RATIOS AND STANDARDIZATION

RATIOSRatio - 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%

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

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 to1 deaths per 10 person months

or 10 deaths per 100 person months

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 JanuaryPoint prevalence = 6/30 = 0.2020% of the class had the flu in January

RATIOSIncidence: a proportion or rate measuring new disease

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 = 0.125or 12.5% of the first year MPH students contracted herpes in 2012Incidence rate: 10/65 = 0.154or 154 new cases of herpes per 1,000 person-years

RATIOS

Probability:

Odds:

Example: 5 people out of 20 diedprobability = 5/20 = 0.25odds death: 5:15 or 1:3

EXAMPLE FOR RATIOS

---------------------XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXD-----------------------------------------------------XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------D------------------------------------------------------------------------------------------------------------XXXXXXXD______________________________________________________________________________ JAN FEB MARCH APRIL MAY JUNE JULY AUGUST SEPT

X = HAS DISEASED = DIED--- = NO DISEASEPERSON-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

RATIOS OF RATIOS

RR: Relative Risk, aka Risk Ratio

RR =

Example: male child aged 2 -19 only

Obese Not obese TotalBelow poverty 113 423 5363.5 times poverty 128 947 1075

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?

RATIOS OF RATIOSOR: Odds ratio

OR = 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 50 100

No copy gene variant 2 98 100

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?

WEIGHTED AVERAGES

Subject Grade Credit hoursEnglish C 3Math B+ 3Science B 3History A 3PE D 1

What is the GPA?

WEIGHTED AVERAGES

GPA is a weighted average with the credit hours of each course as the weights

GPA = Σ(numeric score*hours)/ Σ hours

WEIGHTED AVERAGES

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

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

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)

DirectIndirect

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

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

STANDARDIZATION OF RATES

Group 1 Group 2

Pop. Deaths Pop. Deaths

<15 370 4 104 1

15-24 200 3 110 2

25-44 320 3 133 1

45-64 150 2 143 3

65+ 20 6 192 8

1060 18 682 15

Crude rate 18/1060 = 0.017 15/682 = 0.022

STANDARDIZATION OF RATESChoose a standard population (usually large and stable):

Age groups

Population Deaths Rates

<15 2,400 20 0.008315-24 1,900 17 0.008925-44 2,100 14 0.006745-64 1,900 21 0.0111

65+ 1,800 35 0.0194

10,100 107

STANDARDIZATION OF RATESDIRECT 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. DeathsAge

specific Rates

Pop. DeathsAge

specific Rates

<15 370 4 0.0108 104 1 0.0096

15-24 200 3 0.0150 110 2 0.0182

25-44 320 3 0.0094 133 1 0.0075

45-64 150 2 0.0133 143 3 0.0210

65+ 20 6 0.3000 192 8 0.0417

STANDARDIZATION OF RATESDIRECT METHOD

Age-specific mortality rates per 1000 population

Expected

Age Standard Group 1 Group 2 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 1,900 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

STANDARDIZATION OF RATESINDIRECT METHOD

Use rate from standard population:Group 1 Group 2

Standard rates per age group

Pop.Deaths

Pop.Deaths

O E 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 3 2.14 133 1 0.89

45-64 0.0111 150 2 1.67 143 3 1.59

65 + 0.0194 20 6 0.39 192 8 3.72

Total 1060 18 9.05 682 15 8.04

STANDARDIZATION OF RATESINDIRECT METHOD

Calculate the SMR:– SMR =

SMRGroup 1 = = 1.99

SMRGroup 2 = = 1.87

Both are higher than the standard population

EXAMPLE STANDARDIZATION Country A Country B Country C

Age groups (in years)

Population Deaths Populations Deaths Population Deaths

0-20 300 6 100 2 800 15

21-50 400 80 150 30 600 56

51-85 300 120 250 100 600 110

Find:Crude death rates for each country

Using C as the standard perform:Direct standardizationIndirect standardization