1. RATIOS AND STANDARDIZATION

2. RATIOS
Ratio - the value obtained when one quantity is divided by another:
 Proportion – a ratio where the numerator is part of the denominator
# diseased/(# diseased + # not diseased)
Percentage – proportion * 100
[# diseased/(# diseased + # not diseased)]*100
Example: Say we have 15 diseased people and 30 not diseased, then:
proportion diseased: 15/(15+30) = 15/45 = 1/3
  percentage diseased: 1/3 * 100 = 33.3%
Say we have 15 diseased and 30 not diseased people
Rate ex: miles per hour, deaths per year, cost per pound

3. RATIOS Another common ratio:
Rate - change in one quantity divided by change in another quantity (usually a measure of time)
Incidence rate: number of new cases in an initially disease free population per person-time
Mortality rate: number of deaths in a population per person-time

4. RATIOS
Example: have 5 deaths in a population of 50 person months Mortality rate: 5/50 = 0.10 or 0.1 death per person month Which is equivalent to 1 deaths per 10 person months or 10 deaths per 100 person months

5. RATIOS Basic measures of disease:
Prevalence: a proportion measuring current disease
Point prevalence: # existing cases total population (at a point in time)
Period prevalence: # existing cases over a specified time period total population
Example: 6 people have the flu in a classroom of 30 in January
Point prevalence = 6/30 = 0.20
20% of the class had the flu in January

6. RATIOS Incidence: a proportion or rate measuring new disease
Cumulative incidence: # new cases over a specified time period # in population at risk
Incidence rate: # new cases observed person−time
Example: 10 new infections of herpes among the 80 first year MPH students in 2012 which was a total of 65 person-years
Cumulative incidence: 10/80 = 0.125
or 12.5% of the first year MPH students contracted herpes in 2012
Incidence rate: 10/65 = 0.154
or 154 new cases of herpes per 1,000 person-years

7. RATIOS Probability: # outcomes of interest # all possible outcomes
Odds: # outcomes of interest # outcomes not of interest
Example: 5 people out of 20 died
probability = 5/20 = 0.25
odds death: 5:15 or 1:3

8. EXAMPLE FOR RATIOS Find: proportion with disease?
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
XXXXXD
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX D
XXXXXXXD
______________________________________________________________________________
JAN FEB MARCH APRIL MAY JUNE JULY AUGUST SEPT
X = HAS DISEASE
D = DIED
--- = NO DISEASE
PERSON-MONTHS = NUMBER OF MONTHS EACH PERSON WAS DISEASE FREE IN THE STUDY
Find: proportion with disease?
prevalance of disease?
cumulative incidence?
incidence rate until June

9. RATIOS OF RATIOS RR: Relative Risk, aka Risk Ratio
RR = probability of disease among the exposed probablity of disease among the unexposed
Example: male child aged only
Obese
Not obese
Total
Below poverty
113
423
536
3.5 times poverty
128
947
1075

10. RATIOS OR RATIOS What is the Relative Risk?
What is the probability of a male child aged being obese if they reside in a poverty level family?
What if they reside in a family whose income is 3.5 times higher than the poverty level?
What is the Relative Risk?

11. RATIOS OF RATIOS OR: Odds ratio
OR = odds of having disease among the exposed odds of having diease among the unexposed
Example: Want to compare disease among people with a copy of a gene variant to those without the gene variant
Disease
No Disease
Total
One copy gene variant 50
100
No copy gene variant 2 98

12. RATIOS OF RATIOS
What are the odds of disease in the presence of the gene variant? What are the odds of disease in the absence of the gene variant? What is the Odds Ratio?

13. WEIGHTED AVERAGES
Subject Grade Credit hours English C 3 Math B+ 3 Science B 3 History A 3 PE D 1 What is the GPA?
A = 4
A- = 3.7
B+ = 3.33
B = 3
C = 2
D = 1
E = 0

14. WEIGHTED AVERAGES
GPA is a weighted average with the credit hours of each course as the weights GPA = Σ(numeric score*hours)/ Σ hours

15. WEIGHTED AVERAGES English C 3 2 x 3 = 6 Math B+ 3 3.33 x 3 = 10
Subject Grade Hours Weighted score
English C x 3 = 6
Math B x 3 = 10
Science B x 3 = 9
History A x 3 = 12
PE D x 1 = 1
Total
GPA = 38/13 = 2.9
weighted score: grade weight x hours
A = 4
A- = 3.7
B+ = 3.33
B = 3
C = 2
D = 1
E = 0

16. WEIGHTED AVERAGE
An important and much used weighted average is the technique of STANDARDIZATION Study population(s) are compared using a ‘standard‘ population which is large and stable in size

17. STANDARDIZATION OF RATES
Standardization refers to methods of adjustment based on weighted averages Two ways to control for an important characteristic (age, sex, race, etc) Direct Indirect
Two of the most common, but by no means the only standardization

18. STANDARDIZATION OF RATES
Direct method – uses the structure of a third ‘standard’ population and the rates of the populations to be compared – can compare two different populations Indirect method – uses the rates from a third ‘standard’ population and the structures of the populations to be compared – cannot compare two different population, can only compare each to a standard population used to calculate SMRs and SIRs

19. STANDARDIZATION OF RATES
Example: have two populations:
Group 1 has a crude mortality rate of per 1,000 people per year
Group 2 has a crude mortality rate of per 1,000 people per year
Group 1 crude mortality rate < Group 2 crude morality rate
Which group is healthier?

20. STANDARDIZATION OF RATES
Group 1
Group 2
Pop.
Deaths
<15
370 4
104 1
15-24
200 3
110 2
25-44
320
133
45-64
150
143
65+ 20 6
192 8
1060 18
682 15
Crude rate
18/1060 = 0.017
15/682 = 0.022
Here is some more information – need to account for age differences

21. STANDARDIZATION OF RATES
Choose a standard population (usually large and stable):
Age groups
Population
Deaths
Rates
<15
2,400 20
0.0083
15-24
1,900 17
0.0089
25-44
2,100 14
0.0067
45-64 21
0.0111
65+
1,800 35
0.0194
10,100
107

22. STANDARDIZATION OF RATES DIRECT METHOD
First need to calculate age specific death rates for both groups: rateaj = (# deaths in age group/population in age group)
Group 1
Group 2
Age
Pop.
Deaths
Age specific Rates
<15
370 4
0.0108
104 1
0.0096
15-24
200 3
0.0150
110 2
0.0182
25-44
320
0.0094
133
0.0075
45-64
150
0.0133
143
0.0210
65+ 20 6
0.3000
192 8
0.0417
4/370 = , etc

23. STANDARDIZATION OF RATES DIRECT METHOD
Age-specific mortality rates per 1000 population
Expected
Age
Standard
Group 1
Group 2
< 15
2,400
0.0108
0.0096
25.92
23.04
16-24
1,900
0.0150
0.0182
28.50
34.58
25-44
2,100
0.0094
0.0075
19.74
15.75
45-64
0.0133
0.0210
25.27
39.90
65 +
1,800
0.3000
0.0417
540.00
70.89
10,100
639.43
184.16
Age adjusted rates per 1,000:
63.3
18.6
Group 1 age adjusted rate > Group 2 age adjusted rate
Expected: rate of group by age group * # people standard age group
i.e. group 1: *2400 = 25.92
Add all the expected across all age groups then divide by the total population in the standard pop – here 10,000

24. STANDARDIZATION OF RATES INDIRECT METHOD
Use rate from standard population:
Group 1
Group 2
Standard rates per age group
Pop.
Deaths O E
< 15
0.0083
370 4
3.07
104 1
0.86
16-24
0.0089
200 3
1.78
110 2
0.98
25-44
0.0067
320
2.14
133
0.89
45-64
0.0111
150
1.67
143
1.59
65 +
0.0194 20 6
0.39
192 8
3.72
Total
1060 18
9.05
682 15
8.04
Expected: rate of country by age group * proportion of population in age group
i.e. mexico: 16.93*24/1000 = 0.41

25. STANDARDIZATION OF RATES INDIRECT METHOD
Calculate the SMR:
SMR = O E
SMRGroup 1 = = 1.99
SMRGroup 2 = = 1.87
Both are higher than the standard population

26. EXAMPLE STANDARDIZATION
Country A
Country B
Country C
Age groups
(in years)
Population
Deaths
Populations
0-20
300 6
100 2
800 15
21-50
400 80
150 30
600 56
51-85
120
250
110
Find:
Crude death rates for each country
Using C as the standard perform:
Direct standardization
Indirect standardization