Frequency and

Measures of Association

DESCRIPTIVE EPIDEMIOLOGY

IncidencePrevalence

Holistic Diagnosis(BIOPSYCHOSOSIAL)

Risk Factors

Diagnostic Tools

ANALYTIC EPIDEMIOLOGY

Therapy, PrognosisCLINICAL EPIDEMIOLOGY(Prognostic Study, Clinical Trial, Meta Analysis)

Triad EpidemiologyHost – Agent - Environment

Lecture Contents• Frequency

– Prevalence– Incidence

• Cumulative• Density

• Precision– P value– Confidence level

• Association- Relative risk

- Rate ratio- Risk ratio

- Odds ratio- Risk difference

Frequency Measures

• Two types:

– Someone has the disease already: PREVALENCE

– Someone gets the disease in the future: INCIDENCE

Study Design

Direction of inquiry

CohortCase-control

Historical cohort

Survey / Cross Sectional

TODAY

Prospective CohortStart here

**

*

+

-+

-to t1

Free ofoutcome

Exposure Outcome

Historical Cohort Start here

**

*

+

-+

-to t1

Free of outcome

Exposure Outcome

Case Control Start here

Case

Control

+

Population

-+

-

Exposure Outcome

RASIO DAN PROPORSI

RASIO• PERBANDINGAN SECARA UMUM• TAK ADA KAITAN PEMBILANG DAN

PENYEBUT

PROPORSI• PEMBILANG MERUPAKAN BAGIAN

DARI PENYEBUT

A/B

A/(A+B)

Frequency measures: diagnostic research

• Suppose: you see a patient with symptoms that possibly point at arthritis

• Research question ?

Frequency measures: diagnostic research

• Suppose: you see a patient with symptoms that possibly point at venous thrombosis

• Research question: What is the probability of arthritis given the physical exam / tests?

Frequency measures: prevalence

• Cross-sectional studies– Determinant and disease measured at the

same time

• Prevalence – Number of persons with the disease at a

certain moment

Frequency measures: prevalence

• Prevalence (%) =

Number of persons with the disease

Total population

Numerator is part of denominator

ANGKA POINT PREVALENSI

MERUPAKAN NILAI PROPORSIPADA SATU SAAT TERTENTU

GUNA EVALUASI PENGOBATAN

S KASUS (BARU+LAMA) SATU SAATS SELURUH POPULASI SAAT ITU

POINT PREVALENCE• Tujuan : mengetahui prevalensi artritis di suatu

komunitas di suatu hari tertentu• Hari itu kita lakukan kunjungan dari rumah ke

rumah untuk melakukan anamnesis dan pemeriksaan fisik untuk menentukan berapa orang yang mengalami artritis pada hari itu

Prevalensi (point) =

Jumlah orang yang mengalami artritis hari itu

Jumlah penduduk di komunitas hari itu

PERIOD PREVALENCE

S BARU+LAMA SUATU PERIODES SELURUH POPULASI PERIODE

TERSEBUT

Frequency measures: prevalence

• Examples– 50% of the persons with a suspicion of

lung cancer had a lesion on the thorax X-ray

– In a general practice population of 2500 persons, 50 had asthma

– 30% of the Dutch people smoke

Frequency measures: prognostic research

• Suppose: You see a patient diagnosed as MCI post CABG who asks for her prognosis

• Research question?

Frequency measures: prognostic research

• Suppose: You see a patient diagnosed as MCI post CABG who asks for her prognosis

• Research question: What is the probability that I die within 5 years / get a relapse?

ANGKA INSIDENSI

POPULASI RENTAN = BEBAS KASUSMENURUT PERIODE WAKTU

PENYEBUT = POPULASI RENTAN (memiliki kemungkinan untuk menjadi

kasus)EVALUASI PENCEGAHAN

S KASUS BARU DLM SUATU PERIODES POPULASI RENTAN DLM PERIODE

TERSEBUT

• Incidence per 1000 =

• Incidence per 10.000 =

S KASUS BARU DLM SUATU PERIODEX 1000

S POPULASI RENTAN DLM PERIODE TERSEBUT

S KASUS BARU DLM SUATU PERIODEX 10000

S POPULASI RENTAN DLM PERIODE TERSEBUT

Frequency measures: Incidence

• Incidence– Number of new cases– In the population at risk

• Two types of incidence– Cumulative Incidence Risk (CIR)– Incidence Density Rate (IDR)

Cumulative Incidence Risk (CIR) calculation

Outcome

(+) (-)

Exposure a b

Non Exposure c d

a /(a +b) = CIR outcome in expose

c /(c +d) = CIR outcome in non expose

Post CABG Outcome

Dead Alive

Anterior/Inferior MCI 8 21

Non Anterior/Inferior MCI

12 97

Calculate :

• CIR death post CABG MCI anterior/inferior ?

• CIR death pada post CABG non MCI ant./inf ?

• CIR death post CABG MCI anterior/inferior ?

8/29 = 0.2759 = 27.59%

• CIR death pada post CABG non MCI ant./inf ?

12/109 = 0.1101 = 11.01%

Post CABG Outcome

Dead Alive

Anterior/Inferior MCI 8 21

Non Anterior/Inferior MCI

12 97

Frequency measures: Incidence

• Cumulative incidence– new cases in a certain time period in the

population at risk (free of the disease/outcome at the start)

– proportion / probability– varies between 0 and 1– within certain time period

Frequency measures: Incidence

• Cumulative incidence: examples– 5-year risk of a second MI– 10-year survival for women with breast

cancer– 1-year risk of a fracture for osteoporotic

women

Frequency measuresIncidence

• Incidence Density = number new patients

person-years of the population at risk

• 10 per 1000 person-years (PY)

• between 0 and infinity

Incidence Density Rate (IDR) calculation

Outcome(+)

Person-time

Exposure a t1

Non Exposure c t2

a /(t 1) = IDR outcome in expose

c /(t 2) = IDR outcome in non expose

PERSON-TIME CONCEPT

• Documents/ASIALINK/life table.doc

Incidence Density Rate (IDR) calculation

35 WEEKS

Relaps(+)

Person-time

Non Radiotherapy 21 182

Radiotherapy 9 359

a /(t 1) = IDR relaps in non radiotherapy ?

c /(t 2) = IDR relaps in radiotherapy ?

RESULTAfter 35 weeks follow up, we have 9 events of

new cell growth in Ca cerviks stage 2 with radiotherapy out of 359 person-week, giving an incidence rate of new cell growth in patient Ca cervix stage 2 with radiotherapy is :

• 9 / 359 = 0.025 • 9 cases / 359 person-weeks = • 25 cases / 1000 person in 35 weeks or • 37 cases / 1000 person in a year

RESULTAfter 35 weeks follow up, we have 21 events

of new cell growth in Ca cerviks stage 2 without having radiotherapy out of 182 person-week, giving an incidence rate of new cell growth in patient Ca cerviks stage 2 without having radiotherapy is

• 21 / 182 = 0.115 • 21 cases / 182 person-weeks = • 115 cases / 1000 person in 35 weeks or • 172 cases / 1000 person in a year

INSIDENCE DAN PREVALENCE

2002 20042003

HUBUNGAN NILAI

P = I x d

Prevalens

Insidens

Exercise 1

Exercise 1

Ad question 1: tonsillitisA. Dutch population

B. 1 year

C. incidence

D. 19/1000 or 1.9%

Exercise 1

Ad question 2: asthmaA. Children in the general practice

B. Certain moment (look into practice data at a certain moment)

C. Prevalence

Exercise 1

Ad question 3: breast cancerA. Women

B. Life

C. Incidence

Exercise 1

Ad question 4: vertebral collapseA. 9%

B. 55-59 year-old men and women

C. Certain moment

D. Prevalence

Exercise 1

Ad question 5: fracturesA. Post-menopausal women

B. Follow-up duration of the study

C. Incidence

Frequency measures: Incidence

• How do we calculate a cumulative incidence?

Frequency measures: example cohort

• 13 persons followed for 5 years for mortality– A-----------------------------x--Moves away – B-----------------------------x-------------Death – C-------breast cancer/death– D-----------------------------x------------------------------------------- alive– E-----------------------------x--------lost to follow-up – F-----------------------------x--------------------------------------------alive– G-----------------------------x---------------------------breast cancer/death– H-----------------------------x-Myocardial infarction/death– I--------death– J------------------------------x-------------------------------------------alive– K-------------lost to follow-up– L-----------------------------x----------------moves from the area– M--------1---------------2--x----------3---------------4-------------------alive

Frequency measures: example cohort

• CI = 5/13 = 38%

• Incidence density ?

Frequency measures:Etiologic research

• Suppose: you see a patient with lung cancer, who asks for the possible cause

• Research question?

Frequency measures:Etiologic research

• Suppose: you see a patient with lung cancer, who asks for the possible cause

• Research question: Is smoking a risk factor for lung cancer?

Measures of association

• Epidemiology – Disease = f (determinants)– Is the determinant associated with the

disease? – Is the probability of disease different for

exposed and non-exposed

Ratio risk : Outcome risk in exposed

Outcome risk in non exposed

CIR ratio or IDR ratio

Measures of association:Cohort approach

• Research question? Is smoking associated with lung cancer?

• Cohort approach– divide the cohort in smokers and non-smokers– estimate the incidence density (or CI) in each

group– prior: ID smokers > ID not smokers

Association measurement

• RELATIVE RISK (RR) =

Outcome incidence in expose group

Outcome incidence in non expose group

– RISK RATIO (CIR ratio)

– RATE RATIO (IDR ratio)

(CIR)

Outcome Risk Ratio

(+) (-)

Exposed a b

Non exposed c d 1,00

Risk Ratio =

a /(a +b)c /(c +d)

)1(%95 ZRRCI

Post CABG Outcome

Dead Alive

Anterior/Inferior MCI 8 21

Non Anterior/Inferior MCI

12 97

Calculate :

Risk of death in post CABG ant/inf MCI compare to non ant/inf MCI ?

HasiljadiRR (95% CI)

Mati Hidup

Anterior/inferior 8 21

Bukan ant./inferior 12 97 1,00

Risk Ratio =

a /(a +b)c /(c +d)

Interpretation ?

2.51 (1.13-5.55)

HasiljadiRR (95% CI)

Mati Hidup

Anterior/inferior 8 21 2,51 (1,13-5,55)

Bukan ant./inferior 12 97 1,00

Kesimpulan:

Pasien IMA anterior / inferior secara signifikan mempunyai risiko mati 2,5 kali lipat lebih tinggi jika dibandingkan dengan pasien penderita IMA bukan anterior/inferior, post CABG di ICCU.

Interpretasi hasil :

RR (OR) < 1 = exposure as protective factor for outcome occurance

RR (OR) = 1 = No occurance difference between exposed and non exposed

RR (OR) > 1 = exposure as risk factor for outcome occurance

Rumus dasar (IDR)Rate Ratio

Outcome

(+)

Person-time

Exposed a t1

Non exposed c t2 1,00

Rate Ratio =

a /(t 1)

c /(t 2)

)1(%95 ZRRCI

Measures of association: Cohort approach

• Smoking and lung cancer Lung cancer

Yes No Rokok 440 - 22.008 py

DeterminantTidak Rokok 212 - 21.235 py

• Hitung:Risiko terjadinya Ca PARU pada perokok dibandingkan dengan tidak perokok?

Measures of association: Cohort approach

• Smoking and lung cancer Disease

Yes No Yes 440 - 22.008 py

DeterminantNo 212 - 21.235 py

RR = (440/22.008) / (212/21.235) = 2.0

Measures of association

• Risk difference (RD) between exposed and non-exposed reflects public health impact = CIRexposed – CIR nonexposed or

= IDRexposed - IDR nonexposed

• Risk difference smoking and lung cancer– RD = 20/1000 py - 10/1000 py = 10 / 1000 py

Measures of association:Case Control approach

• Research question: Does smoking increase the risk of lung cancer ?

• Patient control study– select cases and controls – Estimate the frequency of smoking among cases

and controls– prior: % smokers among cases > % smokers

among controls

Measures of association: Case Control approach

Disease

Yes No

Yes a b

Determinant

No c d• RR?• Odds ratio = (a/c) / (b/d) = ad / bc

Measures of association:Case Control approach

• Smoking and lung cancer (controls = 10% random sampling from cohort) Disease

Yes No Yes 440 300 740

DeterminantNo 212 350 562

• Odds ratio (440/212) / (300/350) = 2.42• RR = (440/740) / (212/562) = 1.57 (shouldn’t be

calculated)

Measures of association• Smoking and lung cancer

Disease Yes No

Yes 440 3000 3440Determinant

No 212 3500 3712

• Now entire cohort as control• RR = (440/3440) / (212/3712) = 2.23• Odds ratio =(440/212) / (3000/3500) = 2.42• RR (a/(a+b)) / (c/(c+d)) ~ (a/c) / (b/d)

Frequency measures:Therapeutic research

• Suppose: you see a patient with an increased blood pressure who you want to treat with blood pressure decreasing drugs. He asks about the effect of this treatment on the prognosis

• Research question: Does treatment decrease the probability of CVD?

Frequency measures:Incidence

• Intervention study (RCT) – Estimate incidence density (or CI) for each group– prior: ID treated < ID not treated

Exercises 2 and 3

Exercise 2

A. People of age 55 years and older

B. 5 years

C. Incidence (probably cumulative)

D. Relative risk and risk difference

Exercise 2

Risksmokers = 41/1736 = 0.024

Risknon-smokers = 107/5949 = 0.018 - RR = 0.024/0.018 = 1.3

Smokers have a 1.3 x higher probability of CVD than non-smokers

- RD = 0.024 - 0.018 = 0.006 Smokers have a 5-year risk of CVD that is 0.6% higher than that of non-smokers

Exercise 3

1. Case-control study

2. Severe head injury

3. Population

4. Alzheimer’s disease

5. Odds ratio

Exercise 3

Severe head injury in the past

Alzheimer Yes

No

Severe Yes 33 31

Head injury No 165 167

OR = (33x167)/(31x165)=1.1

SummaryFrequency and measures of

association

• Frequency– Prevalence– Incidence

• cumulative• density

• Association- Relative risk

- Rate ratio- Risk ratio

- Odds ratio- Risk difference

How to handle measures of association?

Some other concepts

INFERENCE

populasi

statistik

XSP

inferens

parameter

sampel

msp

Validity and Reliability

Neither Valid

nor Reliable Reliable but not Valid

Valid & Reliable

Fairly Valid but not very Reliable

Think in terms of ‘the purpose of tests’ and the ‘consistency’ with which the purpose is fulfilled/met

Reliability

• Do not use– Layman’s concept (someone without

professional training in the subject area can understand, so that they may comprehend the issue to some degree)

– Character of persons– Someone is/ is not reliable

• What do we use?

Validity

Absence of: • Systematic errors• Bias (distortion)

• Bias seleksi• Bias perancu

Precision (or accuracy)

The absence of • Random error

Depends on• Standardisation of measurements• Numbers

– Number of persons– Number of (repeated) observations /

measurements

Outcome measures

• Diagnostics?• Prognostics?• Etiology?• Intervention?

Outcome measures• Diagnostics

–Prevalence, Se, Sp, PV+, PV-, OR, • Prognostics

– Incidence, RR,• Etiology

– Incidence, RR, OR• Intervention

– Incidence (abs. risk), RR, RD, mean difference, NNT

Effect estimate

• Does a single effect estimate, e.g. RR=1.5 or RR=1.0 give sufficient information?

Effect estimate

• No, because it does not tell anything about precision

What kind of information do P and CI provide?

• No information about the validity of the study!

Then what?

• Dari nilai sampel, kita dapat :– Mengestimasi nilai populasi (confidence interval)– Menggeneralisir nilai sampel terhadap keadaan

di populasi pengujian hipotesis

Berdasarkan peluang untuk memperoleh hubungan tersebut secara kebetulan. (p value)

Semakin kecil peluang adanya kebetulan, semakin besar keyakinan bahwa hubungan itu memang ada.

Hipotesa Ho : menyatakan tidak ada hubunganHa : menyatakan ada hubungan

Contoh :Is smoking a risk factor for lung cancer?

Ho : Rokok bukan faktor risiko ca paruHa : Rokok adalah faktor risiko ca paru

P value

Dari uji statistik didapatkan nilai p( probability )

P-value:

besar kemungkinan hasil yang didapat/adanya hubungan hanya akibat kebetulan (often with arbitrary cut-off of 5% 0.05)

P-values

• Statistical significance (is not the same as clinical relevance)

• Dependent on– Size of the effect– Size of the study population

P-values

Nilai p ini dibandingkan dengan alpha yang ditetapkan sebelumnya (often with arbitrary cut-off of 5% 0.05)

Bila : P < alpha Ho ditolak p > alpha Ho diterima

Example

• American study on losing weight in obese people

• Intervention: 1. Half an hour per day sports+ diet advice

2. only half an hour sports

• Numbers: 2 x 10.000 people

Example

• BMI before– Group 1: 30.0– Group 2: 30.0

• P < 0.0001

Effect size turned out to be

in group 1: 27.6

in group 2: 27.8

Example

• Similar study in England• Now with 2 x 50 people• BMI before

– Group 1: 28.5– Group 2: 28.4

• Weight after– Group 1: 23.5– Group 2: 25.5 p=0.15

P-values

• Paradoxal results possible:

1. Significant effect, but clinically not relevant

2. Clinically relevant effect, but not significant

ESTIMASI• Walaupun kita hanya mengambil

sampel, sebenarnya kita ingin mengetahui nilai populasi

• CLT nilai sampel = populasi, bila sampel diambil berulang kali

• Kenyataan sehari-hari tidak memungkinkan pengambilan sampel berulang kali

• Memperkirakan nilai populasi dengan nilai sampel

• Confidence interval:

Range of possible effect estimates that you would find if you would repeat the research (infinitely) often

Objective impression of the size of the effect and the precision of the effect estimate

ESTIMASI POPULASI

Point estimation

Konsep deterministik

Interval estimation

Konsep probabilistik

ESTIMASI INTERVAL• Menentukan nilai minimum dan

maksimum di populasi• Confidence Interval• Ditentukan dengan persentase• 99 %, 95 %, 90 %

Relation p-values and CI

• For OR and RR; if the 95%CI does not contain 1 than p < 0.05

• For mean difference; if 0 not in the 95%CI than p < 0.05

• And vice versa

Concluding

• Never consider p-values alone, but also effect estimates

• Present effect estimates always with confidence intervals