Help Aids Top
Description:
Odds Ratio (OR) refers to the ratio of the odds of the outcome in two groups in a retrospective study.
Absolute Risk Reduction (ARR) is the change in risk in the 2 groups and its inverse is the Number Needed to Treat (NNT).
Patient expected event rate (PEER) is the expected rate of events in a patient received no treatment or conventional treatment.
The Z-test for Odds Ratio shows whether the exposure affect the odds of outcome.
OR=1 means exposure has no effect on the odds of outcome.
OR>1 means exposure leads to higher odds of outcome and vice versa.
The Z-test for 2 Proportions shows whether there is difference between the proportions of events in 2 groups.
The Chi-square test for Association tests the association between the groups of feature and test result.
Procedure:
- Enter
a) Value of Outcome Positive and Negative in the Feature Present and Absent
b) Value of 1-£\, the two-sided confidence level
- Click the button ¡§Calculate¡¨ to obtain
a) The Odds Ratio and the corresponding 100(1-£\)% confidence interval
b) The Absolute Risk Reduction (ARR) and the corresponding 100(1-£\)% confidence interval
c) The Relative Risk Reduction (RRR) and the corresponding 100(1-£\)% confidence interval
d) The Number Needed to Treat (NNT) and the corresponding 100(1-£\)% confidence interval
e) The Patient Expected Event Rate (PEER)
e) The p-value of Z-test for Odds Ratio
f) The p-value of Z-test for the difference between proportions of having Positive Outcomes in 2 groups
g) The p-value of Chi-square test for association
- Click the button ¡§Reset¡¨ for another new calculation
Variables:
|
Outcome Positive |
Outcome Negative |
Totals |
|
|
Feature Present |
a |
b |
n1=a+b |
|
Feature Absent |
c |
d |
n2=c+d |
|
Totals |
m1=a+c |
m2=b+d |
N=n1+n2 |
For Odds Ratio (OR), 
Define:
The 100(1-£\)% (Woolf, logit) confidence interval is defined as:
For Absolute Risk Reduction (ARR), 
Define: 
The 100(1-£\)% confidence interval is defined as:
For Relative Risk Reduction (RRR), 
The 100(1-£\)% confidence interval is defined as:
For Number Needed to Treat
(NNT), 
The 100(1-£\)% confidence interval is defined as:
The relation between PEER and NNT:
For Patient Expected Event
Rate (PEER), 
For Z-test for Odds Ratio (OR),
The standard error of log odd
ratios:
The test statistic:
For Z-test for 2 Proportions,
Define: 
The standard error: 
The test statistic:
For Chi-square test for Association,
The test statistic: 
with degree of freedom =1,
where
= Yates¡¦ corrected Pearson's cumulative test statistic
Notation:
100(1-£\)% confidence interval: We are 100(1-£\)% sure the true value of the parameter is included in the confidence interval
: The z-value for standard normal distribution with left-tail probability
Example Top
Suppose the disease is breast cancer (BC) and a woman is considered to have the feature if she gave birth at or after the age of 25.
|
|
Outcome Positive |
Outcome Negative |
Totals |
|
Feature Present |
a=75 |
b=75 |
n1=150 |
|
Feature Absent |
c=100 |
d=150 |
n2=250 |
|
Totals |
m1=175 |
m2=225 |
N=400 |
The Odds Ratio (OR) is 1.5 and the 95% C.I. ((1-£\) =0.95) is (0.99747, 2.25571).
The Absolute Risk Reduction (ARR) is -0.1 and the 95% C.I. is (-0.20045, 0.00045).
The Relative Risk Reduction (RRR) is -0.25 and the 95% C.I. is (-0.55851, 0.00256).
The Number of Needed Treat (NNT) is -10 and the 95% C.I. is (-4.98876, 2219.47656).
The Patient Expected Event Rate (PEER) is 0.4.
The One-tail and two-tail p-values of normal test of Odds Ratio are 0.02572 and 0.05144 respectively.
The One-tail and two-tail p-values of normal test of 2 proportions are 0.03237 and 0.06473 respectively.
The One-tail and two-tail p-values of Chi-square test of association are 0.03232 and 0.06465 respectively.