

Disease





Yes 
No 

Test

Positive 
TP 
FP 


Negative 
FN 
TN 






Sensitivity
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
Specificity
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
Accuracy
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
Prevalence
Total number with disease at a certain time
Incidence
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
Power
 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
Confidence
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 ttest
 tests differences in population with normal distribution
 compares 2 continous variables
Chi square
 compares two or more discrete non continous variables
ANOVA
 analysis of variance
 compares one dependent variable amongst 3 or more groups simultaneously
MANOVA
 compares multiple dependent variables amongst 3 or more groups
KaplanMeier 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 ProportionalHazard 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
RCT
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