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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!.

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  • Be able to understand statistical terminology, interpret stats in papers and explain them to patients.
  • Pass the AKT
why should you care
Why should you care?
  • 10% of questions
  • Much less than 10% of the work
  • Easy marks
plan don t despair
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
  • Types of research:
    • Types of studies
    • Grades of evidence
    • Types of bias
    • Tests of statistical significance
  • Significance of results :
    • P value
    • Confidence intervals
    • Type 1 and type 2 error
  • Magnitude of results:
    • NNT, NNH
    • Absolute risk reduction, Relative risk reduction
    • Hazard ratio
    • Odds ratio
  • Clinical tests
    • Sensitivity, specificity
    • Positive predictive value, negative predictive value
    • Likelihood ratios for positive and negative test
  • Pretty pictures:
    • Forest plot
    • Funnel plot
    • Kaplan-Meier survival curve
the normal distribution
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
Standard deviation
  • A measure of spread
sd and the normal distribution
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
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’.
parametric and non parametric
Parametric and non-parametric
  • If it’s normally distributed, it’s parametric
  • If it’s skewed, it’s non-parametic
mean median and mode
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
types of data1
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 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


Case controlled

Cross sectional

Group work




Example where it would be the most appropriate study to use

Types of research
  • 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







Not exposed


  • Longitudinal/follow-up studies.
  • Usually prospective
  • Assessed using relative risk


case control



Not exposed






Not exposed

Case control
  • Usually retrospective
  • Reverse cohort study
  • Assessed using odds ratio
cross sectional
  • Prevalence study
  • Evaluate a defined population at a specific time.
  • Used to assess disease status and compare populations
levels of evidence
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
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)
  • III – case, correlation and comparative
  • IV – panel of experts




  • Confounding
  • Observer
  • Publication
  • Sampling
  • Selection


For bonus points, spot the odd one out!

  • 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
Avoiding Bias
  • Confounding
    • Study design
  • Observer
    • Blinding
  • Publication
    • Journals accept more outcomes with non-significant results
  • Sampling
    • Compare groups statistically
  • Selection
    • Randomisation
types of significance tests qualitative
Types of significance testsQualitative
  • 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
Types of significance testsQuantitative - 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
Types of significance testsQuantitative – 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
Types of significance testssummary table

*Chi squared – can be used to compare quantitative data if look at proportions/percentages

p value
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%

  • Null hypothesis – states that there is no difference between the 2 treatments
  • Type I error:
    • 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
confidence intervals
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
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 intervals1
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 – 3.6 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
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
Magnitude of results
  • NNT, NNH
  • Absolute risk reduction, Relative risk reduction
  • Hazard ratio
  • Odds ratio
relative risk
Relative risk
  • How many times more likely if….?
  • EER = Exposed (or experimental) event rate
  • CER = Control event rate
  • RR = EER / CER
relative risk reduction or increase
Relative risk reduction (or increase)



RRI = relative risk reduction

EER = exposed event rate

CER = control event rate

Watch your R’s!

  • 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
Number needed to treat (NNT)Number needed to harm (NNH)
  • How many patients need to be treated to...
  • Absolute risk reduction (ARR)=EER-CER


  • 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.

What is the relative risk of passing?

  • What is the RRR/RRI?
  • What is the NNT?
odds ratio
Odds ratio
  • Used in case control studies
  • Odds ratio: case odds/control odds

It doesn’t need the total.

how good is a test at predicting disease
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?
sensitivity and specificity
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
predictive values
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
likelihood ratios
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
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
Pretty pictures
  • Forest plot
  • Funnel plot
  • Kaplan-Meier survival curve
forest plots aka blobbograms
Forest plotsaka Blobbograms
  • Used in meta analysis
  • Graphical representation of results of different RCT’s

Odds ratio

of study




Size of box

= study size

Odds ratio of



Summary measure

Confidence interval


funnel plot
Funnel plot
  • Used in meta-analysis
  • Demonstrates the presence/absence of publication bias

Y axis –

Measure of


Individual study

X axis –

Treatment effect

Increased precision of study = reduced variance

Asymmetrical funnel = publication bias (missing data/studies)

kaplan meier survival curve
Kaplan-Meier Survival Curve
  • What % of people are still alive
  • 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


Time (units)