Yes No  


Positive TP FP  
  Negative FN TN  




The ability of a test to detect those with the index condition

- number with the condition

- true positives + false negatives


True positives / True positives + False negatives


Sensitivity =            TP

                        TP +  FN    



Ability to exclude those without the index condition

- number without the condition

- true negatives + false positives


True negatives / True negatives + False Positives


Specificity=             TN

                         TN + FP




The chance that the test result is correct


True positives + True negatives / total number of tests


Accuracy =                TN + TP    

                        TN + TP + FN + FP


Negative Predictive Value / NPV


The value of the negative test


NPV =            TN

                    TN + FN                


True negative / Total Number of negative tests


Positive Predictive Value / PPV


Positive Predictive Value=            TP

                                                TP +FP


The value of the positive test

- True positive / Total number of positive tests




Total number with disease at a certain time




Number of new cases within time period


Relative Risk


Probability of an outcome in one group divided by the probability of that outcome in a second group


Group 1:  Incidence 500 in 1 000 000 : 0.0005

Group 2:  Incidence 100 in 1 000 000 : 0.0001


Relative risk = 0.0005/0.0001 = 5


Absolute Risk


Probability of a specific outcome

- 0 - 1

- may be expressed as a percentage


Absolute Risk Reduction


Calculated by subtracting the AR in the experimental group from the AR in the control group

- the absolute risk in the experimental group must be less than the control


Example A

  Death Survival  
New Treatment 19 38 57
Old Treatment 29 29 58


ARR = 29/58 - 19/57 = 17%


Example B


Drug reduces risk of MI by 25%

Normal mortality is 1%


ARR = 1/100 - 0.75/100 = 0.25/100 = 0.25%


Number Needed to Treat


Inverse of the Absolute Risk Reduction


Error Types


Null hypothesis

- there is no difference between the two groups


Type 1 / Alpha error

- null hypothesis is true, but is rejected

- incorrectly rejects true null hypothesis

- false positive conclusion

- conclude treatment works when it does not

- set to 0.05 / 1 in 20 / p value of 0.05


Type 2 / Beta error

- null hypothesis is false, but is rejected

- incorrectly accepts a false null hypothesis

- false negative conclusion

- conclude that a treatment does not work, when it does

- typically set to 0.20 or 20% chance of false negative

- as power increased, probability of a type 2 error decreases



- ability to test null hypothesis / probability of detecting a true positive difference

- increased by increasing sample size / improved design

- Power = 1 - beta

- usually set at 80%

- i.e. the study had a power of 80% to detect a certain difference in two groups




Level to set not purely by chance alone


P value / level of significance

- what is the chance that the null hypothesis is incorrect

- probability of a type 1 error

- generally p < 0.05 (less than 5% chance null hypothesis is incorrect)

- means low chance of type 2 error

- derived from the sample mean and the standard error


Sample Size


To calculate sample size you need:

- SD of the population (previous data, pilot data)

- confidence interval you want to accept (90,95,99)

- set the error (usually alpha =0.05)


Statistical Tests


Student t-test

- tests differences in population with normal distribution

- compares 2 continous variables


Chi square

- compares two or more discrete non continous variables



- analysis of variance

- compares one dependent variable amongst 3 or more groups simultaneously



- compares multiple dependent variables amongst 3 or more groups


Kaplan-Meier Curve

- used for estimating probability of surviving a unit time

- used to develop a survival curve when survival times are not exactly known


Multivariate analysis

- an analysis where the effects of many variables are considered


Hazard rate

- probability of an endpoint

- technical name for failure rate


Hazard ratio

- relative risk of an endpoint at any given time


Cox Proportional-Hazard Model

- multivariate analysis used to identify combination of factors predicting prognosis in a group of patients

- can test the effect of individual factors independantly


Levels of Evidence


Level 1


Well designed randomised controlled trial


Systemic review of Level 1 RCT


Level 2


Lesser quality RCT


Prospective comparative study

- two groups

- no randomisation


Systemic review of Level 2 studies


Level 3


Case control

- two groups of similar patients

- one with treatment or disease of interest, one without

- look to see differences


Retrospective comparative

- two groups with different interventions

- not prospective


Level 4


Case series


Level 5


Expert opinion


Types of Studies


1.  Therapeutic Study

- investigates the result of a treatment




2.  Prognostic Study

- investigating the effect of a patient characteristic on  the outcome of a disease


Prospective cohort


3.  Diagnostic Study

- investigating a diagnostic test