RATIOS AND STANDARDIZATION

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%

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: (at a point in time) Period prevalence: 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 newdisease Cumulative incidence: Incidence rate: 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: Odds: Example: 5 people out of 20 died probability = 5/20 = 0.25 odds death: 5:15 or 1:3

8. EXAMPLE FOR RATIOS ---------------------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 = Example: male child aged 2 -19 only

10. RATIOS OR RATIOS What is the probability of a male child aged 2 -19 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 = Example: Want to compare disease among people with a copy of a gene variant to those without the gene variant

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?

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 Subject Grade Hours Weighted score English C 3 2 x 3 = 6 Math B+ 3 3.33 x 3 = 10 Science B 3 3 x 3 = 9 History A 3 4 x 3 = 12 PE D 1 1 x 1 = 1 Total 13 38 GPA = 38/13 = 2.9

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

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 0.017 per 1,000 people per year Group 2 has a crude mortality rate of 0.022 per 1,000 people per year Group 1 crude mortality rate < Group 2 crude morality rate

20. STANDARDIZATION OF RATES

21. STANDARDIZATION OF RATES Choose a standard population (usually large and stable):

22. STANDARDIZATION OF RATESDIRECT METHOD First need to calculate age specific death rates for both groups: rateaj = (# deaths in age group/population in age group)

23. STANDARDIZATION OF RATESDIRECT METHOD

24. STANDARDIZATION OF RATESINDIRECT METHOD Use rate from standard population:

25. STANDARDIZATION OF RATESINDIRECT METHOD Calculate the SMR: • SMR = SMRGroup1 = = 1.99 SMRGroup 2 = = 1.87 Both are higher than the standard population

26. EXAMPLE STANDARDIZATION Find: Crude death rates for each country Using C as the standard perform: Direct standardization Indirect standardization