Standardization of Rates

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Standardization

of Rates26 May 2015



Aims

Concepts and basic methods forderiving measures that arecomparable across populations thatdier in age and other demographic

variables.



Introduction

Virtually every large population isheterogeneous in regard to sociodemographic e.g.! age! gender!

education! religion"! geographic! genetic!

occupational! dietary! medical history!and other personal attributes andenvironmental factors related to health.



Introduction

#n overall measure that does notta$e e%plicit account of thecomposition of the population is

called crude. &t is an average of the values for the

individual subgroups strata"!'eighted by their relative si(es. )he larger the subgroup! the more

in*uence it 'ill have on the crudemeasure.

)he death rate for a population is a



Crude rate

Consider a population of si(e +consisting of ,ve age strata. -achage stratum has ni i1 to 5" people.

/uring the follo'ing year! eachstratum 'ill e%perience somenumber of deaths di.

)he total population si(e! + ni!

the total number of deaths! / di!

and the crude mortality rate is /+.



Crude rate

)he crude rate can also be 'rittenas a 'eighted average of thestratum-specic mortality rates!dini! as follo's

+ote 'i1.



Crude rate

)he crude rate is the simplest andmost straightfor'ard summary ofthe population.

3ut mortality is strongly related toage! so the stratum4speci,cmortality rates 'ill dier greatly

from one another. Crude rate glosses over thisheterogeneity of stratum4speci,cmortality rates.



Crude rate

&f the populations dier incomposition some of 'hat 'eobserve may be attributable to these

dierences.

+eed a method to average thestratum4speci,c rates to allo' acomparison bet'een populations.



Standardization

tandardi(ation refers to methods ofadustment based on 'eightedaverages in 'hich the 'eights are

chosen to provide an appropriate basisfor the comparison. )he number of persons in various strata of

one of the populations in the comparison. #n aggregate of these populations! or ome e%ternal relevant population.



Motivating example



Remarks

)he dierence in crude death ratesbet'een #las$a and Miami resultsfrom dierences in age distributions

rather than dierential age4speci,cdeath rates.

&t follo's intuitively that if Miamiand #las$a had the same agedistribution regardless of 'hat thatdistribution might be" their crude

death rates 'ould be similar! since



Direct Standardization

&n direct standardi(ation thestratum4speci,c rates of studypopulations are applied to the age

distribution of a standardpopulation. &n the e%ample above! each age group is

a stratum.

)he directly age4standardi(ed deathrates are e7uivalent to the crude

death rates 'hich Miami and #las$a8 8




Computation of direct standardi(edrates is straightfor'ard



xample

)he standardi(ed death rate for'hite Miami 'omen 19:0 ;..population of 'hite 'omen as the

standard" is



xample! cont"d

)he corresponding standardi(ed ratefor #las$a is



Some points to consider

)he directly standardi(ed rate is a'eighted average.

)he crude death rate in a populationcan be regarded as an average ofthe population<s stratum4speci,c

death rates 'eighted by its o'n agedistribution.



Motivation forstandardization ummary rates from t'o or more

populations are more easilycompared than multiple strata4

speci,c rates. &mportant 'hen comparing rates from

several populations or 'hen each

population has a large number of strata.

mall numbers in some strata may

lead to unstable stratum4speci,c



Standardized ratios ordi#erences =ates that have been standardi(ed

by the direct method! using thesame standard population! may be

compared in relative or absoluteterms as a ratio or as a dierence

>e can obtain a 8tandardi(ed =ate=atio8 ==" by dividing the

standardi(ed rate for Miami by that



Standardized ratios ordi#erences

imilarly! the dierence of the t'orates 'ould be a 8standardi(ed ratedierence8

=/ 6.92?6.:10.21 per 1!000 ? the ratio has no need for the

scaling factor! but the dierence does.



Standardized ratios ordi#erences ince the rates are virtually

identical! the == is close to 1! andthe =/ is close to (ero! all give the

same message

)he mortality e%perience in #las$a!

Miami! and the total ;.. are allabout the same 'hen the dierencesdue to age structure are eliminated.



Standardized ratios ordi#erences # directly standardi(ed rate can be

compared to the crude rate in thestandard population.

)he crude rate in the standardpopulation and the directly

standardi(ed rates are all 'eightedaverages based on the same set of'eights.

)he proportional age distribution in the



Standardized ratios ordi#erences o



Sparse data

tandardi(ed rates are not al'aysmeaningful for sparse data.

@or the comparisons to be meaningful

there must be large enough numbers inall important strata. &n strata constituting substantial 'eight in the

standardi(ation procedure.

)here are various rules of thumb for 'hatconstitutes 8large enoughA. #t least 10 or 20 events e.g.! deaths! cases"

and a denominator of at least 100.



Indirect Standardization

;sed 'hen data sparse.

#n 8indirect8 standardi(ationprocedure is often used and a8standardi(ed mortality ratio88M=8" computed.

Mirror image of the directstandardi(ation.




&ndirect standardi(ation ta$esstratum4speci,c rates from astandard population.

)hese rates are then averaged usingas 'eights the stratum si(es of the

study population. &n direct standardization! the studypopulation provides the rates and thestandard population provides the

'eights.




Comparison of indirectly4standardi(ed rates can beproblematic. -ach study population<s standardi(ed

rate is based on its o'n set of 'eights.

Bnly comparison that is al'ayspermissible the study population vsthe standard population.



Calculating SMR

)a$e the observed number of deathsor events in the study population

Compare to an 8e%pected8 number ofdeaths.

)he number of deaths that 'ould bee%pected in the study population ifits stratum speci,c rates 'ere the

same as for the standard population.



Calculating SMR

)he ratio of observed to e%pecteddeaths is termed the tandardi(edMortality Morbidity" =atio M=".

)he e%pected number of deaths isobtained as follo's



Calculating SMR



Calculating SMR

)he M= indicates the relativee%cess or decrement in the actualmortality e%perience in the study

population 'ith respect to 'hatmight have been e%pected had ite%perienced the force of mortality in

the standard population.



Comparison of SMR$example



Comparison of SMR$example )hough both occupations have

e%actly the same stratum4speci,crates! their M=<s dier! due to the

substantially dierent agedistributions for the t'ooccupations.

o'ever! the directly standardi(edrates for both occupations are thesame



%otes

)he apparent e7uivalence of thedirectly standardi(ed rates ismisleading. @e' deaths in the younger age stratum

in Bccupation # and in the older agestratum in Bccupation 3.

)he only conclusion 'e can be

con,dent of is that both occupationshave elevated mortality ratescompared to the standardpopulation.

+o evidence from standardi(ation to



Calculating ISR

&ndirectly standardi(ed rate &="can be obtained from an M= asfollo's

&f the study population has t'ice themortality rate of the standardpopulation! the standardi(ed rate forthe study population should be t'ice

the observed death rate in the



Mortality example

Miami

#las$a



Summary of rates



&ey messages

Dopulations are heterogeneous ?they contain disparate subgroups.o any overall measure is a

summary of values for subgroups. )he observed 8crude8" rate is in fact

a 'eighted average of

subgroup48speci,c8 rates! 'eightedby the si(e of the subgroups.

Comparability of 'eighted averages

depends on similarity of 'eights.



&ey messages

8tandardi(ed8 and other $inds ofadusted" measures are also'eighted averages! 'ith 'eights

chosen to improve comparability. Crude rates are 8real8! standardi(ed

rates are hypothetical.

)he 8direct8 method 'eights ta$enfrom an e%ternal standardpopulation" gives greater

comparability but re7uires more



&ey messages

)he 8indirect8 method 'eightsta$en from the internal studypopulation" re7uires fe'er data but

provides less comparability. Choice of 'eights can aect both

rates! comparisons of rates! and

comparability to other populations. #ny summary conceals informationE

if there is substantial heterogeneity!

the usefulness of a summary is open



Study designs



Study types

1. Case reports 2. Case series F. -cologic G. Cross4sectional 5. Case4control

6. @ollo'4upcohort :. &ntervention trialscontrolled

trials



Study types

/esigns 1 and 2 are employed inclinical studies.

/esigns F and G are regarded asprimarily descriptive.

/esigns 5 and 6 can be employed inanalytic hypothesis testing" or

descriptive modes. /esign : is primarily analytic.



'( cologic

-cologic studies obtain data at thelevel of a group! community orpolitical entity! often by ma$ing use

of routinely collected data. -cologic studies may also be the

only 'ay to study the eects of

group4level constructs! for e%ample!la's e.g.! impact of a seatbelt la'"!services availability of a suicide

prevention hotline"! or community



)( Cross-sectional

# cross4sectional study is one in 'hichsubects are sampled 'ithout respect todisease status and are studied at a

particular point in time. )he current or historical status of

individuals is assessed and may bee%amined in relation to some current or

past e%posure. Most useful for conditions that are not

rapidly fatal! not terribly rare e.g.!elevated blood pressurecholesterol! many

s chiatric disorders diet etc. .

) C ti l



)( Cross-sectional$strengt*s Can study entire populations or a

representative sample. Drovide estimates of prevalence of

all factors measured. Hreater generali(ability.

) C ti l



)( Cross-sectional$ +eaknesses usceptible to selection bias e.g.

selective survival" usceptible to misclassi,cation e.g.

recall" &nformation on all factors is

collected simultaneously! so it can be

diicult to establish cause and eect +ot good for rare diseases or rare

e%posures



,( Case-control

# case4control study is one in 'hichpersons 'ith a condition 8cases8" areidenti,ed! suitable comparison subects

8controls8" are identi,ed! and the t'ogroups are compared 'ith respect to priore%posure.

3ecause case4control studies select

participants on the basis of 'hether ornot they have the disease! the case4control design does not provide anestimate of incidence or prevalence of the

disease.



,( Case-control

Strengt*s Hood for rare diseases -icient in resources and time

eaknesses usceptible to selection bias e.g.! cases

or controls may not be appropriately

8representative8" usceptible to misclassi,cation bias e.g.

selective recall" May be diicult to establish that 8cause8

preceded 8eect8.



.( /ollo+-up0co*ort

&n a follo'4up study! people 'ithout thedisease are follo'ed up to see 'hodevelops it! and disease incidence in

persons 'ith a characteristic is compared'ith incidence in persons 'ithout thecharacteristic.

&f the population follo'ed is a de,ned

group of people a 8cohort8"! then thestudy is referred to as a cohort study.

#lternatively! the population under studymay be dynamic e.g.! the population of a

eo ra hical re ion .



.( /ollo+-up0co*ort

Strengt*s 3etter for rare e%posures Iess confusion over relative timing of

e%posure and disease. eaknesses Costly and time consuming if disease is

rare andor slo' to develop.

Ioss to follo'4up may lead to selectionbias.

=elatively statistically ineicient unlessdisease is common.

1 I t ti



1( Interventiontrials0controlled trials #n intervention trial is a follo'4up

study in 'hich the primary e%posureunder study is applied by the

investigator. &n an intervention trial! the

investigator decides 'hich subects

are to be 8e%posed8 and 'hich arenot.

1 I t ti



1( Interventiontrials0controlled trials Strengt*s Most li$e an e%periment Drovides strongest evidence for

causality in relation to temporalityand control for un$no'n8confounders8

@ul,lls the basic assumption ofstatistical hypothesis tests

1 I t ti



1( Interventiontrials0controlled trials eaknesses -%pensive! time consuming!

sometimes ethically 7uestionable. ubects are often a highly selected

group selected for 'illingness tocomply 'ith treatment regimen!

level of health! etc." and may not berepresentative of all people 'homight be put on the treatment i.e.!generali(ability may suer".

Standardization of Rates

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