An Idiots Guide to Statistics Curriculum 3'6

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An Idiots Guide to StatisticsCurriculum 3.6

• Daisy de Ferranti
• Stephanie de Giorgio
• Lindo Van der Merwe

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Overview

• Why bore you with Statistics
• Definitions
• How to work through the stats questions

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Why bore you with Statistics

• AKT- Definitions, interpretation of terms, 2 by 2
  table (and forest plot for statisticians!)

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Definitions

• Sensitivity (True positive rate) How good is
  this test at picking up people who have the
  condition?
• a/ac

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Specificity

• True negative rate
• How good is this test at correctly excuding
  people without the condition
• d/bd

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Positive Predictive value

• Post test probability of a positive test
• If a person tests positive, what is the
  probability that he has the condition
• a/ab

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Negative predictive value

• Post test probability of a negative test
• If a person tests negative what is the probabilty
  that he does not have the condition
• d/cd

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How to remember this!

• SnNOUT with high sensitivity a negative result
  rules OUT the diagnosis
• SpPin with high specificity, a positive result
  rules IN the diagnosis

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An example
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• Sensitivity
• 20/25 0.8
• Specificity
• 45/75 0.6
• PPV
• 20/50 0.4
• NPV
• 45/50 0.9

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Accuracy

• What proportion of all tests have given the
  correct result (ie true positives and true
  negatives as a proportion of all the results)
• ad/abcd

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Likelihood ratio of a positive test

• How much more likely is positive test to be found
  in a person with, as opposed to without, the
  condition
• Sensitivity/1-specificity

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Interventions
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Risk

• Chance of being dead in control group
• X
• Chance of being dead in surgical group
• Y

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Relative Risk

• RR of death is the risk in surgical pts compared
  with controls.
• y/x

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Relative risk reduction

• Amount by which the risk of death is reduced by
  surgery

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Another practical example treatment of candida
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• Risk in placebo group 40/1000.440
• Risk in treatment group 20/1000.220
• Absolute risk reduction (ARR)
• 80/100 60/100 20
• Relative risk reduction
• Risk in placebo (40) risk in treatment(20)
  0.5
• Risk in placebo (40)

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Glossary Index
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Hierarchy of Evidence

• Systematic review meta-analysis
• RCT
• Cohort studies
• Case-control studies
• Cross-sectional surveys
• Case reports

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Types of Study

• Case control
• Retrospective
• Group of cases with condition group of controls
  without are studied to determine relative
  frequency of particular exposures of interest in
  2 groups
• Concerned with aetiology of disease rather than
  Rx
• Cohort
• Prospective
• Two groups of people are selected on basis of
  differences in their exposure to particular agent
  followed up to establish how many in each group
  develop a particular disease
• Follow up period generally years
• Concerned with aetiology of disease

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Types of Study

• 1. Case reports
• Describes medical hx of single pt in form of
  story.
• 2. Cross-sectional surveys
• Population or sample of population examined to
  determine prevalence of certain condition

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Types of Study

• 5. RCT
• Participants in trial are randomly allocated to
  either one intervention (ie drug) or another (ie
  placebo)
• Both groups followed up for specified time
  analysed in terms of specific outcomes defined at
  onset (ie death, MI)
• Often short follow up due to costs pressure to
  produce timely evidence
• 6. Systematic Reviews Meta-analysis
• Systematic review Summary of medical literature
  that uses explicit methods to perform a thorough
  search critical appraisal of individual studies
  
• Meta-analysis A systematic review that uses
  quantitative methods to summarise results
  pooling all information from number of different
  (but similar) studies

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Statistics which describe Data

• Mean
• Median
• Mode
• Standard Deviation

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• Mean
• Sum of all values, divided by the number of
  values
• Used in normal distribution spread of data is
  fairly similar on each side of mid point

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• Median
• It is the point which has half the values above
  half below
• Used to represent average when data not
  symmetrical - skewed distribution
• Meanmedian in symmetrical distribution but not
  in skew distribution
• Mode
• Most common set of events

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• Standard
  Deviation
• Good news not necessary to know how to
  calculate the SD!
• Used for data which is normally distributed
• SD indicates how much a set of values is spread
  around the mean
• /- 1 SD (range of one SD above below the mean)
  includes 68.2 of the values
• /- 2 SD includes 95.4 of values
• /- 3 SD includes 99.7

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Statistics which test confidence

• P value
• Confidence interval

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P value

• Test of probability ie any observed difference
  having happened by chance
• Used to determine whether a hypothesis is true
• Null hypothesis no difference between two
  groups/treatments
• P value lt0.05 statistically significant ie
  unlikely to have happened by chance, hence
  important
• The lower the p value, the less likely the
  difference happened by chance thus the higher
  the significance
• Significant p rejects Null hypothesis

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Confidence interval

• When is it used?
• Typically when, instead of simply wanting mean
  value of sample, we want a range that is likely
  to contain the true population value
• True value is mean value that we would get if
  we had data for the whole population
• What does it mean?
• CI gives the range in which the true value is
  likely to be (usually with level of 95
  certainty)
• Provides same information as p value, but more
  useful
• Size of CI related to sample size of study
  larger studies have narrower CI
• If CI crosses 0 Null hypothesis true

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Forest Plot/blobbogram
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Forest Plot

• Allows readers to see information from individual
  studies that went into the meta-analysis at a
  glance
• Results of component studies are shown as squares
  centred on point estimate of result of each study
• Horizontal line runs through to show its CI
• Diamond symbol represents the overall estimate
  from meta-analysis and its CI
• Significance is achieved if the diamond is clear
  of the line of no effect

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• Interpretation
• i. Wide CI, crosses 0
• ii. Does not cross 0, intervention works but weak
  evidence
• iii. Narrow CI, crosses 0, intervention no
  benefit
• iv. Narrow CI, intervention works
• v. Intervention detrimental
• vi. Meta-analysis intervention works

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Key definitions

• Incidence proportion of a defined group
  developing a disease within a stated period
• Prevalence proportion of a defined group having
  a disease at any one time
• Single blinded subjects did not know which
  treatment they were receiving
• Double blinded neither investigators nor
  subjects knew who was receiving which treatment
• Unblinded all participants were aware of who
  received which intervention
• Power ability of a study to minimise
  uncertainties that arise because of chance
  variation between samples - ie larger samples
• Type II error common accept null when
  alternative is true
• Type I error less common accept alternative
  when null is true

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Enough of the theory heres the practical bit!!

• What do we need to be able to do?
• 1. Interpret drug rep data
• 2. Explain risk/benefits to our patients
• 3. Understand evidenced based medicine

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Survival analysis and risk reduction

• Use of ramipril in preventing stroke double
  blind randomised trial. BMJ 324699-702
• To determine the effect of ramipril on secondary
  prevention of stroke.
• 267 hospitals in 19 countries
• 9297 patients with vascular disease or diabetes
  followed for 4.5 yrs (HOPE study)

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• Outcome stroke, TIA and cognitive function
  measured. Blood pressure recorded at entry to
  study, after 2 years and at end.
• Results
• Reduction in BP modest
• Relative risk of stroke reduced by 31 in
  ramipril group compared to placebo, relative risk
  of fatal stroke reduced by 61

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Summary of results
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• Risk of stroke in ramipril group
• 156/4635 0.036 3.36
• Risk of stroke in placebo group
• 226/4652 0.048 4.48
• Relative risk reduction (4.86 3.36)/4.86
• 0.31
• 31

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• Absolute risk reduction (ARR)
• Risk in placebo risk in rampril
• 4.86 3.36 1.5
• NNT 100 100 67
• ARR 1.5

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• For fatal stroke
• Risk in ramipril group 17/4635 0.0036
• Risk in placebo group - 44/4652 0.0094
• RRR 0.0094 - 0.0036 0.617 61
• 0.0094

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• Rampril reduced risk of stroke in high risk
  patients by 31, which seems good.
• However, have to treat 67 people for 4 ½ years in
  order to benefit 1 patient by preventing 1 stroke

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Odds ratios and CI

• Systematic r/v of long term anticoagulation or
  antiplatelet treatment in pts with atrial
  fibrillation BMJ 322321-326
• Objective - to examine benefits/risks of warfarin
  compared to aspirin/indomethacin
• Methods - meta-analysis of RCT. Odds ratios (95
  CI) calculated to estimate treatment effects

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Results for one of the trials
Odds of vascular death in patients on
warfarin number of times an event happens
16 0.088 number of times it does not happen
197-16 Odds of vascular death in aspirin pts
14 0.080
188 - 14
Odds ratio odds in warfarin pts 0.088
1.10 odds in aspirin pts
0.080 Odds ratio of gt1 indicates that rate of
vasc death increased in warfarin pts over those
in aspirin pts.
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• If the confidence interval for the Odds Ratio
  containes 1 ie no difference, then the difference
  in results is NOT statistically significant
• Seen by CI plot line crossing the line at 1.
• Overall the study did not show any benefit of
  long term anticoagulation and an increased risk
  of bleeding

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In summary

• Important to understand for career, not just for
  exam.
• Try to understand basic concepts well as can then
  apply to most questions.