Frequency and

measures of association

Center for Clinical Epidemiology and Evidence-Based Medicine (CEEBM)Faculty of Medicine, University of Indonesia – Cipto Mangunkusumo Hospital

Frequency measures

• Two types:– Someone has the disease already:

prevalence = measure population disease status

– Someone gets the disease in the future: incidence

=measure frequency of disease onset

Measure of disease occurrence (example)

• Incidence: the rain arriving• Prevalence: the water in the puddle, new and old• Period prevalence: the water in the puddle, during a

period• Point prevalence: at one point of time

The water draining away into the soil or into drains reduce the puddle (i.e. the prevalence) just as recovery or death reduce the number of patients with a problem

Prevalence

• Proportion of population affected by the disease at a given point in time

• Expressed as a percentage:(number of diseased)/(population) * 100

Number of cases of disease at a specific time

Population exposed at that time

Frequency measures: prevalence

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

time – Used in diagnostic research

• Prevalence – Number of persons with the disease at a certain

moment

• Prevalence (%)– Number of persons with the disease / total

population

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 Indonesian people smoke

Frequency measures: prevalence

• Interpretation / relevance– Quantification amount of disease: a priori

probability– public health planning

• Issues– non-response

• prevalence of MI• prevalence of dementia

– selective mortality

New events…

• Incidence• Incidence rate• Incidence density• Attack rate• Cumulative incidence• Risk• ……

Frequency measures: Incidence

• Incidence– number of new cases– in the population at risk

• Two types of incidence– Cumulative incidence– Incidence density (incidence rate)

Frequency measures: Incidence

• Used in prognostic research• Incidence density

– The number of new disease cases in the population divided by the observation time

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

risk (free of the disease 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

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. (point) 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. (point) 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 an incidence?

Frequency measures: Incidence

• Cohort approach– Group of persons with the same

characteristics– All participants have the same starting

point (start cohort) • However, baseline can differ in time

– All participants are followed during a certain time period

Cumulative incidence

• Cumulative incidence excludes prevalence at baseline

• Example:Population 350.000

New cases 1.250

Cumulative incidence 3.6/1000 per year

Number of NEW cases of disease during a period

Population exposed during the period

Frequency measuresIncidence density

• # new patients / person-years of the population at risk– 10 per 1000 person-years– between 0 and infinity

Number of new/incident cases

Amount of at-risk experience time

Frequency measures:Incidence: cohort

• 5 persons followed during a year• (N at risk = 5)

– A------------------------------– B------------------------------– C-------------breast cancer– D------------------------------– E------------------------------

• 1-year risk of breast cancer = CI = 1/5=20% per year• ID = 1/4.5 person-years = 222/ 1000 person-years

Frequency measures: example cohort

• 13 persons followed for 5 years for mortality– A-----------------------------x--Moves away t=2.5

– B-----------------------------x-------------Death t=3.0

– C-------breast cancer/death t=1.0

– D-----------------------------x------------------------------------------- alive t=5.0

– E-----------------------------x--------lost to follow-up t=3.0

– F-----------------------------x--------------------------------------------alive t=5.0

– G-----------------------------x---------------------------breast cancer/death t=4.0

– H-----------------------------x-Myocardial infarction/death t=2.5

– I--------death t=1.0

– J------------------------------x-------------------------------------------alive t=5.0

– K-------------lost to follow-up t=1.5

– L-----------------------------x----------------moves from the area t=3.5

– M--------1---------------2--x----------3---------------4-------------------alive t=5.0

• Total amount time at-risk = 42 years

Frequency measures: example cohort

• CI = 5/13 = 38%

• ID = 5/42 x 1000 = 199/1000 person-years

Item Prevalence Cumulative incidence

Incidence density

Numerator All cases counted in a single occasion

New cases occurring during a specified follow-up period

New cases occurring during a specified follow-up period

Denominator All individual examined – cases and non cases

All susceptible individuals present at the start of the study

Sum of time periods during which all individuals could have developed disease

Time Single point or period

Defined period Measure for each individual from beginning of study until disease event or study end

Interpretation Probability of having disease at a point in time

Probability of developing disease over a specific period

How quickly new cases develop over a specified period

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?

Measures of association

• 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

Measures of association

Disease

Yes No

Yes a - PY1

Determinant

No c - PY0

ID1 a/py1

ID0 c/py0

RR = =

Measures of association

• 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 between exposed and non-exposed– CI or ID– public health impact

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

personyears

Measures of association

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

• Case-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

Disease

Yes No

Yes a b

Determinant

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

– Odds= the chance of something happening/the chance of it not happening

– Odds Ratio - a ratio of two odds

Measures of association

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

DiseaseYes No

Yes 440 300 740Determinant

No 212 350 562

• Odds ratio (440/212) / (300/350) = 2.42

Measures of association

• Smoking and lung cancer Disease

Yes No Yes 440 300 740

DeterminantNo 212 350 562

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

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

Outcome measures

• Diagnostics?

• Prognostics?

• Etiology?

• Intervention?

Outcome measures• Diagnostics

– Prevalence (abs. risk), posterior probability, Se, Sp, PV+, PV-, OR, AUC

• Prognostics– Incidence (abs. risk), OR, AUC

• Etiology– Incidence (abs. risk), 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

P-values versus confidence intervals

• P-value: The probability that the found association (or more extreme) occurs given the nullhypothesis is true (often with arbitrary cut-off of 5%)

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

P-values

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

• Dependent on– Size of the effect

– Size of the study population

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

• After p<0.0001

Effect size not in article but 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

Confidence interval (CI)

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

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

• Don't do this, because information CI is not fully used

Concluding

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

• Present effect estimates always with confidence intervals