1.6 standardization

Types of rates• Crude rate: number of events in a total population /

person-time for which the population at risk has been observed

• Specific rates: number of events in a subpopulation / person-time for which the subpopulation at risk has been observed (e.g. for age groups)

• Standardized or adjusted rates: have undergone statistical transformation to permit comparison of rates across populations or among groups differing in the distribution of some characteristic (e.g., age) that may affect the risk of disease

Standardization

Comparing crude rates• A crude rate represents the actual experience of the

population and is thus a valuable way to describe the disease experience

• Comparing crude rates between two or more populations can be misleading because populations may differ with respect to characteristics that affect morbidity and mortality

• What are some of the principal factors that influence morbidity and mortality?

Standardization

• Consider age-specific rates…• The crude rate can be thought of as a weighted average

of the age-specific rates– the weights are the proportion of the population in

each age category• Crude rate = ∑(age-specific rate x proportion of pop in

that age category)• Even if two populations had identical age-specific rates,

the crude rates for the two populations would differ if the age structure of the two populations were different

Standardization

• Population 1:– 500,000 people aged 20-24– 500,000 people aged 25-29

• Population 2:– 200,000 people aged 20-24– 800,000 people aged 25-29

• In both populations– CI among 20-24 = 0.002– CI among 25-29 = 0.009

• What are the crude “rates” in populations 1 & 2?

Standardization

• Crude rate = ∑(age-specific rate x proportion of pop in that age category)

• Population 1, crude CI = 0.002*0.5 + 0.009*0.5 = 0.0055• Population 2, crude CI = 0.002*0.2 + 0.009*0.8 = 0.0076• What do you think about comparing the health experience of these

two populations using their CI values?

Population 1 Population 2

Age rate proportion rate proportion

20-24 0.002 0.5 0.002 0.2

25-29 0.009 0.5 0.009 0.8

Standardization

• Standardization of rates allows direct comparison of rates between populations– A standardized rate is a summary rate that has been

adjusted to account for the differences in the distribution of characteristics that affect disease (e.g., age) between populations

– Standardized rates allow fair comparisons to be made between populations

– Answers the question: what would the death rate be in each population, if they had identical distributions of {X}? e.g. age

– Counterfactual idea

Standardization

• Compare the death rates in these two states• Concerns about direct comparison of these crude rates?

– Age structures of the populations of these two states are quite different

Standardization

Direct standardization• Choose a standard population (e.g., 1990 or 2000 US

population from US Census)• Use the actual age-specific rates from each study

population (e.g., state)• Apply these rates to the standard population in each

age category• Calculate the number of outcomes that would have

been observed in the study population if it had the age distribution of the standard population – a counterfactual idea

• Calculate the adjusted rate of the outcome

Standardization

• Age adjusted rate = total expected outcomestotal standard population

Standardization

Key for direct adjustment:

Age specific rates come from your study population

Age specific population sizes (i.e, the weights) come from the standard population

• Where to start – set up table with age intervals• Fill in age specific rates from study population(s)• Fill in age specific population sizes from standard population (from

outside source, e.g., US Census)

StandardizationDirect Standardization

• Calculate expected number of deaths for study population(s) within age strata

• E = RateStudy*PopulationStandard

• EFL<5 = (179.26/100,000)*18,900,000 = 33,880


• Sum expected deaths for study population(s) and calculate age adjusted rates

• Rateadj = EStudy/PopulationStandard

• RateadjFL =1,912,628/248,800,000 = 0.007686 = 768.6/100,000


Standardization

• Compare the death rates in these two states again

Direct Standardization

• Choice of standard population– Distribution of one of the two populations you want to

compare– Distribution of the two populations combined– Some outside standard (e.g., US population from

census)– Choice should be driven by the counterfactual

question you want to ask• What would the rates be if my two study populations had the

same age structure as population X?

Standardization

• Beware: the values you calculate will depend on the standard population chosen– Can get different results from different standards if

the standards have notably different age structures• Note that the actual value of the new adjusted

rate is a product of the choice of a standard population – it is not a “real” rate

Standardization

Pros:• Directly standardized rates can be used to compare

disease rates across areas and time

Cons:• Requires age-specific rates that are not often available

at a local level or in certain populations• Rates may not be stable for small number of events

(approximately <100 events)

Standardization

Standardization• At home exercise (for lab)

– Prostate cancer mortality by race

– White men: 1359 deaths / 4,738,246 men– 28.7 deaths per 100,000 men

– Black men: 121 deaths / 418,992 men– 28.9 deaths per 100,000 men

Standardization• At home exercise (for lab)

• Calculate age adjusted rates of prostate cancer mortality by race

• There may be situations in which age-specific rates are not available for your study population– Common in occupational studies – number of cases available

from records but unable to reconstruct rates• You still want to be able to make a comparison between

the disease experience of your study population and another population accounting for differences in the distribution of characteristics (e.g., age)

• If you know the age structure of your study population, indirect standardization is an option

Standardization

• Choose a standard population for which rates of your outcome are available

• Use the age-specific rates from the standard population

• Apply these rates to the study population in each age category

• Calculate expected number of deaths that would have occurred in the study population

• This expected number of deaths is counterfactual– It’s the number of deaths that would have occurred in the study

population if it had the same age-specific rates as the standard population

• Compare the observed number of deaths in the study population to the expected number of deaths if the standard rates applied

Standardization

Standardization• SMR = total observed

outcomesx 100 total expected

outcomes

• Standardized morbidity/mortality ratio (SMR):– Ratio of the observed number of outcomes in the study

population to the expected number of outcomes if the study population had the same age-specific rates as the standard population

– Answers question: is the morbidity/mortality experience greater than, less than, or similar to that which is expected in the standard population? (if equal, SMR = 100)

• Direct vs. indirect standardization summary

Population used (weight)

Rate applied

Direct Standard Study (observed)

Indirect Study (observed)

Standard

Standardization

Key for indirect adjustment:

Age-specific rates come from your standard population

Age-specific population sizes (also called weights) come from the study population

Standardization

• Example: we have data from two health care organizations on the numbers of occupational injuries reported– Health care organization 1: 95– Health care organization 2: 64

• We are wondering how these health care organizations compare to the US average for those working in health care regarding injuries

Standardization

• Where to start – set up table with age intervals• Fill in age-specific rates from standard population• Fill in age-specific population sizes from study population(s)

StandardizationIndirect Standardization

• Calculate expected number of injuries for study population(s) within age strata

• E = RateStandard*PopulationStudy

• EOrg1,15-30 = (60/10,000)*5700 = 34.2


• Sum expected injuries for study population(s) and calculate SMR(s)• SMR = O/E• SMROrg1 = (95/66.7)*100 = 142


• Interpret each SMR as a comparison of that study population to the standard– Health care organization 1 had a 42% higher rate of injury than the

health care workers in the US population– Health care organization 2 had a 9% lower rate of injury than the health

care workers in the US population• You cannot compare SMRs to each other


Pros:• Indirect standardization does not require age-specific rates, only

total number of events in the study population and age structure of the study population

Cons:• SMRs cannot be directly compared

– Each SMR captures a counterfactual comparison within that specific population• E.g, Observed deaths from pop A/Expected deaths from pop A

(ifstandard rates applied)

– The two study populations may have different age structures and the expected deaths depends on the age structure of each study population

• Unlike directly standardized rates, SMRs give no idea of the actual burden of disease

Standardization

Standardization• Examining the lack of comparability of SMRs by uncovering the

true age-specific injury rates in our two health care organizations

Standardization• Age-specific injury rates are IDENTICAL in the two health care

organizations

Standardization

• Why are the SMRs so different?• Org 1 has a younger population and the age-specific rates in that

younger population are higher than in the standard• Org 2 has an older population and the age-specific rates in that older pop

are lower than in the standard• Each SMR is a comparison of one study population to the standard – not

a comparison of one study population to another

• Direct vs. indirect standardization summary

Population used (weight)

Rate applied

Direct Standard Study (observed)

Indirect Study (observed)

Standard

Standardization

1.6 standardization

Health & Medicine

Transcript of 1.6 standardization