Transcript Slide 1

Statistics for GP and the AKT
Sept ‘11
Aims
• Be able to understand statistical terminology,
interpret stats in papers and explain them to
patients.
• Pass the AKT
Why should you care?
• 10% of questions
• Much less than 10% of the work
• Easy marks
Plan – don’t despair!
•
Representing data:
– Parametric v non parametric
data
– Normal distribution and
standard deviation
– Types of data
– Mean, median, mode
– Prevalence and incidence
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– P value
– Confidence intervals
– Type 1 and type 2 error
Clinical tests
– Sensitivity, specificity
– Positive predictive value,
negative predictive value
– Likelihood ratios for positive and
negative test
Types of studies
Grades of evidence
Types of bias
Tests of statistical significance
Significance of results :
Magnitude of results:
– NNT, NNH
– Absolute risk reduction, Relative
risk reduction
– Hazard ratio
– Odds ratio
Types of research:
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Pretty pictures:
– Forest plot
– Funnel plot
– Kaplan-Meier survival curve
The Normal Distribution
•Frequency on y axis and continuous variable on x
•Symmetrical, just as many have more than average as less than average
•Generally true for medical tests and measurements
Standard deviation
• A measure of spread
SD and the normal distribution
•68.2% of data within 1SD
•95.5% of data within 2SD
•99.8% of data within 3SD
•95% of data within 1.96 SD
Defining ‘normal’
•Can be used to define normal for medical tests e.g. Na
•But be definition 5% of ‘normal’ people will be ‘too high’ and 5% ‘too low’.
Normality
Positive and negative skew
Parametric and non-parametric
• If it’s normally distributed, it’s parametric
• If it’s skewed, it’s non-parametic
Mean, median and mode
• Use mean for parametric data
• Median for non parametric data
• In a normal distribution:
Mean = median = mode
• For a negatively skewed distribution:
Mean < median < mode
• For a positively skewed distribution:
Mean > median > mode
• Remember alphabetical order, <for negative, >for positive
What sort of distribution is this?
Which is a normal distribution?
Types of data
Types of data
• Continuous – can take any value e.g. height
• Discrete – can only take integers e.g. number
of asthma attacks
• Nominal – into categories in no particular
order e.g. colour of smarties
• Ordinal – into categories with an inherent rank
e.g. Bristol stool chart
Prevalence and incidence
• Prevalence – proportion of people that have a
disease at a given time
• Incidence – number of new cases per population
per time
• Prevalence = incidence x length of disease
Types of research
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RCT
Cohort
Case controlled
Cross sectional
Group work
• Definition
• Strengths
• Weaknesses
• Example where it would
be the most
appropriate study to
use
RCT
• Interventional study
• Used to compare treatment(s) with a control group.
• Control group have placebo or current best
treatment.
• Best evidence but….
• Expensive and ethical problems
• Two types
– Group comparative
– Cross-over
Cohort
• Longitudinal/follow-up studies.
• Usually prospective
Disease
Exposed
Well
Population
selection
Time
Disease
Not exposed
Well
• Assessed using relative risk
Case control
• Usually retrospective
• Reverse cohort study
Exposed
Disease
Not exposed
selection
Time
Exposed
Well
Not exposed
• Assessed using odds ratio
Population
Cross-sectional
• Prevalence study
• Evaluate a defined population at a specific
time.
• Used to assess disease status and compare
populations
Levels of Evidence
• Ia – Meta analysis of RCT’s
• Ib – RCT(s)
• IIa – well designed non-randomised trial(s)
• IIb – well designed experimental trial(s)
• III – case, correlation and comparative
• IV – panel of experts
Grades of Evidence
• Ia – Meta analysis of RCT’s
• Ib – RCT(s)
• IIa – well designed non-randomised trial(s)
• IIb – well designed experimental trial(s)
A
B
• III – case, correlation and comparative
• IV – panel of experts
C
Bias
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Confounding
Observer
Publication
Sampling
Selection
CARD SORT
For bonus points, spot the odd one out!
Bias
• Confounding
– Exposed and non-exposed groups differ with respect characteristics
independent of risk factor.
• Observer
– The patient/clinician know which treatment is being received.
– Outcome measure has a subjective element.
• Publication
– Clinically significant results are more likely to be published
– Negative results are less likely to be published
• Sampling
– Non-random selection from target population.
• Selection
– Intervention allocation to the next person is known before
recruitment.
Avoiding Bias
• Confounding
– Study design
• Observer
– Blinding
• Publication
– Journals accept more outcomes with non-significant
results
• Sampling
– Compare groups statistically
• Selection
– Randomisation
Chance…
Types of significance tests
Qualitative
• Single sample (my sample vs manufacturer’s
claim)
– Binomial test
• >1 independent sample (drug A vs drug B)
– Small sample – Fisher exact test
– Larger sample – Chi-squared
• Dependent sample
– Percentage agreement (+/- Kappa statistic)
Types of significance tests
Quantitative - Parametric
• Single sample
– Student one-sample t-test
• Two independent samples
– Student independent samples t-test
• Two dependent samples
– Student dependent samples t-test
• >2 independent samples
– One-way ANOVA
• >2 dependent samples
– ANOVA
• Correlation
– Pearson correlation coefficient
Types of significance tests
Quantitative – Non-parametric
• Single sample
– Kolmogorov-Smirnov test
• Two independent samples
– Mann-Whitney
• Two dependent samples
– Wilcoxon matched pairs sum test
• >2 independent samples
– Kruskal-Wallis test
• >2 dependent samples
– Friedman test
• Correlation
– Spearman
Types of significance tests
summary table
Samples
Qualitative
1
Binomial
2
>2
Correlation
Ind: Fishers / *Chi squared
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Dep: % agreement
Quantitative
Student
Student
Ind: one-way
ANOVA
Pearson
Parametric
Dep: ANOVA
Quantitative Kolmogorov
Ind: Mann-Whitney
-Smirnov
Nonparametric
Ind: KurskalWallis
Spearman
Dep: Wilcoxon
Dep: Friedman
*Chi squared – can be used to compare quantitative data if look at
proportions/percentages
P value
“The p value is equal to the probability of
achieving a result at least as extreme as the
experimental outcome by chance”
• Usually significance level is 0.05
i.e. the chance that there is no real difference is
less than 5%
Hypothesis
• Null hypothesis – states that there is no
difference between the 2 treatments
Errors
• Type I error:
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False positive
The null hypothesis is rejected when it is true
Probability is equal to p value
Depends on significance level set not on sample size
Risk increased if multiple end points
• Type II error:
– False negative
– The null hypothesis is accepted when it is true i.e. fail to
find a statistical significant difference
– More likely if small sample size
Error
Sample populations
Confidence intervals
• 95% confidence interval means you are 95%
sure that the result for the true population lies
within this range
• The bigger the sample, i.e. the more
representative of the true population, the
smaller the confidence interval.
Confidence intervals (the maths)
• For 95% confidence interval:
Mean ± 1.96 x SEM
• Standard error of the mean
= SD / √n
i.e. standard deviation divided by square root of
number of samples
As number of samples increases, SEM
decreases.
Confidence intervals
• We measure the concentration span of a sample of
36 VTS trainees. The mean concentration span is 2.4
seconds and the standard deviation is 1.2 seconds.
• What is the approximate 95% confidence interval?
1.
2.
3.
4.
5.
6.
1.2 – 3.6 seconds
Too short to measure and getting shorter
2.2 – 2.6 seconds
2.3 – 2.5 seconds
2.0 – 2.8 seconds
I don’t care
Confidence intervals and trials
• If the confidence interval of a difference doesn’t
include 0, then the result is statistically significant.
After 30 minutes of stats, the mean reduction in attention span was
2.3 minutes (0.8 – 3.8).
• If the confidence interval of a relative risk doesn’t
include 1, then the result is statistically significant.
Relative risk of death after learning about stats was 0.7(0.3 – 1.1)
Magnitude of results
– NNT, NNH
– Absolute risk reduction, Relative risk reduction
– Hazard ratio
– Odds ratio
Relative risk
• How many times more likely if….?
Disease
Total
Exposed
A
B
EER = A/B
Control
C
D
CER = C/D
• EER = Exposed (or experimental) event rate
• CER = Control event rate
• RR = EER / CER
Relative risk reduction (or increase)
RRR (RRI) = EER-CER
CER
RRI = relative risk reduction
EER = exposed event rate
CER = control event rate
Watch your R’s!
Hazard
• Hazard ratio (HR) – estimate of RR over time
– Deaths rate in A/Death rate in B
(2=twice as many, 0.5=half as many)
– Note: hazard ratio does not reflect median survival time it
is relative probability of dying
Number needed to treat (NNT)
Number needed to harm (NNH)
• How many patients need to be treated to...
• Absolute risk reduction (ARR)=EER-CER
NNT = 1/ARR = 1/EER-CER
Scenario
• Claire Stewart thought women with no hair
were more likely to pass CSA because having
hair would distract trainees by getting in their
eyes.
• She tested this by randomising her female
trainees.
Pass CSA
Fail CSA
Control group
15
15
Shaved trainees
20
5
• What is the relative risk of passing?
• What is the RRR/RRI?
• What is the NNT?
Odds ratio
• Used in case control studies
RF
No RF
Odds
Case
A
B
A/B
Control
C
D
C/D
• Odds ratio: case odds/control odds
It doesn’t need the total.
How good is a test at predicting
disease?
• If the test is negative, how sure can you be
that you don’t have the disease?
• If the test is positive, how sure can you be that
you do have the disease?
Tests
Learn this!
Sensitivity and specificity
• Sensitivity – proportion people that have the
disease that test positive
• Specificity – proportion of people that don’t
have the disease that test negative
Sensitivity and specificity
Predictive values
• Positive predictive value – proportion of
positive tests that actually represent disease
• Negative predictive value – proportion of
negative tests that don’t have disease
Learn this!
Likelihood ratios
• Take into account prevalence of disease so are more useful
• Likelihood ratio for a positive test =
sensitivity / 1 – specificity
• Likelihood ratio for a negative test =
1 – sensitivity / specificity
• A likelihood ratio of greater than 1 indicates the test result is
associated with the disease.
• A likelihood ratio less than 1 indicates that the result is
associated with absence of the disease.
• A likelihood ratio close to 1 means the test is not very useful
An example….
• In a VTS group of 110 people, 30 people have
the dreaded lurgy. A test is developed for this.
Of the 30 people with the dreaded lurgy, 18
have a positive test. 16 of the others also have
a positive test.
• What is the likelihood ratio for a positive test?
Pretty pictures
– Forest plot
– Funnel plot
– Kaplan-Meier
survival curve
Forest plots
aka Blobbograms
• Used in meta analysis
• Graphical representation of results of different
RCT’s
Studies
Confidence
interval
Odds ratio
of study
Size of box
= study size
Odds ratio of
summary
measure
Summary measure
Confidence interval
OR (CI)
Funnel plot
• Used in meta-analysis
• Demonstrates the presence/absence of
publication bias
Y axis –
Measure of
precision
Individual study
X axis –
Treatment effect
Increased precision of study = reduced variance
Asymmetrical funnel = publication bias (missing data/studies)
Kaplan-Meier Survival Curve
• What % of people are still alive
Scenario
• We’ve driven Sarah Egan to insanity by not doing
enough learning logs.
• She’s gone on a rampage with a gun because
basically life will be better without any of us around
(nothing to do with pregnancy hormones…obviously)
• Draw the Kaplan-Meier survival curve for MK GP
trainees
Number of
trainees
Time (units)
Any questions?