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Statistics for GP and the AKT

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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Statistics for GP and the AKT

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  1. Statistics for GP and the AKT Sept ‘11

  2. Aims • Be able to understand statistical terminology, interpret stats in papers and explain them to patients. • Pass the AKT

  3. Why should you care? • 10% of questions • Much less than 10% of the work • Easy marks

  4. 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

  5. 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

  6. Standard deviation • A measure of spread

  7. 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

  8. 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’.

  9. Normality

  10. Positive and negative skew

  11. Parametric and non-parametric • If it’s normally distributed, it’s parametric • If it’s skewed, it’s non-parametic

  12. 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

  13. What sort of distribution is this?

  14. Which is a normal distribution?

  15. Types of data

  16. 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

  17. 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

  18. RCT Cohort Case controlled Cross sectional Group work Definition Strengths Weaknesses Example where it would be the most appropriate study to use Types of research

  19. 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

  20. Disease Exposed Well Population selection Disease Not exposed Well Cohort • Longitudinal/follow-up studies. • Usually prospective • Assessed using relative risk Time

  21. Exposed Disease Not exposed Population Time selection Exposed Well Not exposed Case control • Usually retrospective • Reverse cohort study • Assessed using odds ratio

  22. Cross-sectional • Prevalence study • Evaluate a defined population at a specific time. • Used to assess disease status and compare populations

  23. 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

  24. 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

  25. Bias • Confounding • Observer • Publication • Sampling • Selection CARD SORT For bonus points, spot the odd one out!

  26. 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.

  27. Avoiding Bias • Confounding • Study design • Observer • Blinding • Publication • Journals accept more outcomes with non-significant results • Sampling • Compare groups statistically • Selection • Randomisation

  28. Chance…

  29. 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)

  30. 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

  31. 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

  32. Types of significance testssummary table *Chi squared – can be used to compare quantitative data if look at proportions/percentages

  33. 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%

  34. Hypothesis • Null hypothesis – states that there is no difference between the 2 treatments

  35. 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

  36. Error

  37. Sample populations

  38. 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.

  39. 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.

  40. 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

  41. 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)

  42. Magnitude of results • NNT, NNH • Absolute risk reduction, Relative risk reduction • Hazard ratio • Odds ratio

  43. Relative risk • How many times more likely if….? • EER = Exposed (or experimental) event rate • CER = Control event rate • RR = EER / CER

  44. 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!

  45. 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

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