Stats Equations Flashcards
Standardised Mortality Ratio (SMR)
Standardised Mortality Ratio =
Number of Deaths in Study Group/
Number of “Expected Deaths” x100
SMR<100 = fewer deaths in study population than would be expected in the general population
SMR>100 = more deaths than expected.
SMR 100 = the number of deaths is the same as would be expected for the general population.
Absolute Risk (AR)
Absolute Risk =
Number of Events of Interest/
Total Number of People in Group
Absolute Risk Reduction (ARR)
Absolute Risk Reduction =
Absolute Risk Control Group - Absolute Risk Intervention Group
Number needed to treat (NNT)
Number Needed to Treat=
1/
Absolute Risk Reduction
(100/ARR if in percentage)
Relative Risk (Risk Ratio)
Relative Risk (Risk Ratio) =
AR Intervention Group/
AR Control Group
Relative Risk of 1 = no difference in risk between the two groups
Relative Risk of >1= the risk of that event is increased in group of interest compared to control group
Relative Risk <1 = the risk of that event is reduced in the group of interest compared to the control group
e.g Relative Risk of 1.3 = risk of event is 30% higher in group of interest.
Relative risk of 3 = risk of event is three times higher in the group of interest.
Usually given with 95% CIs. If the CI does not include 1 it is statistically significant.
Relative Risk Reduction
Relative Risk Reduction =
1 – Relative Risk
Odds
Odds =
Number of Events of Interest/
Number of Non Events
Odds Ratio (OR)
Odds Ratio =
Odds of Event in Exposed Group/
Odds of Event in Control Group
OR of 1= there is no difference in outcome. The odds are the same in each group.
OR >1= the odds of that event is increased in those who have been exposed
OR <1 = the odds of that event is reduced in those that have ben exposed.
Usually given with 95% CIs. If the CI does not include 1 it is statistically significant.
Hazard Ratio
Hazard Ratio =
Hazard Rate (Risk of Hazard) in Intervention Group/
Hazard Rate (Risk of Hazard) in Control Group at a given interval of time.
Incorporates time
Used in survival graphs
Hazard rate is the probability of an event occuring in a set time period.
Hazard Ratio of 1 = no difference between groups of event occuring
HR of 2 = twice the risk in intervention group
HR <1 = reduced risk in intervention group.
Mortality Rate
Mortality Rate =
Number of Deaths/
Population
It is the risk of dying over a certain time period.
Mitigates against changes in population size, so can compare different populations.
e.g number of covid deaths in 30-40yr olds/no of 30-40 yr olds in the population.
Case Fatality Rate
Case Fatality Rate =
Number of Deaths from the disease/
Number of People Diagnosed with the Disease
Proportion of people who die frp, a disease out of all those diagnosed with the disease over a certain period of time.
Used to determine disease severity.
Incidence
Incidence = Number of new cases/population
It is the rate of new cases of a disease over a given time period.
Frequency of **new **cases.
Prevalence
Prevalence = all cases/population
It is the frequency of existing cases.
All cases
Positive likelihood ratio
Positive likelihood ratio = sensitivity/ (1-specificity)
How much getting a positive test result affects your probability of having the disease.
Compares your odds of having the disease if the test is positive vs the baseline odds of having the disease (the pre-test probability)
A positive LR of 2 means that if the test result is positive, the chances that the patient actually has the disease have doubled.
A LR of 1 means the test is useless. It does not change your probability ofn having a disease.
Negative Likelihood ratio
Negative Likelihood ratio = (1-sensitivity)/specificity
Compares your odds of having the disease if the test is negative vs the baseline odds of having the disease.
It is how much the risk of having the disease has decreased if the test is negative (compared to pre-test probability).
