MUSM Libraries: Calculators
Estimating the size of the treatment effect

Outcome Yes 
Outcome No 
Treated (Y) 
a 
b 
Control (X) 
c 
d 
Risk of Outcome: Y = a/(a+b)
Risk of Outcome: X =
c/(c+d)
 Absolute Risk Reduction (ARR) is the difference in risk
between the control group (X) and the treatment group (Y). ARR =
XY
 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.
 Number Needed to Treat (NNT) is the number of patients that
must be treated over a given period of time to prevent one adverse outcome.
NNT = 1/ARR
 Odds Ratio (OR)
The ratio of the odds of having the target
disorder in the experimental group relative to the odds in favor of having the
target disorder in the control group (in cohort studies or systematic reviews)
or the odds in favor of being exposed in subjects with the target disorder
divided by the odds in favor of being exposed in control subjects (without the
target disorder).
 Relative Risk (RR) is the risk of the outcome in the treated
group (Y) compared to the risk in the control group. RR = Y/X
 Relative Risk Reduction (RRR) is the percent reduction in
risk in the treated group (Y) compared to the control group (X). RRR = 1RR
x 100%
Likelihood ratios
A Likelihood ratio for a given diagnostic test result compares the
likelihood of that result in patients with disease to the likelihood of that
result in patients without disease. It provides an estimate of how much a test
result will change the odds of disease in a patient.
Please enter data into the 2 by 2 table
to determine the likelihood ratio
How much do LRs change disease likelihood?
LRs greater than 10 or less than 0.1  cause large changes 
LRs 5  10 or 0.1  0.2  cause moderate changes 
LRs 2  5 or 0.2  0.5  cause small changes 
LRs less than 2 or greater than 0.5  cause tiny changes 
LRs = 1.0  cause no change at all

 Sensitivity  the proportion of patients who test positive and
have the target disorder. Sen = a/a+c
 Specificity  the proportion of patients who test negative and
do NOT have the target disorder. Spec = d/b+d
 LR + = a/(a + c) over b/(b + d)
 LR  = c/(a + c) over d/(b + d)
Key Properties of LRs:
 posttest Odds = LR x Pretest Odds of Disease
 independent of prevalence of disease
Pretest Probabilities are estimated from published studies of
prevalence, data from your practice setting, and your clinical intuition.
How much do LRs change disease likelihood?
LRs greater than 10 or less than 0.1 
cause large changes 
LRs 5  10 or 0.1  0.2 
cause moderate changes 
LRs 2  5 or 0.2  0.5 
cause small changes 
LRs less than 2 or greater than 0.5 
cause tiny changes 
LRs = 1.0 
cause no change at all 
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