Introduction to Medical Statistics

Why Do Statistics? Extrapolate from data collected to make general conclusions about larger population from which data sample was derived 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 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 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

Walter Frank Raphael Weldon

Karl Pearson

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

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

Statistical Terms Mean:  the average of the data  sensitive to outlying data Mean:  the average of the data  sensitive to outlying data Median:  the middle of the data  not sensitive to outlying data Median:  the middle of the data  not sensitive to outlying data Mode:  most commonly occurring value Mode:  most commonly occurring value Range:  the spread of the data Range:  the spread of the data IQ range:  the spread of the data  commonly used for skewed 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 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 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 Skewed data:  not normally distributed  (mean  median  mode)  report median & IQ Range

Standard Normal Distribution

Mean +/- 1 SD  encompasses 68% of observations Mean +/- 2 SD  encompasses 95% of observations Mean +/- 3SD  encompasses 99.7% of observations

Steps in Statistical Testing Null hypothesis Ho: there is no difference between the groups Null hypothesis Ho: there is no difference between the groups Alternative hypothesis H1: there is a difference between the groups Alternative hypothesis H1: there is a difference between the groups Collect data Collect data Perform test statistic eg T test, Chi square Perform test statistic eg T test, Chi square Interpret P value and confidence intervals Interpret P value and confidence intervals P value  0.05 Reject Ho P value > 0.05 Accept Ho Draw conclusions Draw conclusions

Meaning of P P Value: the probability of observing a result as extreme or more extreme than the one actually observed from chance alone 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 Lets us decide whether to reject or accept the null hypothesis P > 0.05Not significant P > 0.05Not significant P = 0.01 to 0.05Significant P = 0.01 to 0.05Significant P = to 0.01Very significant P = to 0.01Very significant P < 0.001Extremely significant P < 0.001Extremely significant

T Test T test checks whether two samples are likely to have come from the same or different populations T test checks whether two samples are likely to have come from the same or different populations Used on continuous variables Used on continuous variables Example: Age of patients in the APC study (APC/placebo) Example: Age of patients in the APC study (APC/placebo) PLACEBO: APC: mean age 60.6 years mean age 60.5 years SD+/- 16.5SD +/ SD+/- 16.5SD +/ n= 840n= 850 n= 840n= % CI % CI % CI % CI What is the P value? What is the P value? P =  not significant  patients from the same population (groups designed to be matched by randomisation so no surprise!!) P =  not significant  patients from the same population (groups designed to be matched by randomisation so no surprise!!)

T Test: SAFE “Serum Albumin” 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 PLACEBO ALBUMIN n mean28 30 SD % CI

RANDOMIZED CONTROLLED TRIALS

Reducing Sample Size Same results but using much smaller sample size (one tenth) Same results but using much smaller sample size (one tenth) ALIVE DEAD TOTAL % DEAD ALIVE DEAD TOTAL % DEAD PLACEBO 58 (69.2%) 26 (30.8%) 84 (100%) 30.8 DEAD 64 (75.3%) 21 (24.7%) 85 (100%) 24.7 TOTAL 122 (72.2%) 47 (27.8%) 169 (100%)  Reduction in death rate = 6.1% (still the same)  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

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