1. Medical Statistics as a science

2. Why Do Statistics?
Extrapolate from data collected to make general conclusions about larger population from which data sample was derived
Allows general conclusions to be made from limited amounts of data
To do this we must assume that all data is randomly sampled from an infinitely large population, then analyse this sample and use results to make inferences about the population

3. Statistical Analysis in a Simple Experiment
Define population of interest
Randomly select sample of subjects to study (clinical trials do not enrol a randomly selected sample of patients due to inclusion/exclusion criteria but define a precise patient population)
Half the subjects receive one treatment and the other half another treatment (usually placebo)
Measure baseline variables in each group (e.g. age, Apache II to ensure randomisation successful)
Measure trial outcome variables in each group (e.g. mortality)
Use statistical techniques to make inferences about the distribution of the variables in the general population and about the effect of the treatment

4. Data Categorical data:  values belong to categories
Nominal data: there is no natural order to the categories e.g. blood groups
Ordinal data: there is natural order e.g. Adverse Events (Mild/Moderate/Severe/Life Threatening)
Binary data: there are only two possible categories e.g. alive/dead
Numerical data:  the value is a number (either measured or counted)
Continuous data: measurement is on a continuum e.g. height, age, haemoglobin
Discrete data: a “count” of events e.g. number of pregnancies

5. Descriptive Statistics:
concerned with summarising or describing a sample eg. mean, median
Inferential Statistics:
concerned with generalising from a sample, to make estimates and inferences about a wider population eg. T-Test, Chi Square test

6. Statistical Terms
Mean:  the average of the data  sensitive to outlying data
Median:  the middle of the data  not sensitive to outlying data
Mode:  most commonly occurring value
Range:  the spread of the data
IQ range:  the spread of the data  commonly used for skewed data
Standard deviation:  a single number which measures how much the observations vary around the mean
Symmetrical data:  data that follows normal distribution  (mean=median=mode)  report mean & standard deviation & n
Skewed data:  not normally distributed  (meanmedian mode)  report median & IQ Range

7. Standard Normal Distribution

8. Standard Normal Distribution
Mean +/- 1 SD  encompasses 68% of observations
Mean +/- 2 SD  encompasses 95% of observations
Mean +/- 3SD  encompasses 99.7% of observations

9. Steps in Statistical Testing
Null hypothesis Ho: there is no difference between the groups
Alternative hypothesis H1: there is a difference between the groups
Collect data
Perform test statistic eg T test, Chi square
Interpret P value and confidence intervals
P value  Reject Ho
P value > Accept Ho
Draw conclusions

10. Meaning of P
P Value: the probability of observing a result as extreme or more extreme than the one actually observed from chance alone
Lets us decide whether to reject or accept the null hypothesis
P > Not significant
P = to 0.05 Significant
P = to 0.01 Very significant
P < Extremely significant

11. T Test PLACEBO: APC: mean age 60.6 years mean age 60.5 years
T test checks whether two samples are likely to have come from the same or different populations
Used on continuous variables
Example: Age of patients in the APC study (APC/placebo)
PLACEBO: APC: mean age 60.6 years mean age 60.5 years
SD+/ SD +/
n= n= 850
95% CI % CI
What is the P value?
0.01
0.05
0.10
0.90
0.99
P =  not significant  patients from the same population (groups designed to be matched by randomisation so no surprise!!)

12. T Test: SAFE “Serum Albumin”
PLACEBO ALBUMIN n
mean SD
95% CI
Q: Are these albumin levels different? Ho = Levels are the same (any difference is there by chance) H1 =Levels are too different to have occurred purely by chance
Statistical test: T test  P < (extremely significant) Reject null hypothesis (Ho) and accept alternate hypothesis (H1) ie. 1 in chance that these samples are both from the same overall group therefore we can say they are very likely to be different

13. Effect of Sample Size Reduction
PLACEBO ALBUMIN n
mean SD
95% CI
smaller sample size (one tenth smaller)
causes wider CI (less confident where mean is)
P = (i.e. approx 0.01  P is significant but less so)
This sample size influence on ability to find any particular difference as statistically significant is a major consideration in study design

14. Reducing Sample Size (again)
PLACEBO ALBUMIN n
mean SD
95% CI
using even smaller sample size (now 1/100)
much wider confidence intervals
p=0.41 (not significant anymore)
 SMALLER STUDY has LOWER POWER to find any particular difference to be statistically significant (mean and SD unchanged)
POWER: the ability of a study to detect an actual effect or difference

15. Chi Square Test Proportions or frequencies Binary data e.g. alive/dead
PROWESS Study: Primary endpoint: 28 day all cause mortality
Reduction in death rate = 30.8%-24.7%= 6.1% ie 6.1% less likely to die in APC group
ALIVE DEAD TOTAL % DEAD
PLACEBO (69.2%) (30.8%) 840 (100%)
DEAD (75.3%) (24.7%) 850 (100%)
TOTAL (72.2%) (27.8%) 1690 (100%)
Perform Chi Square test  P = (very significant)
6 in 1000 times this result could happen by chance  994 in 1000 times this difference was not by chance variation

16. Reducing Sample Size
Same results but using much smaller sample size (one tenth)
Reduction in death rate = 6.1% (still the same)
ALIVE DEAD TOTAL % DEAD
PLACEBO (69.2%) (30.8%) (100%)
DEAD (75.3%) (24.7%) (100%)
TOTAL (72.2%) (27.8%) (100%)
Perform Chi Square test  P = in 100 times this difference in mortality could have happened by chance therefore results not significant
Again, power of a study to find a difference depends a lot on sample size for binary data as well as continuous data

17. Summary Size matters=BIGGER IS BETTER Spread matters=SMALLER IS BETTER
Bigger difference=EASIER TO FIND
Smaller difference=MORE DIFFICULT TO FIND
To find a small difference you need a big study