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