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Public Health: Measurements

Medical Statistics

...in medical statistics, all answers are approximate, but some are approximately useful."
-- Martin Bland

Proportion, Rate, and Ratio, oh my!

  • Proportion
    • A proportion is the comparison of a part to the whole.
    • It is a type of ratio in which the numerator is included in the denominator.
    • You might use a proportion to describe what fraction of clinic patients tested positive for HIV, or what percentage of the population is younger than 25 years of age.
    • A proportion may be expressed as a decimal, a fraction, or a percentage.
  • Rate
    • Rate is a measure of the frequency with which an event occurs in a defined population over a specified period of time.
    • Because rates put disease frequency in the perspective of the size of the population. 
    • Rates are particularly useful for comparing disease frequency in different locations, at different times, or among different groups of persons with potentially different sized populations; that is, a rate is a measure of risk.
  • Ratio
    • The relative magnitude of two quantities or a comparison of any two values.
    • Calculated by dividing one interval- or ratio-scale variable by the other.
    • The numerator and denominator need not be related.
    • The result is often expressed as the result “to one” or written as the result “:1.

Probability versus Odds! They aren't the same thing!

  • Probability
    • Is a percentage.
    • The number of events of interest divided by the total number of events.
    • Ranges between 0 and 1 or 0% to 100%.
    • Formula: Probability = events / events & non-events.
    • Formula example: Probability = Number of people with a cold / Total number of people in the sample
  • Odds
    • Is a ratio.
    • The odds are the probability that the event will occur divided by the probability that the event will not occur.
    • Ranges from 0 to infinity.
    • Formula: Odds = events / non-events/
    • Formula example: Odds = Number of people with a cold / Number of people without a cold. 
      • Note the denominator is NOT the total sample.

Relative Risk & Odds Ratio

Relative Risk (RR) and Odds Ratio (OR) measure the strength of an association between an exposure and a disease.

Relative Risk (RR)

  • Tells you how many times exposure to a risk factor increases a person’s risk of contracting the disease.
  • Is the ratio of incidence of disease in exposed persons to the incidence of disease in unexposed persons. 
  • Studies that create a sample population based on exposure can use relative risk- like controlled trials or cohort studies.
  • Formula: RR = p of getting the disease if exposed / p of getting the disease if not exposed

Interpretation

  • RR = 1
    • If the incidence in the exposed group and the unexposed group is the same then there is no increased risk and no association between the exposure and the outcome.
  • RR > 1
    • The incidence in the exposed group is greater than that of the unexposed group, so there is a greater risk and a positive association between the exposure and the outcome.
  • RR < 1 The
    • incidence in the exposed group is less than that of the unexposed group so there is decreased risk and a negative association between the exposure and the outcome.

Odds Ratio (OR)

  • A clinical odds ratio usually refers to the odds that a person with a disease was exposed to a risk factor in the past divided by the odds that the control group had exposure to the risk factor.
  • Is a way of comparing patients that already have a certain condition with patients that don’t. 
  • Case Control studies compare cases that have experienced the event and controls who haven’t and then looks at whether each individual was exposed or not.
  • Formula: OR = odds of the exposure in people with disease / odds of the exposure in people without disease.

Interpretation

  • OR = 1
    • The exposure is not associated with the disease.
  • OR > 1
    • The exposure is positively associated with the disease.
  • OR < 1 The
    • The exposure is negatively associated with the disease.

Since all the cases already have the disease/outcome, you can’t calculate incidence and therefore can’t calculate risk.

 

RR is calculated using incidence data to measure the probability of developing disease. Since the calculation is dependent on incidence data and only Controlled Trials and Cohort Studies can be used to calculate incidence, you should only see RR in Controlled Trials or Cohort Studies. This is also why you see RR less than OR even though it is easier to calculate and understand – Controlled Trials and Cohort Studies are expensive and time consuming so there are fewer of them.

Number Needed to Treat & Number Needed to Harm

Number Needed to Treat (NNT)
  • Can be thought of as the number of patients that would need to be treated to prevent one additional bad outcome.

Other measurements

Absolute Risk

  • The likelihood of an event occurring under specific conditions.

Absolute Risk Reduction (ARR)

  • Absolute risk reduction is just the absolute difference in outcome rates between the control and treatment groups. We are asking what proportion of participants benefit from the intervention.

Attributable Risk

  • Attributable Risk (AR) is the difference in the disease rates in exposed and unexposed individuals. AR is calculated from prospective data.

Control Event Rate (CER)

  • The proportion of patients in the control group who experience the studied event.

Experimental Event Rate (EER)

  • The proportion of patients in the experimental treatment group who are observed to experience the outcome of interest.

Relative Risk Reduction (RRR)

  • Relative risk reduction measures how much the risk is reduced in the experimental group compared to a control group. We are asking what proportion of affected participants in the control group would benefit by being in the experimental group.
  • RRR is calculated as 1 minus the relative risk.

How to calculate the NNT by Dr Shaneyfelt

References

Absolute Risk vs. Relative Risk: What’s the Difference?: (EUFIC). (n.d.). Retrieved February 3, 2020, from https://www.eufic.org/en/understanding-science/article/absolute-vs.-relative-risk-infographic
Bonita, R., Beaglehole, R., & Kjellström, T. (2006). Basic epidemiology (2. ed). World Health Organization.
Irwig, L., Irwig, J., Trevena, L., & Sweet, M. (2008). Relative risk, relative and absolute risk reduction, number needed to treat and confidence intervals. Hammersmith Press. https://www.ncbi.nlm.nih.gov/books/NBK63647/
Principles of Epidemiology: Home|Self-Study Course SS1978|CDC. (2019, March 7). https://www.cdc.gov/csels/dsepd/ss1978/index.html
Schechtman, E. (2002). Odds ratio, relative risk, absolute risk reduction, and the number needed to treat—Which of these should we use? Value in Health: The Journal of the International Society for Pharmacoeconomics and Outcomes Research, 5(5), 431–436. https://doi.org/10.1046/J.1524-4733.2002.55150.x
Schmidt, C. O., & Kohlmann, T. (2008). When to use the odds ratio or the relative risk? International Journal of Public Health; Basel, 53(3), 165–167. http://dx.doi.org/10.1007/s00038-008-7068-3

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