Epid 5310: Lecture 4

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Measures of association

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Reflect the magnitude of a statistical relation between two variables (e.g., exposure and disease)

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Types of measures of association

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1. Absolute
Often used in public health planning
examples: attributable risk, PAR, risk difference
2. Relative
Often used to assess causal associations
Examples: relative risk, odds ratio

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Attributable risk

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Estimates the proportion of disease occurrence attributable to an exposure.
*assumes a causal relationship between exposure and outcome
Indicates the proportion of the disease occurrence that potentially would be eliminated if exposure to the risk factor were prevented.
Synonym for attributable risk is etiologic fraction or excess fraction
**Indicates the proportion of the disease occurrence that potentially would be eliminated if exposure to the risk factor were prevented

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Attributable risk

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* ALSO called ETIOLOGIC FRACTION
* Should be interpreted as such only when there is a reasonable certainty of a causal connection between exposure and outcome.
Also called excess fraction

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Attributable risk measures...

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Impact or effect

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Increased use of attributable risk

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*the concept of attributable risk is applied more frequently now, and is used in a wide range of research (Epidemiology, social sciences and other disciplines)
*The increase is due to new methodology developed especially for the situation when disease risk is related to multiple explanatory variables

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Attributable risk

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*May be calculated for exposed individuals only
OR-
*May be calculated for the population as a whole

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What is needed to calculate attributable risk?

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-Cumulative incidence
-incidence density
-mortality from cohort studies
-prevalence from cross-sectional studies

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Attributable risk in exposed

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Difference between the risk estimates of different exposure levels and a reference exposure level

AR exp=q(+)-q(-)

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Note For attributable risk

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Because most exposure effects are cumulative, cessation of exposure usually does not reduce risk in the exposed to the level found in those who were never exposed.

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Percent attributable risk

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AR expressed as a percentage of total
%AR exp=0.018-0.003/0.18 *100=83.3%
Interpretation: 83.3% of the total risk of MI in hypertensives is attributable to hypertension

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Percent attributable risk can also be expressed as

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Can also be expressed as:
%ARexp=RR/RR-1*100
Advantage of this formula is that is can be used in case-control studies, where incidence data is not available.
**Assumption here is that OR is an estimate of RR (when outcome is rare)

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Population attributable risk

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PAR is most commonly defined as:
-the proportional reduction in average disease risk over a specified time interval that would be achieved by eliminating the exposure of interest from the population while distributions of other risk factors in the population remain unchanged.
-Can also be interpreted as the proportion of disease cases over a specified time that would be prevented following elimination of the exposures, assuming the exposures are causal.
-IN OTHER WORDS, reduction in disease risk achieved by eliminating the exposure of interest.

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PAR

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Usually expressed as the percent population attributable risk
-is expressed as a function of the exposure prevalence in the population and the relative risk

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PAR

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Is a function of prevalence of the exposure in the population and the relative risk.

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Magnitude of the % PAR

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What proportion of the population is exposed to that variable?
If you have a risk ratio of 50 (really high) and only .01 exposed (prevalent) then only 32.9% of the population is affected.

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Interpretation

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The elimination of smoking could possibly reduce lung cancer by at least half and potentially by more than 90%

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Attributable and absolute risk of lung cancer death by smoking status: Findings from the Japan Collaborative Cohort Study

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Few studies have estimated the population attributable risk (PAR)
-Estimated the proportion of lung cancers attributable to cigarette smoking
-

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Cohort study

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calculate relative risk
you start with total exposed and total unexposed and you followed them forward through time to see who develops the outcome.
-calculate relative risk=the ratio of incidence in exposed to incidence in unexposed
-Can also calculate probability odds ratio= the odds of developing disease

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More on p-value

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-Over-reliance on p values for making causal inferences is common among scientists
-often misunderstood and misinterpreted
-Pvalue is NOT the probability that the null hypothesis is true or that the result was due to chance.

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NOT RECOMMENDED

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Although NOT RECOMMENDED, the result of a statistical test is often reported as "significant" (usually when p<.05)
-This cutoff value for the accepted probability of a Type I error is arbitrary
-Has NO scientific value for making causal inferences

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P-value

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The probability of obtaining the observed result (test statistic) or a more extreme values if the hypothesis is true
-the smaller the p-value, the less compatible the hypothesis is with the observed results.
-In most applications, the hypothesis tested is the null hypothessis

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Interpretation of RR=6.0

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Subjects with sever systolic hypertension have times the risk of myocardial infarction incidence compared with those with normal systolic blood pressure.

OR- In this population, the one year risk of having a myocardial infarction for individuals with severe systolic hypertension is six times the corresponding risk for those with normal systolic blood pressure.

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Confidence Intervals

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Represent the range within which the true magnitude of the effect lies.
-The width of the CI indicates the amount of random error stemming from measurement error and sampling variability=PRECISION
-The larger the study, the more stable the estimate, the narrower the CI
-The wider the CI, the greater variability in the estimate of effect, and the smaller the sample size

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Statistical Interpretation of a 95% CI

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If a study was repeated 100 times and 100 point estimates and 100 CIs were calculated, 95 out of 100 CIs would contain the TRUE measure of association.
-The remaining 5% will exclude the true measure of association

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Confidence intervals

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Most epidemiologists use 95%, but some use 90% or 99%
-For this course, do NOT use language regarding "95% confident that the true measure of association..."
-Strongly discourage the degradation of CIs into the dichotomous designations of statistically significant and not statistically significant because this practice can result in misleading conclusions.

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95% confidence interval: (3.1-8.4)
Interpret it

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The data are compatible with odds ratios (relative risks, etc) ranging from 3.1 to 8.4

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Prob. OR approximates RR

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We see that the probability OR in this case is nearly the same as the RR.
-This is because the outcome being investigated is rare.
This does not work when the outcome is common

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Relative risk vs. Probability OR

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If the incidence is fairly high, it is usually better to report the relative risk.
-Use of the OR as an estimate of RR biases it in a direction opposite the null value.

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Rarity assumption

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For the OR to approximate the RR in any type of case-control study, the disease must be rare in both exposure groups (e.g., <5%)
-Does not apply to situations in which the control group is a sample of the total population

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When rarity assumption is not necessary

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-Using as a control group the total study population at baseline, rather than only the noncases.
-If this is done in a cohort study, the case-control study is called a case-cohort study.
**The rarity assumption does not apply for case-cohort studies

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Advantages of case-cohort

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Allows direct estimation of the RR and thus does not have to rely on rarity assumption
-Because control group is a sample of total reference population, an unbiased estimate of exposure prevalence needed for the estimation of PAR can be obtained
-There are occasions in which excluding cases from control group is logistically difficult and can add costs and participants' burden.

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Examples

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Diseases with high proportion of subclinical phase (e.g. prostate cancer)
-Excluding cases from pool of eligible controls would require conducting invasive examinations.

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Measures of association for Case-cohort and Nested Case-control

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Case-cohort: Relative Risk
Nested Case-control: Rate ratio

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Attributable risk in case-control studies

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When OR is a reasonable estimate of RR, we can calculate:
%ARexp= (OR-1)/OR *100

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Assessing strength of associations

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-Use caution when trying to determine importance of factors for an outcome by comparing measures of association.
-Risk factors vary in their exposure levels and units
-Alternative is to estimate exposure intensity necessary to produce an association of the same magnitude as that of well-established risk factors.

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Interpreting attributable risk

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Because the attributable risk is often used to imply a cause-effect relationship, it should be interpreted as a true etiologic fraction only when there is reasonable certainty of a causal connection between exposure and outcome.