UKURAN ASOSIASI

Tipe ukuran yang digunakan dalam epidemiologi

• Ukuran asosiasi– Merefleksikan kekuatan atau besar asosiasi

antara suatu eksposur/faktor risiko dan kejadian suatu penyakit

– Memasukkan suatu perbandingan frekuensi penyakit antara dua atau lebih kelompok dengan berbagai derajat eksposur

– Beberapa ukuran assosiasi digunakan untuk mengestimasi efek

Basic Question in Analytic Epidemiology

• Are exposure and disease linked?

Exposure Disease

Ukuran-ukuran asosiasi• Ukuran rasio (perbandingan relatif)

– rasio dua frekuensi penyakit membandingkan kelompok terpajan dengan kelompok tidak terpajan

• Ukuran perbedaan efek (perbandingan absolut)– perbedaan antara ukuran frekuensi penyakit

suatu kelompok terpajan dan kelompok yang tidak terpajan

Arithmetic

• Suppose you have $2 and I have $1• Absolute comparisons made by

subtraction• $2 – $1 = $1• “I have $1 more than you”

• Relative comparisons made by division• $2 ÷ $1 = 2 [$ units cancel out]• “I have twice as much as you”

Arithmetic • Suppose that the 5-year rate of a

disease • in smokers is 2 per 100• in non-smokers is 1 per 100

• Absolute comparison: (2 per 100) – (1 per 100) = 1 per 100• There is one addition case per 100 smokers

• Relative comparison: (2 per 100) ÷ (1 per 100) = 2 [no units; “per 100” units cancel out]• Smokers are at twice the risk of non-

smokers

UKURAN ASOSIASI

• Relative : –RR (relative risk)

•Risk ratio•Rate ratio

–OR• Absolute :

–RD (risk difference)

Measures of Association

• How much greater the frequency of disease is in one group compared with another.

• Often presented in the form of a

two-by-two table.

Two-By-Two Table

a b

c d

DiseaseYes No

Yes Exposure No

Total a+c b+d

Total

a+b

c+d

a+b+c+d

Hypothetical Two-By-Two Table

70 300

15 700

Lung cancerYes No

Yes Smoking No

Total 85 1,000

Total

370

715

1,085

Relative Risk (RR)• Measures how likely the exposed group

will develop a disease compared to the unexposed group.

RR = incidence in the exposed = a/(a+b)

incidence in the unexposed c/(c+d)

Example: Hypothetical StudyLung cancer

Yes No Total

Yes 70 300 370

Smoking No 15 700 715

Total 85 1,000 1,085

Relative Risk = 70/(70+300) = 9.0 15/(15+700)

Which means… participants who smoked were 9 times more likely to develop lung cancer than those who did not smoke.

Interpreting Measures of Association

RR of 1.0 indicates that the occurrence of disease in the exposed an unexposed groups are identical:

–No association observed between exposed and unexposed groups.

Interpreting Measures of Association (Continued)

• RR greater than 1.0 indicates a positive association, or an increased risk among the exposed.

• RR less than 1.0 means that there is a decreased risk among the exposed group.

Ukuran-ukuran asosiasi• Ukuran rasio

– Rasio risiko atau risiko relatif (RR)

terpajantidakkelompokpadaRisikoterpajankelompokpadaRisikoRR

– Rasio Insidens Kumulatif (RIK)

terpajantidakkelompokpadakumulatif InsidensterpajankelompokpadakumulatifInsidensRIK

Perhitungan RR untuk CI

Outcome (+) Outcome (-) Total

E (exposed) a b a + b

NE (unexposed) c d c + d

Total a + c b + d N (a + b + c + d)

CI pada populasi exposed (E) --- a/(a + b)RR=

CI pada populasi unexposed (NE) --- c/(c + d)

THEN, FOLLOW TO SEE WHETHER

Totals

Incidence rates

of Disease

Disease Develops

Disease Does Not Develop

Exposed a b a + b

NotExposed c d c + d

FIRST,

SELECT

aa+b

cc+d

Incidence in exposed

Incidence in non-exposed

=

=

aa+b cc+d

Relative Risk ( RR ) = incidence in exposed incidence in non-exposed =

A Prospective Study of 3,000 Smokers and 5,000 Non-smokers to Investigate Smoking and Coronary Heart Disease (CHD)

Example :

DevelopCHD

Do Not Develop CHD

Total

Incidence per 1,000 per year

Healthy Smokers 84 2,916 3,000 28.0

Healthy Non-Smokers 87 4,913 5,00

0 17.4

THEN FOLLOW UP TO SEE HOW MANY

FIRST,SELECT

Ukuran-ukuran asosiasi• Ukuran rasio

– Rasio rate atau rasio densitas insidens (RDI)

terpajantidakkelompokpadainsidensDensitasterpajankelompokpadainsidens DensitasRDI

– Rasio Prevalens (RP)

terpajantidakkelompokpada PrevalensterpajankelompokpadaPrevalensRP

Perhitungan RR untuk IR

Outcome (+) Person-time

E (exposed) a N1

NE (unexposed) c N0

Total a + c T

IR pada populasi exposed (E) --- a/N1

RR=IR pada populasi unexposed (NE) --- c/N0

Contoh 5.Tabel 1. Kaitan antara merokok dan angka insidens stroke dalam suatu kohort.

Kategori merokok

Jumlah kasus stroke

Orang-tahun observasi (lebih dari 8 tahun)

Tingkat insidens stroke (per 100.000 orang tahun)

Tidak pernah merokok 70 395.594 17,7Mantan perokok 65 232.712 27,9Perokok 139 280.141 49,6

Total 274 908.447 30,2

Sumber: diterjemahkan dari:Beaglehole et al. Basic Epidemiology. WHO. 1993. 18.

Ukuran-ukuran asosiasi• Dari Tabel 1.• Hitunglah:

– Rasio rate atau rasio densitas insidens (RDI)

terpajantidakkelompokpadainsidensDensitasterpajankelompokpadainsidens DensitasRDI

8,217,749,6RDI

Postmenopausal Hormone Supplement and CHD

CHD Person-years

Ever use 30 54,308.7 Past use 19 24,386.7 Current 11 29,922.0Never use 60 51,477.5

RR ever use vs never use = (30/54,308.7) / ( 60/51477.5) = 0.5

RR past use vs never use = (19/24386.7) / (60/51477.5) = 0.7

RR current use vs never use = (11/29922.0) / (60/51477.5) = 0.3

Ukuran-ukuran asosiasi

• Ukuran rasio– Rasio odds (Odds ratio = OR)

• Nama lain: Odds relative; rasio kros-produk• rasio dua odds yang digunakan dalam studi

kasus-kontrol untuk mengestimasi rasio rate atau rasio risiko

Ukuran-ukuran asosiasi

• Ukuran rasio– Rasio odds (Odds ratio = OR)

• odds untuk satu kelompok dibagi dengan odds untuk kelompok yang lain

• Bisa diinterpretasikan sama seperti risiko relatif, dg syarat tertentu (misal: incidence rendah rare disease assumption)

Ukuran-ukuran asosiasi

• Odds suatu kejadian– rasio probabilitas bahwa kejadian terjadi

terhadap probabilitas kejadian tidak terjadi

P = Probabilitas suatu kejadian terjadi1 – P = Probabilitas suatu kejadian tidak terjadi

P1PperistiwasuatuOdds

THEN, FOLLOW TO SEE WHETHER

Totals

Incidence rates

of Disease

Disease Develops

Disease Does Not Develop

Exposed a b a + b

NotExposed c d c + d

FIRST,SELECT

aa+b

cc+d

Incidence in exposed

Incidence in non-exposed

=

=

PROSPECTIVE STUDY

CASE – CONTROL (REPROSPECTIVE STUDY)

CASES

( with diseas

e)

CONTROLS ( without disease)

WereExposed a b

Were Not

Exposedc d

Totals a + c b + d

Proportion

exposed

aa+c

bb+d

FIRST,SELECT

THEN,MEASURE

PAST EXPOSUR

E

=

Figure 11-5 A, Odds ratio (OR) in a cohort study. B, Odds ratio (OR) in a case-control study.

Downloaded from: StudentConsult (on 8 October 2009 11:44 AM)© 2005 Elsevier

In case-control studies, the odds ratio is the ratio of the odds of the cases having been exposed to the odds of the controls having been exposed, i.e:

In prospective studies, the odds ratio is the ratio of the odds of the exposed people developing the disease to the odds non-exposed people developing the disease, i.e: a

b cd

=adbc

ab

cd =

adbc :

ac bd

=adbc

ac =

adbc : b

d

The odds ratio (Relative Odds)

Tabel 1. Tabulasi silang pemajan dan status sakit, insidens sakit dan Probabilitas odds sakit

pada studi kohort.Status sakit

Pemajan Sakit Tidak sakit

Total Insiden sakit (Risk)

Probabilitas odds sakit

+ a b a + b a/(a+b)

- c d c + d c/(c+d)

Total a + c b + d a+b+c+d

ba

baabaa

1

dc

dccdcc

1

Odds Ratio (OR) = Relative Odds = Cross Product Ratio pada studi kasus kontrol

Faktor Kasus Kontrol Total

Perokok 650 (a) 950 (b) 1600

Bukan perokok

50 (c) 350 (d) 400

Total 700 1300 2000

kontroluntukpemajanOddskasusuntukpemajanOddsRatioOdds

Odds Ratio (OR) = Relative Odds

cxbdxa

dbca

RatioOdds

kontroluntukpemajanOddskasusuntukpemajanOddsRatioOdds

8,450950350650

xx

cxbdxaRatioOdds

Perokok mempunyai risiko menjadi kasus 4,8 kali dari yang bukan perokok.Interpretasinya: odds perokok menjadi kasus 4,8 kali lebih besar dari odds bukan perokok

Prevalence Odds Ratio (POR) = Cross Product Ratio bila data didasarkan pada kasus-kasus

prevalens

Faktor Kasus Kontrol TotalPerokok 650 (a) 950 (b) 1600

Bukan perokok

50 (c) 350 (d) 400

Total 700 1300 2000

8,450950350650Prevalence xxRatioOdds

25,3125,0

40625,0400/501600/650)(Prevalence Ratioproportion

The odds ratio ( relative odds) is a good approximation of the relative risk when :

1.The cases are representative of all cases with regard to exposure;

2.The controls are representative of all control with regard to exposure;

3.The disease being studied is rare

=

Odds Ratio & Risk RatioThe odds ratio will provide a good estimate of therisk ratio when:

1. The outcome (disease) is rareD+ D-

E+ a bE- c d

OR = (a / c) / (b / d)OR = (ad) / (bc)

a / (a +b )RR = ------------

c / (c +d)If the disease is rare, thencells (a) and (c) will be small

a / (a +b ) a / b adRR = ------------ = ------ =-- = OR

c / (c +d) c / d bc

Figure 11-6 Example: The odds ratio is a good estimate of the relative risk when a disease is infrequent.

Downloaded from: StudentConsult (on 8 October 2009 11:44 AM)© 2005 Elsevier

Figure 11-7 Example: The odds ratio is not a good estimate of the relative risk when a

disease is not infrequent.Downloaded from: StudentConsult (on 8 October 2009 11:44 AM)

© 2005 Elsevier

In a prospective study/cohort study, the Relative Risk can be calculated directlyIn a retrospective study /case control study , the RR cannot be calculated directly, so that the Relative Odds or ODDS RATIO ( Cross Products Ratio ) is used as an estimate of the RR, when the risk of the disease is low

OR & RR

• Pada penyakit yang jarang terjadi,nilai Odds Ratio hampir sama dengan nilai Relative Risk (Risk Ratio). Nilai Prevalence Odds Ratio hampir sama dengan nilai Prevalence Proportion Ratio.

• Pada penyakit yang umum terjadi, nilai Odds Ratio lebih ekstrim dari pada Risk Ratio.

Incidence Odds Ratio (POR) = Cross Product Ratio bila data didasarkan pada kasus-kasus

insidens

Faktor Sakit Tidak sakit TotalPerokok 20 (a) 980 (b) 1000

Bukan perokok

10 (c) 990 (d) 1000

Total 30 1970 2000

02,29801099020I xxRatioOddsncidence

00,201,002,0

1000/101000/20)(Incidence Ratioriskproportion

Gerstman Chapter 8 (partial) 46

Interpretation of Odds Ratio• Relative odds associated with exposure

OR = 1 no associationOR > 1 positive associationOR < 1 negative association

• Size of OR indicates strength of association

• OR ≈ RR when disease rare (i.e., risk < 5%); when disease not rare, OR still a valid measure of association

RR < 1 RR = 1 RR > 1

Risk comparison between exposed and unexposed

Risk for disease is lower in the

exposed than in the unexposed

Risk of disease are equal for exposed and unexposed

Risk for disease is higher in the exposed than in the unexposed

Exposure as a risk factor for the disease?

Exposure reduces disease

risk(Protective

factor)

Particular exposure is not a

risk factor

Exposure increases

disease risk(Risk factor)

R ela tive riskR R O R

A ttrib u tab le ris kA R P A R

M easu re o fA ssoc ia tion

Gerstman Chapter 8 (partial) 49

Epidemiology Kept Simple

Chapter 8 Measures of Association

If it’s not clear…• Gordis Leon, M.D., M.P.H., Dr.P.H. 2009.

Epidemiolgy. W.B. Saunders Company. Philadelphia ,Chapter 11

• Epidemiology in Medicine. Henneckens CH, Buring JE. Edited by Mayrent SL, Chapter 4