# Statistics

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