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 t-test
- 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
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
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