The strength of the association

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The strength of the association - PowerPoint PPT Presentation

The strength of the association . Measures of association FETP India. Competency to be gained from this lecture. Calculate correctly the measure of association that corresponds to a study design . Key areas. Cohort studies Case control studies Cross-sectional survey .

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The strength of the association

Measures of association

FETP India

Competency to be gained from this lecture

Calculate correctly the measure of association that corresponds to a study design

Key areas
• Cohort studies
• Case control studies
• Cross-sectional survey

Ill Non-ill Total

Exposed a b a+b

Non-exposed c d c+d

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

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

Total a+c b+d L1 + L0

Cohorts

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

Total a+c b+d L1 + L0

R = (a+c)/(L1 + L0)

Cohorts

Risk among exposed and unexposed in a cohort study

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

Total a+c b+d L1 + L0

Risk among exposed : R1 = a/L1

Risk among unexposed : R0 = c/L0

Cohorts

• Risk difference
• Multiplicative approach
• Cumulative incidence
• Relative risk
• Person-time analysis
• Relative rate
• Alternative approach
• Disease odds ratio

Cohorts

Calculation of a risk difference in a cohort study

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

Total a+c b+d L1 + L0

Risk difference = R1- R0 = (a/L1) - (c/L0)

Cohorts

Risk of leishmaniasis according to water bodies within 25 metres of house, Chatrakhali, West Bengal, 2004-6

Leishmaniasis Non-ill Total

Water bodies 139 487 626

No water bodies 11 114 125

Total 150 601 751

Risk difference = (139/626) - (11/125) = 22% - 9% = 13%

Cohorts

Calculation of a relative risk in a cohort study

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

Total a+c b+d L1 + L0

Relative risk = R1/R0 = (a/L1) / (c/L0)

Cohorts

Risk of leishmaniasis according to water bodies within 25 metres of house, Chatrakhali, West Bengal, 2004-6

Leishmaniasis Non-ill Total

Water bodies 139 487 626

No water bodies 11 114 125

Total 150 601 751

Relative risk = (139/626) / (11/125) = 22% / 9% = 2.5

Cohorts

Calculation of a relative rate in a cohort study

Events Person-time Rate

Exposed a PT1 Rate1

Non-exposed c PT0 Rate0

Total a+c PT Rate

Relative rate = Rate1/Rate0 = (a/PT1) / (c/PT0)

Cohorts

The odds

Probability of occurrence of an event

______________________________________

Probability of non-occurrence of this event

Cohorts

Calculation of a disease odds ratioin a cohort study

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

Total a+c b+d L1 + L0

Odds of disease in exposed: = (a/L1)/(b/L1)= a/b

Odds of disease in unexposed = (a/L0)/(b/L0) = c/d

Disease odds ratio (OR): (a/b) / (c/d) = ad/bc

Cohorts

• The relative risk corresponds to an intuitive notion
• The OR is less meaningful to most readers
• The OR is larger than the relative risk

Cohorts

Calculation of an exposure-odds ratioin a cohort study

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

Total a+c b+d L1 + L0

Odds of exposure in ill: = (a/a+c)/(c/a+c)= a/c

Odds of exposure in non-ill = (b/b+d)/(d/d+d0) = b/d

Exposure odds ratio (OR): (a/c) / (b/d) = ad/bc

Cohorts

Magical trick #1

In a cohort study, the ratio of the odds of disease among exposed and unexposed is equal to the ratio of the odds of exposure among ill and non-ill

Cohorts

Ill Non-ill Total

Exposeda b L1

Non-exposedc d L0

Totala+c b+d L1 + L0

b # a+b; d # c+d

Relative risk = a (c+d)/c(a+b) # ad/bc

Cohorts

Magical trick #2

In a cohort study, when the disease is rare, the ratio of the odds of disease is almost equal to the relative risk

Cohorts

Case Control Total

Exposed a.f1 b.f2 N/A

Non-exposed c.f1 d.f2 N/A

Total C1.f1 C0.f2 N/A

Cases are sampled from all cases (sampling fraction: f1)

Controls are sampled from all controls (sampling fraction: f2)

f1 and f2 are unknown, risks cannot be calculated

Case control

Case Control Total

Exposed a.f1 b.f2 N/A

Non-exposed c.f1 d.f2 N/A

Total C1.f1 C0.f2 N/A

Odds of exposure among cases= (a.f1)/(c.f1)

Odds of exposure among controls = (b.f2)/(d.f2)

Case control

Magical trick #3

In a case control study, the exposure-odds ratio is equal to the disease-odds ratio of the corresponding cohort

Case control

Magical trick #2 + #3 = #4

In a case control study, when the disease is rare, the exposure-odds ratio is almost equal to the relative risk in the corresponding cohort

Case control

Sleeping in work clothes and scrub typhus, Darjeeling, West Bengal, India, 2005-6

S. typhus Controls Total

Sleeping in work clothes 66 13 79

Changing clothes to sleep 56 33 89

Total 122 46 168

Odds ratio = (66x33)/(56x13) =3.0

Case control

Presentation of the data of an analytical cross-sectional study in a 2 x 2 table

Ill Non-ill Total

Exposed a b L1

Non-exposed c d L0

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

Prevalence in exposed: P1, Prevalence in unexposed: P0

Prevalence ratio = P1/P0 = (a/L1) / (c/L0)

Formula identical to the relative risk, but could be calculated both ways

Cross sectional studies

Trachoma No trachoma Total

Dirty face 54 337 391

Clean face 50 1459 1509

Total 104 1796 1900

Prevalence ratio = (54/391)/(50/1509) = 4.2

Cross sectional studies

Limitations of causal inference in analytical cross-sectional studies
• Prevalent cases
• Exposure and outcome examined simultaneously

Cross sectional studies

Take-home messages
• Calculate relative risks in cohort studies
• Calculate odd ratio in case control studies, it will approximate the relative risk if the disease is rare
• Calculate prevalence ratio in cross-sectional surveys and beware of chicken-and-egg causality issues
Association does not systematically mean causation: Potential explanations for an association
• Bias
• Chance
• Confounding factor
• Causation
• After the first three have been ruled out