each
  category (usually expressed as a multiple)
• RR 1 means the risk is the same for both
  categories of the explanatory variable

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Relative risk
Risk of relapse for drinkers 0.606 Risk of
relapse for non-drinkers 0.333 Relative risk
0.606/0.333 1.8. So the risk of relapse is 1.8
times greater for drinkers.
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RR ?OR
Relative risk 0.606/0.333 1.8. The risk of
relapse is 1.8 times greater for drinkers OR
1920/624 3. There is a three fold greater odds
for people who consume alcohol to
relapse.Oftentimes in the media an OR is
interpreted like a RR.Bad bad bad!!! Odds
ratios are not intuitive and hard to interpret,
but mathematically have good properties and are
often used.
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Music videos linked to alcohol abuse November 2,
1998(CNN) -- Young people who watch a lot of
television -- especially music videos -- are
more likely to become teen-age drinkers,
according to a Stanford University study. ...The
study found that playing computer and video games
had no effect in drinking habits, but watching
movies in a VCR actually led to an 11 percent
decrease in risk. But researchers also
discovered that an increase of one hour each day
in watching music videos leads to a 31 percent
increase in the risk of drinking over the next
18 months. An hour increase in other types of
television corresponded with a 9 percent
increase in drinking risk. "What we're pointing
the finger at," said Robinson, "is media
representations of alcohol use and advertising."
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• Design.  Prospective cohort study.
• Setting.  Six public high schools in San Jose,
  California.
• Participants.  Ninth-grade students (N  1533
  mean age  14.6 years).
• Outcome Measures.  Students reported hours of
  television, music video, and videotape viewing
  computer and video game use and lifetime and
  past 30 days' alcohol use at baseline and
  18 months later. Associations between baseline
  media exposure and subsequent alcohol use were
  examined with multiple logistic regression.

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• Results.  During the 18-month follow-up, 36.2 of
  baseline nondrinkers began drinking and 50.7 of
  baseline drinkers continued to drink. Onset of
  drinking was significantly associated with
  baseline hours of television viewing odds ratio
  OR  1.09 music video viewing OR  1.31and
  videotape viewing OR  0.89 controlling for age,
  sex, ethnicity, and other media use. Computer and
  video game use was not significantly associated
  with the subsequent onset of drinking. Among
  baseline drinkers, there were no significant
  associations between baseline media use and
  maintenance of drinking.
• PEDIATRICS Vol. 102 No. 5 November 1998, p. e54

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How this study was reported November 2,
1998(CNN) -- Young people who watch a lot of
television -- especially music videos -- are
more likely to become teen-age drinkers,
according to a Stanford University study. ...The
study found that playing computer and video games
had no effect in drinking habits, but watching
movies in a VCR actually led to an 11 percent
decrease in risk. But researchers also
discovered that an increase of one hour each day
in watching music videos leads to a 31 percent
increase in the risk of drinking over the next
18 months. An hour increase in other types of
television corresponded with a 9 percent
increase in drinking risk. "What we're pointing
the finger at," said Robinson, "is media
representations of alcohol use and advertising."
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Assessing Discrimination in Hiring and Firing
Layoffs by Ethnic Group for Labor Department
Employees

• Discrepancy handled using Odds Ratio

Odds of being laid off compared with being
retained are three times higher for African
Americans than for whites.
Source Gastwirth and Greenhouse, 1995.
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Misleading statistics

• Baseline risk is missing
• The time period of risk is not identified
• The reported risk is not necessarily your risk

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Conditional Percentages and Rates

• Rate the number of individuals per 1000 or
  per 10,000 or per 100,000.
• Percentage rate per 100

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Relative Risk of Developing Breast Cancer

• Risk for women having first child at 25 or older
  31/1628 0.0190
• Risk for women having first child before 25
• 65/4540 0.0143
• Relative risk 0.0190/0.0143 1.33

Risk of developing breast cancer is 1.33 times
greater for women who had their first child at 25
or older.
Source Pagano and Gauvreau (1988, p. 133).
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Odds Ratio

• Odds Ratio ratio of the odds of getting the
  disease to the odds of not getting the disease.

Odds Ratio for Breast Cancer

• Odds for women having first child at age 25 or
  older 31/1597 0.0194
• Odds for women having first child before age 25
  65/4475 0.0145
• Odds ratio 0.0194/0.0145 1.34

Alternative formula
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Relative Risk and Odds Ratios in Journal Articles
Researchers often report relative risks and odds
ratios adjusted to account for confounding
variables.