Medical Statistics as a science

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Medical Statisticsas a science
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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

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Statistical Analysisin 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

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Data

• Categorical data ? values belong to categories
• Nominal data there is no natural order to the
  categoriese.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
  categoriese.g. alive/dead
• Numerical data ? the value is a number(either
  measured or counted)
• Continuous data measurement is on a
  continuume.g. height, age, haemoglobin
• Discrete data a count of events e.g. number of
  pregnancies

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• 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

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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 ? (meanmedianmode)
  ? report mean standard deviation n
• Skewed data ? not normally distributed
  ? (mean?median ?mode)
  ? report median IQ Range

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Standard Normal Distribution
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Standard Normal Distribution
Mean /- 1 SD ? encompasses 68 of
observations Mean /- 2 SD ? encompasses 95 of
observations Mean /- 3SD ? encompasses 99.7 of
observations
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Steps in Statistical Testing

• Null hypothesisHo there is no difference
  between the groups
• Alternative hypothesisH1 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 ? 0.05 Reject Ho
• P value gt 0.05 Accept Ho
• Draw conclusions

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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 gt 0.05 Not significant
• P 0.01 to 0.05 Significant
• P 0.001 to 0.01 Very significant
• P lt 0.001 Extremely significant

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T Test

• 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/- 16.5 SD /- 17.2
• n 840 n 850
• 95 CI 59.5-61.7 95 CI 59.3-61.7
• What is the P value?
• 0.01
• 0.05
• 0.10
• 0.90
• 0.99
• P 0.903 ? not significant ? patients from the
  same population(groups designed to be matched
  by randomisation so no surprise!!)

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T Test SAFE Serum Albumin

• PLACEBO ALBUMIN
• n 3500 3500
• mean 28 30
• SD 10 10
• 95 CI 27.7-28.3 29.7-30.3

• 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 lt 0.0001 (extremely
  significant)Reject null hypothesis (Ho) and
  accept alternate hypothesis (H1) ie. 1 in 10 000
  chance that these samples are both from the same
  overall group therefore we can say they are very
  likely to be different

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Effect of Sample Size Reduction
PLACEBO ALBUMIN n 350
350 mean 28 30 SD 10 10 95
CI 27.0-29.0 29.0-31.0

• smaller sample size (one tenth smaller)
• causes wider CI (less confident where mean is)
• P 0.008 (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

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Reducing Sample Size (again)

• PLACEBO ALBUMINn 35 35
• mean 28 30
• SD 10 10
• 95 CI 24.6-31.4 26.6-33.4

• using even smaller sample size (now 1/100)
• much wider confidence intervals
• p0.41 (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

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Chi Square Test

• Proportions or frequencies
• Binary data e.g. alive/dead
• PROWESS Study Primary endpoint 28 day all cause
  mortality

ALIVE DEAD TOTAL
DEAD PLACEBO 581 (69.2)
259 (30.8) 840 (100)
30.8 DEAD 640 (75.3) 210
(24.7) 850 (100) 24.7 TOTAL
1221 (72.2) 469 (27.8) 1690 (100)

• Perform Chi Square test ? P 0.006 (very
  significant)
• 6 in 1000 times this result could happen by
  chance ? 994 in 1000 times this difference
  was not by chance variation

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Reducing Sample Size

• Same results but using much smaller sample size
  (one tenth)

• 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)

• Perform Chi Square test ? P 0.39 39 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

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Summary

• Size mattersBIGGER IS BETTER
• Spread mattersSMALLER IS BETTER
• Bigger differenceEASIER TO FIND
• Smaller differenceMORE DIFFICULT TO FIND
• To find a small difference you need a big study