Measure of association

Question 1

Relative Measures

Answer 1

Calculated as a ratio

• Risk Ratio
• Odds Ratio
• Rate Ratio
• Prevalence Ratio

Often preferred in etiologic studies to determine association

Question 2

Absolute (Additive) Measures

Answer 2

Calculated as a DIFFERENCE

• Risk Difference
• Attributable Risk
• Rate Difference

Often preferred to quantify public health impact

Question 3

Risk Ratio (relative Risk)

Answer 3

Risk Ratio = CI (exposed) / CI (unexposed) Denominator is the risk in the reference group

Interpretation:

The relative magnitude of the risk of disease in the exposed compared to the risk of disease in the unexposed (reference)

Question 4

Rate Ratio

Answer 4

Rate Ratio = IR in Exposed/ IR in non-exposed = (A/PY expose)/(C/PY non-exposed)

• Interpretation:

The relative magnitude of the rate of disease incidence in the exposed compared to the rate of disease incidence in the unexposed

Question 5

Prevalence Ratio

Answer 5

Prevalence Ratio = a/(a+b)/(c/(c+d)

The relative magnitude of the prevalence in the exposed compared to the prevalence in the unexposed

Question 6

Odds Ratio

You cannot calculate a measure of disease incidence or prevalence from a case-control study – why?

Answer 6

• Case-control studies select participants based on disease status. The proportion of diseased and non-diseased people in a case control study is set by the investigators, and does not reflect the prevalence or incidence of the disease in the population.

Question 7

Odds Ratio cont.

Answer 7

OR = (A*D/C*D)

Case-control studies select participants based on disease status. The proportion of diseased and non-diseased people in a case control study is set by the investigators, and does not reflect the prevalence or incidence of the disease in the population.

• The odds ratio over-estimates the risk ratio and thus is only a good approximation for rare diseases. Using an odds ratio on common diseases will over estimate risk

Question 8

What is the (frequentist) interpretation of a 95% confidence interval?

Answer 8

• If the study is repeated a large number of times, 95% of such intervals will encompass the true value!

Question 9

Interpreting Relative Measures of Association

Answer 9

Risk Ratio:

•The risk of the outcome is X times as high in the exposed group as compared to the unexposed group

Rate Ratio:

•The rate of the outcome is X times as high in the exposed group as compared to the unexposed group

Prevalence Ratio:

•The prevalence of the outcome is X times as high in the exposed group as compared to the unexposed group

Odds Ratio:

•The odds of exposure is X times as high in cases compared to controls

Question 10

When do we use each measure of association?

Answer 10

•Relative measures are best for etiologic questions.

• provide a measure of the strength of the association between a factor and a disease or outcome.

•Additive measures have clinical or public health implications of exposure-disease relationship.

• Provide a measure of the public health impact of the risk factor, and focus on the number of cases that could potentially be prevented by eliminating the risk factor.

Question 11

Attributable risk (risk difference)

Answer 11

How is this measure computed?

AR = Cumulative Incidence exposed minus Cumulative Incidence unexposed

Interpretation: If everyone with the exposure were somehow no longer exposed, then the risk of disease among the exposed would be reduced by AR

Question 12

What percentage of disease cases in exposed individuals are caused by exposure?

Answer 12

Measure of Association:

•Attributable Risk Percent (AR%)

•AKA ‘Etiologic fraction in the exposed’ or ‘Exposed Attributable Fraction’
How is this measure computed?

•AR% = (CIexposed - CIunexposed) X 100% = [(RR-1)/RR] x 100%

CIexposed

•Interpretation: AR% of the risk among exposed people could be prevented if the exposure were eliminated

The AR% can be calculated from case-control studies IF the OR is a reasonable estimate of the RR: AR% = [(OR-1) / OR] x 100

Question 13

Example of AR%

Answer 13

Calculate the risk difference between severe influenza cases (exposed) and mild influenza cases (reference) for (1) hospitalization and (2) ICU admission

Risk Difference for hospitalization: (47/100) – (38/300) = 0.34

Risk Difference for ICU admission: (12/100) – (2/300) = 0.11

Interpretation: If all those with severe influenza instead had mild influenza, the risk of hospitalization among the exposed would be reduced by 0.34

If all those with severe influenza instead had mild influenza, the risk of ICU admission among the exposed would be reduced by 0.11

Question 14

Calculate the percent attributable risk among the exposed

Answer 14

Hospitalization AR% = (47/100 – 38/300)/(47/100) = 73%

ICU Admission AR% = (12/100 – 2/300)/(12/100) = 94%

Question 15

Example: In a controlled trial of yellow fever vaccine, 10% of vaccinated children contracted yellow fever during 1 year of follow-up, while 23% of unvaccinated children contracted yellow fever during that same year.

Answer 15

AR% = (0.23 – 0.10) / 0.23 = 0.565

Interpretation: The vaccine had 56.5% efficacy over 1 yr

Question 16

Number Needed to Treat (NNT)

Answer 16

NNT = 1/Attributable Risk

Example: A medication cures 35% of the people who take it over a 6 month period, while 20% of people who do not take the medication will recover spontaneously during the same period. Calculate the Number Needed to Treat:

Incidence of recovery in exposed = CI (exposed) = 0.35

Incidence of recovery in unexposed = CI (unexposed) = 0.20

Attributable Risk = 0.35 - 0.20 = 0.15

Interpretation: If those exposed to the medication were instead unexposed, their incidence of recovery would be reduced by 0.15.

Question 17

Do you need incidence data to calculate AR, AR%, PAR, and PAR%?

Answer 17

• Cross-sectional study: the AR represents the excess of prevalent cases of disease that can be attributed to the exposure of interest.
• Case-control study: the AR is traditionally calculated using the odds ratio to estimate the risk ratio. This approach requires the rare-disease assumption.
• Cohort study: the AR represents the excess of incident disease cases that can be attributed to exposure of interest.
• HOWEVER, cohort studies often over-sample the exposure if the exposure is rare. The potential difference in prevalence of exposure in a cohort study vs. the general population can result in less generalizable AFs.

Question 18

Sumarry of relative measures of association

Answer 18

• Risk Ratio = CIex / CIunex
• Rate Ratio = IRex / IRunex

= IDex / IDunex

• Prevalence Ratio = Pex / Punex
• Odds Ratio = Oddsex/Oddsunex

= a*d/b*c

Question 19

Summary of absolute messures of association

Answer 19

AR = Iex - Iunex

NNT = 1/AR

NNH = 1/AR

AR% = (Iex - Iunex) / Iex

AR% = [(RR-1) / RR] x 100%

AR% = [(OR-1) / OR] x 100% (rare dz)

PAR = Ipop - Iunex

PAR% = (Ipop - Iunex) / Ipop