Statistic in Health Care Management Week 2
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chapter3.pdf
Chapter 3
Quantifying the Extent of Disease
Critical Components of RCT
• Randomization
• Control Group – Ethical Issues
• Monitoring
– Interim Analysis
– Data and Safety Monitoring Board
• Data Management
• Reporting
Learning Objectives
• Define and differentiate prevalence and
incidence
• Select, compute and interpret the appropriate
measure to compare the extent of disease
between groups
• Compare and contrast, compute and interpret
relative risks, risk differences, and odds ratios
Prevalence
• Proportion of participants with disease at a particular
point in time
baselineatexaminedpersonsofNumber
diseasewithpersonsofNumber PrevalencePoint
Example 3.1.
Computing Prevalence
Free of CVD
History of CVD
Total
Men 1548 244 1792
Women 1872 135 2007
Total 3420 379 3799
Prevalence of CVD = 379/3799 = 0.0998 = 9.98%
Prevalence of CVD in Men = 244/1792 = 0.1362 = 13.62%
Prevalence of CVD in Women = 135/2007 = 0.0673 = 6.73%
Example-H1N1 Outbreak
• H1N1 outbreak first noticed in Mexico
• Large outbreak early on in La Gloria-a small village outside of Mexico City.
• Studied extensively in the first report on H1N1 (Fraser, Donelly et al. “Pandemic potential of a strain of Influenza (H1N1): early findings”, Science Express, 11 May 2009.)
• Important questions: Who is most likely to be impacted? What are the characteristics of people commonly impacted?
Computing Prevalence
Age No ILI ILI Total
<44 years 703 522 1225
> 44 years 256 94 350
Total 959 616 1575
Data on H1N1 outbreak in La Gloria, Mexico.
n=1575 villagers (out of 2155) were surveyed to
determine if they had influenza like illness (ILI)
between 2/15/09 and 4/27/09.
Computing Prevalence
Age No ILI ILI Total
<44 years 703 522 1225
> 44 years 256 94 350
Total 959 616 1575
Prevalence of ILI=616/1575=0.3911=39.11%
Prevalence of ILI in <44=522/1225=0.4261=42.61%
Prevalence of ILI in >44=94/350=0.2686=26.86%
Incidence
• Likelihood of developing disease among persons free of
disease who are at risk of developing disease
baselineatriskatpersonsofNumber
period specified a during diseasedevelop whopersonsofNumber IncidenceCumulative
freediseasearepersonswhichduringtimeoflengthstheofSum
period specified a during diseasedevelop whopersonsofNumber Rate Incidence
Computing Incidence
• Cumulative incidence requires complete
follow-up on all participants
• Person-time data is used to take full advantage
of available information in incidence rate
• Incidence rate often expressed as an integer
per multiple of participants over a specified
time
Incidence of CVD?
1 Disease-Free
2 CVD
3 Death
4 Disease-Free
5 CVD
0 5 10 Yrs Study Start
Incidence Rate
freediseasearepersonswhich
duringtimeoflengthstheofSum
period specified a during
diseasedevelop whopersonsofNumber
Rate Incidence
Incidence of CVD
Incidence = 2/(10+9+3+10+5) = 2/37
= 0.054
5.4 per 100 person-years
Example 3.2.
Computing Incidence
Develop CVD
Total Follow-Up Time (years)
Men 190 9984
Women 119 12153
Total 309 22137
Incidence Rate of CVD in Men = 190/9984 = 0.01903
= 190 per 10,000 person-years
Incidence Rate of CVD in Women = 119/12153 = 0.00979
= 98 per 10,000 person-years
Computing Incidence
Developed ILI Total Follow-Up Time (years)
<44 years 522 20,064
> 44 years 94 3,514
Total 616 23,578
Incidence Rate of ILI in <44 = 522/20064 = 0.0260
= 260 per 10,000 person-years
Incidence Rate of ILI in >44 = 94/3514 = 0.0268
= 268 per 10,000 person-years
Comparing Extent of Disease Between
Groups
• Risk difference (excess risk)
unexposedexposed
unexposedexposed
unexposedexposed
Rate IncidenceRate Incidence
Incidence CumulativeIncidence Cumulative
PrevalencePrevalence
Comparing Extent of Disease Between
Groups
• Risk difference of prevalent CVD in smokers versus
non-smokers
smokers-nonsmokers PrevalencePrevalence
Free of CVD
History of CVD
Total
Non-Smoker 2757 298 3055
Current Smoker 663 81 744
3420 379 3799
= 81/744 – 298/3055 = 0.1089 – 0.0975 = 0.0114
Population Attributable Risk of CVD in
Smokers vs Non-Smokers
overall
smokers-nonoverall
Prevalence
PrevalencePrevalence
Free of CVD
History of CVD
Total
Non-Smoker 2757 298 3055
Current Smoker 663 81 744
3420 379 3799
= (0.0998 – 0.0975) / 0.0998 = 0.023 = 2.3%
Comparing Extent of Disease Between
Groups
• Risk difference of history of ILI in Males and Females in La Gloria
MalesFemales PrevalencePrevalence
No ILI ILI Total
Males 517 260 777
Females 442 356 798
959 616 1575
= 356/798 - 260/777 = 0.4461 – 0.3346 = 0.1115
Comparing Extent of Disease Between
Groups
• Relative risk
unexposed
exposed
Prevalence
Prevalence
Comparing Extent of Disease Between
Groups
• Relative risk of CVD in smokers versus non-smokers
smokers-non
smokers
Prevalence
Prevalence
Free of CVD
History of CVD
Total
Non-Smoker 2757 298 3055
Current Smoker 663 81 744
3420 379 3799
= 0.1089/0.0975 = 1.12
Comparing Extent of Disease Between
Groups
• Relative risk of ILI in females versus males
males
females
Prevalence
Prevalence
No ILI ILI Total
Males 517 260 777
Females 442 356 798
959 616 1575
= 0.4461/0.3346 = 1.33
Comparing Extent of Disease Between
Groups
• Odds ratio
)Prevalence(1
Prevalence
)Prevalence(1
Prevalence
unexposed
unexposed
exposed
exposed
Comparing Extent of Disease Between
Groups
• Odds ratio of CVD in hypertensives versus non-
hypertensives
No CVD
CVD Total
Non-hypertensive 2754 188 2942
Hypertensive 659 181 840
3413 369 3782
04.4 932.0/068.0
725.0/275.0
)2942/881(1 188/2942
)840/181(1 181/840
Comparing Extent of Disease Between
Groups
• Odds ratio of ILI in younger group versus older group
Age No ILI ILI Total
<44 years 703 522 1225
> 44 years 256 94 350
Total 959 616 1575
02.2 731.0/269.0
574.0/426.0
)350/94(1 94/350
)1225/522(1 522/1225
Relative Risks and Odds Ratios
• Not possible to estimate relative risk in case-
control studies
• Can estimate odds ratio because of its
invariance property
Invariance Property of Odds Ratio
Cancer
(Case)
No Cancer (control)
Total
Smoker 40 29 69
Non-smoker 10 21 31
50 50 100
Case-control study to assess association between smoking and cancer
Invariance Property of Odds Ratio
Cancer
(Case)
No Cancer (control)
Total
Smoker 40 29 69
Non-smoker 10 21 31
50 50 100
Odds ratio for cancer in smokers versus non-smokers
= (40/29) / (10/21) = 2.90
Odds of smoking in patients with cancer versus not
= (40/10) / (29/21) = 2.90!
