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

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.

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

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

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)

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 0.94-1.82) 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)

Odds ratio interpretation Similar interpretation as RR OR = 4.0 (95% CI 1.3-12.0) 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

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

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 / (0.5-0.3) = 5 5 individuals must receive the exposure to prevent one outcome from occurring Monotonic functions are function that preserves a given ranked order

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

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?