Risk Ratios vs. Odds Ratios vs. Hazard Ratios: Key Difference for Biomedical Researchers

Getting your Trinity Audio player ready...

In biomedical research and literature, the terms risks, rates, and odds are used very frequently. In medicine (particularly epidemiology), risks, rates, and odds are statistical measures calculated to understand the likelihood of an event occurring (e.g., infectious disease or response to treatment in a population or group of individuals). These calculations are important for researchers to determine the relative effectiveness of different treatments or interventions, identify potential risk factors or predictors of an outcome, and make informed decisions about clinical practice or public health policy. Calculating rates of disease can help identify risk factors and guide public health interventions. 

Given the similar meaning of words like risks, rates, and odds in conversational language, they are apt to be confused when used in biomedical statistical analysis. For example, “risk” and “odds” tend to be used interchangeably to mean the “chance” of something happening. However, in biomedical research, these terms have specific meanings and uses.  

To dispel confusion and better understand these related but distinct concepts, we explain these terms below. 

Probability: The probability that an event will occur is the fraction of times an event is expected in many trials. 
– Probability always ranges between 0 and 1.  

Odds: Probability of an event occurring divided by the probability of the event not occurring.  Say, the probability of an event occurring is Y. Then: 
– Odds of the event = Y/(1−Y) 

Ratio: A ratio is the relative magnitude of two quantities or a comparison of any two values. 
– A ratio is dimensionless 
– A ratio can take any value 

Rate: A rate expresses changes in a quantity over a time period (e.g., the incidence rate of a disease = (number of new cases of the disease occurring over a specified period)/(total population at risk during that period).
– Rate has a time dimension  
– Rate is expressed per unit time 

Risk: Risk is the probability associated with an adverse outcome that is likely to occur in the future. In biomedicine, risk allows predictions about a single population. 
– Risk has no dimensions  
– Risk is confined to values between 0 and 1 

Risk factor: A factor that increases the chance of developing a disease; for example, risk factors for cancer might include a family history of cancer, exposure to radiation or certain chemicals, and certain genetic mutations.  

Important statistical measures used in biomedicine 

What is Risk Ratio?

Relative risk or risk ratio (RR) is a statistic that shows whether an intervention or variable has an effect on the outcome.  

What is Odds Ratio?

Odds ratio (OR) is determined as the odds of an event in one group, e.g., those exposed to a drug, divided by the odds in another group not exposed to that drug.  

What is Hazard Ratio?

A hazard ratio (HR) indicates the risk of an event in the intervention group compared with the control group at any particular point in time. 

The table below presents a useful comparison of the above three measures. 

Difference between Relative Risk (RR), Odds Ratio (OR), and Hazard Ratio (HR)

	Relative Risk	Odds Ratio	Hazard Ratio
Calculation	RR = (risk in the intervention group)/(risk in the control or placebo group)	OR = (odds in the intervention group)/(odds in the control or placebo group)	Calculated using survival data and survival analysis:  HR = (hazard rate in the intervention group)/(hazard rate in the control group)
Interpretation	RR = 1: both groups have the same amount of risk  RR ≠ 1: one group has a higher risk than the other (due to the intervention; there is an assumption of causal direction).	OR = 1: Same outcome in both groups, i.e., there is no difference between them  OR > 1: a positive association between the exposure and outcome  OR < 1: a negative association between the exposure and outcome	HR = 1: Both groups experience the same number of events in a period.  HR > 1: The treatment group experiences a higher event probability within any given period than the control group.  HR < 1: The treatment group experiences a lower event probability during a unit of time than the control group.
Applications	RR is commonly used in prospective studies such as cohort studies.	ORs are commonly reported in the medical literature (particularly in case-control studies) as the measure of association between exposure and outcome.	HR is commonly used in clinical trials, epidemiology, and other medical research to analyze the impact of an intervention on survival or time-to-event outcomes. For example, HRs can determine whether an intervention reduces the duration of symptoms or prolongs survival in a disease.

Best practices for statistical analysis and reporting statistical measures in biomedical science

Biomedical researchers should ensure the accuracy and reliability of their results when calculating and reporting risks, rates, and odds. Here are some best practices to achieve this: 

• Use appropriate measures depending on the research question and study design. 
• Clearly define the population, including the inclusion and exclusion criteria. 
• Use appropriate and reliable data sources. 
• Use appropriate statistical methods. 
• Report relevant p-values and confidence intervals to indicate the precision of the results.  
• Avoid biases associated with the perception and interpretation of risk in medical decision-making and report potential biases (e.g., selection bias, measurement bias, and confounding). 
  

Conclusion

In biomedical research, numerous statistical measures can be applied for drawing conclusions about a specific intervention, variable association, or intervention impact over a period. Risk ratios, odds ratios, and hazard ratios are very useful to clinicians, and appreciating the significance of these measures is crucial for making decisions regarding patient care. Understanding the applicability and usage of these measures will enable a more accurate interpretation of study results and a clear understanding of what each value denotes.

Would you like guidance from an expert statistician on how to define your study variables and conduct your analysis? Check out Editage’s Statistical Analysis & Review Services!