Statistics - Educational Notes

Statistics / Evidence Based Medicine When formulating a clinical question – PICO Patient - e.g. In Paediatric Population with NHL Intervention – Rituximab Comparison – to conventional chemotherapy alone Outcome – improve survival Remember to use synonymous terms, E.g. PDA, Patent ductus, etc Ensuring Validity & avoiding Bias – RAMBO Randomisation – similar groups Allocation – does patient know if Rx / Placebo. If < 80% in follow-up & beware. Is drop out equal? Measurement – correct outcome & correct way to measure it Blinding – single v double Objective outcomes – e.g. cant blind surgery v medical treatment Levels of evidence • Ia: systematic review or meta-analysis of RCTs. • Ib: at least one RCT. • IIa: at least one well-designed controlled study without randomisation. • IIb: at least one well-designed quasi-experimental study, such as a cohort study. • III: well-designed non-experimental descriptive studies, such as comparative studies, correlation studies, case-control studies and case series. • IV: expert committee reports, opinions and/or clinical experience of respected authorities. Definitions: Mean = arithmetic (add all & divide by number) = µ Mode = most frequently occurring (can be none / multiple) Median = middle value Range = difference between smallest & largest Percentiles = % above / below number Variance = sum of squared difference from mean / n-1 Standard deviation = square route of variance = s Normal distribution 68% lies within 1 s.d. of mean 95% within 1.96 s.d. 99% within 2.58 s.d. T-distribution Similar to normal distribution, but tails are further spread out. Shape becomes more like normal distribution if increase degrees of freedom Useful for calculation confidence intervals Chi2 distribution Skewed to the right Shape depends on degrees of freedom – more like normal distribution s2 = S(xi – µ)2 n-1 µ - 1.96s µ - 2.58s µs µ+ s Transforming data Data can be transformed from one shape to another to allow statistical analysis e.g. by performing log or squared function to change a curve to a line Confidence intervals e.g. 95% CI for normal distribution = (µ - 1.96s) to (µ + 1.96s) Types of Study RCT Randomised to treatment / placebo. Follow up 2 groups to pre defined end-points. Ideally should be double blinded Cohort Study Start with disease free popn. Prospectively follow them to assess if exposure will lead to developing disease Use to calculate risks Overall risk = total with disease / total in study Risk in exposed group = exposed group with disease / total in group Relative risk = risk in exposed / risk in unexposed = increased / decreased risk. E.g. relative risk of 2 = 2x more likely to get disease Take long period of time therefore expensive & high dropout Case Control Start with diseased population & matched patients who are healty Retrospectively look at exposure to risk factors Excellent if disease is rare Relatively quick to do Often difficult to recruit case controls Should be as closely matched as possible e.g. job, age, gender etc Risk reduction Relative Risk Reduction of 20% - benefit will depend on starting risk If baseline = 1% then à 0.8% If baseline = 10% then à 8% Absolute risk reduction = 0.2% v 2% If absolute risk reduction is 2% then NNT = 50, if ARR = 0.2% then NNT = 500 NNT is dependent on length of trial – longer trial à prevents more events (assuming constant rate of occurrence) If relative risk is 1.38 = 38% extra to baseline Absolute risk increase is Baseline – event e.g. 3.7% - 2.7% = 1% = 1 extra harm event per 100 The Null hypothesis Is that there is no difference Can never be proved, only disproved Confidence interval shows where true effect lies (95% of events will land in CI) If CI is narrow and within bounds of placebo then can say unlikely to be a difference P<0.05 = 1 in 20 chance than events could occur by chance Statistical Errors Type I error – rejecting the null hypothesis when it is true The risk of this occurring (a) will never be more than the P value Type II error – do not reject null hypothesis when it is false The risk of this occurring is b (1 - b) = power of the test. Ideally power should be 100% Power of the test Should be at least 80% to bother doing the study Sample size à increased power Variability of observations à decreases power Effect of interest à larger = more power Significance level – (a) – higher = more power Student T Test Is designed for small samples But should be used if population standard deviation is unknown What is statistically significant? r = -1 or +1 = perfect correlation p < 0.05 t > 1.6 Chi2 – depends on degrees of freedom Sensitivity – ability to find true +ves Specificity – ability to exclude true negatives Type 1 error – false + Type 2 error – false –ve Incidence – no of new cases occurring in a given time e.g. 10 / year Cumulative incidence – cases per year Prevalence = total cases / cases at risk If exact onset cant be determined then incidence can = prevalence Mortality rate - = cumulate incidence e.g deaths / population Case fatality rate = deaths / population with disease Alpha error – systematic bias – can à false +ves Beta error – random errors Prospective cohort study – patients divided based on presence / absence of risk factor prior to study Screening • • Sensitivity = ability to detect +ve cases = True +ve / total with disease Specificity = ability to NOT detect false +ve = a / a+c • • = True –ve / total without disease =d/b+d Positive predictive value = How useful is a +ve result = True +ve / total +ve =a/a+b Negative predictive value = How useful is a –ve Result = True –ve / total –ve =d/c+d NB: screening & sensitivity are ALWAYS constant for a given test NB: PPV & NPV = vary based on prevalence (if higher prevalence, test is more use)