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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!

- 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

- 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’.

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

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

RCT

Cohort

Case controlled

Cross sectional

Group work

Definition

Strengths

Weaknesses

Example where it would be the most appropriate study to use

Types of researchRCT

- 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

Disease

Not exposed

Population

Time

selection

Exposed

Well

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

- 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)
- III – case, correlation and comparative
- IV – panel of experts

A

B

C

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

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 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 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 testssummary table

*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:
- 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

- 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 – 3.6 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….?
- 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.

What is the relative risk of passing?

- What is the RRR/RRI?
- What is the NNT?

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 – proportion people that have the disease that test positive
- Specificity – proportion of people that don’t have the disease that test negative

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

- 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 plotsaka Blobbograms

- Used in meta analysis
- Graphical representation of results of different RCT’s

of study

Confidence

interval

Studies

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

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

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