1. Research Techniques Made Simple: Interpreting Measures of Association in Clinical Research
Michelle Roberts PhD,1,2 Sepideh Ashrafzadeh,1,2 Maryam Asgari MD MPH1,2
1 Department of Dermatology, Massachusetts General Hospital, Harvard Medical School, Boston, MA.
2 Department of Population Medicine, Harvard Pilgrim Health Care Institute, Boston, MA

2. Measures of Association
Coefficients that quantify the relationship between an exposure and an outcome, enabling comparison between different groups
Exposures can be behavioral, genetic, environmental, socioeconomic, etc.

3. Measures of Association
Odds ratio
Relative risk
Hazard ratio
Pearson’s correlation coefficient (r)
Spearman’s correlation coefficient (rho)
Chi-squared/Fisher’s exact tests
Risk difference, relative risk reduction, number needed to treat

4. Measure of association used depends on study design
Study Designs
Experimental
Randomized Controlled Trial
Relative risk
Hazard ratio
Correlation coefficients
Chi-squared tests
Risk difference
Relative risk reduction
Number needed to treat
Quasi-experimental
Observational
Cohort
Case-control
Odds ratio
Cross-sectional
Prevalence ratio (analogous to relative risk)
Ecologic
Rate comparisons
Case study/ case report
Not applicable
Two main categories of study design: experimental and observational. Observational studies lack an intervention, while experimental studies involve assignment of subjects to an intervention or experimental condition

5. 2x2 Contingency Table Summarizes frequencies of exposures and outcomes
Relative risk = disease incidence in exposed = [a/(a+b)]
disease incidence in unexposed [c/(c+d)]
Odds ratio = odds that a case was exposed = [a/c]
odds that a control was exposed [b/d]
2x2 Contingency Table 
Disease present
Disease absent
Exposed a b
Unexposed c d
a/(a+b)
c/(c+d)

6. Relative risk interpretation
RR = 1: No association between exposure and disease
RR > 1: Exposure is a risk factor for disease (incidence in higher in the exposed group)
RR < 1: Exposure is protective against disease (incidence is higher in the unexposed group)
RR = 1.31 (95% CI )
Exposure: dietary Vitamin D intake
Outcome: melanoma risk
Interpretation: Vitamin D intake is nonsignificantly associated with 31% increased risk of melanoma. Since the confidence interval (CI) includes 1, we conclude that the results are not statistically significant.
RR of 1 indicates no association (incidence in the same among exposed and unexposed), an RR < 1 suggests the exposure is protective (incidence among the exposed is less than that among the unexposed), and an RR > 1 suggests that the the exposure is a risk factor for the outcome (incidence among the exposed is greater than that among the unexposed)

7. Odds ratio interpretation
Similar interpretation as RR
OR = 4.0 (95% CI )
Exposure: HPV DNA from β-papillomavirus species 2
Outcome: skin cancer
Interpretation: HPV DNA from beta-papillomavirus species 2 was four times more likely to be identified in squamous cell carcinoma tissue than tissue from healthy controls.
When the outcome is rare, OR approximates RR

8. Other measures of association
Correlation coefficients measure the strength of the association between 2 variables
Range: -1 to 1
r = 0: no association between the variables
r = -1 or 1: perfect linear or monotonic relationship
Negative r values mean as one variable increases, the other decreases
Chi squared tests measure the significance, not strength, of the association between two categorical variables.
Tests the null hypothesis that two variables are independent of one another
Monotonic functions are function that preserves a given ranked order

9. Other measures of association
Risk difference = A/(A + B) – C/(C + D) = 0.3 – 0.5 [or 30% - 50%]
= -0.2 [-20%, or -20/100]
Participants with the exposure had 2 fewer instances of the outcome per 10 people, compared to participants without the exposure
Relative risk reduction = ((C/C + D) – A/(A + B)) / (C/C + D) = (0.5 – 0.3) / 0.5
= 0.4
There is a 40% reduction in risk of the outcome in the exposed group, relative to the unexposed group
Number needed to treat = 1 / ((C/C + D) – A/(A + B)) = 1 / ( ) = 5
5 individuals must receive the exposure to prevent one outcome from occurring
Monotonic functions are function that preserves a given ranked order

10. When interpreting data, consider:
Correlation is NOT causation
Measures of association must be interpreted in the context of methodologic issues such as bias and confounding
Association (even if statistically significant) does not imply causation. Need to

11. When interpreting measures, consider:
Bias, confounding, and statistical significance
Can the presence of biases or confounding explain the results?
Biases and unaccounted-for or unmeasured confounding may affect the validity of the point estimate
What is the variability?
Wide confidence intervals indicate reduced precision of the point estimate
Small studies should be interpreted cautiously
Replication and generalizability
Have the results been replicated?
Is the exposure/intervention likely to have caused the outcome(s) reported?
Do the results apply only to particular groups of people?
Are there differences in the time course of the exposure/intervention under study compared to a clinical population?