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Stats Facts

Stats Facts. Mark Halloran. Diagnostic Stats. Formulae (1). Sensitivity = a / (a+c) Specificity = d / (b+d) LR+ = sens / (1-spec) LR- = (1-sens) / spec PPV = a / (a+b) NPV = d / (c+d) (LR+ = Likelihood ratio for a positive (+) result)

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Stats Facts

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  1. Stats Facts Mark Halloran

  2. Diagnostic Stats

  3. Formulae (1) • Sensitivity = a / (a+c) • Specificity = d / (b+d) • LR+ = sens / (1-spec) • LR- = (1-sens) / spec • PPV = a / (a+b) • NPV = d / (c+d) (LR+ = Likelihood ratio for a positive (+) result) (PPV = Positive Predictive Value, NPV = Neg predictive value)

  4. Formulae (2) • Prevalence = (a+c) / (a+b+c+d) • Pre-test odds = prev / (1-prev) • Post-test odds = pre-test odds x LR • Post-test probability = Post-test odds / Post-test odds + 1

  5. TB treatment RCT

  6. Formulae (3) • Control event rate • = number of events/total for control group • 14/52 =0.27 (CER) (the risk of dying in the control group is 27%) • Experimental event rate • =number of events/ total for experimental group • 4/55 =0.07 (EER) (the risk of dying in the experimental group is 7%)

  7. Formulae (4) • Absolute risk reduction for the outcome - death: • ARR= risk of event in the control group – risk of event in the experimental group • ARR=CER-EER= 0.27 – 0.07 = 0.2 or 20% • Relative risk reduction for the outcome - death: • RRR= absolute risk reduction/ risk of event in control group • RRR =(CER-EER)/ CER = (0.27 – 0.07)/ 0.27 = 0.2/0.27 = 74%

  8. Number Needed to Treat (NNT) • A more useful statistical expression for doctors and patients • NNT = 1 / ARR = 1 / 0.2 = 5 i.e. (in this study) five patients must be treated with streptomycin to prevent one death one death from TB

  9. Number needed to harm (NNH) • What about non-maleficence? • NNH = NNT but for an undesirable event • To calculate the number needed to harm we need to construct another table, this time with the figures for the adverse outcome which was VIIIth nerve damage

  10. Risk and Odds • 9 horse race, all equal chance of winning. • The risk (probability) of your horse winning = 1 / total number of potential winners = 1/9. • The odds of your horse winning are 1 / number of horses not winning = 1/8 • Using the example of a couple expecting a baby: • The risk (probability) of having a baby boy is calculated as the likelihood of that outcome/number of possible outcomes = ½ • The Odds of having a boy is calculated as the likelihood of that outcome/likelihood of it not occurring = 1/1 =1

  11. Back to the streptomycin: risk and odds of death • Risk of death in control group= 14/52 = 0.27 (same as CER) • Risk of death in experimental group = 4/55 = 0.07 (same as EER) • Risk ratio (relative risk) for death in the experimental group compared to the control group= 0.07/0.27 = 0.26

  12. Odds ratio • The odds of death = the number of people dying/ number of people not dying: Control group: odds of death= 14/38=0.37 Experimental group: odds of death 4/51= 0.078 Odds ratio = odds in experimental group/ odds in control group = 0.078/0.37 = 0.21

  13. Formulae (23) • Standard Deviation: σ2 = 1/n Σ(xi - μ)2 • Coefficient of Variation = (sd x 100) / mean) • Standard Error

  14. Standard Deviation

  15. Confidence Interval • Single observation: 95% CI = mean ± 1.96sd • Mean of new sample: 95% CI = mean ± 1.96se

  16. Study Designs

  17. Types of Studies • Cross Sectional: Sample looked at at one point in time to attempt to find associations • Case-Control: Comparing subjects who have a condition to those who do not to identify factors that may contribute • Cohort: Group of people followed to see how variables affect outcome

  18. Levels of Evidence Ia: Systematic review / meta-analysis of RCTsIb: At least 1 RCTIIa: At least one well-designed controlled study (not randomised)IIb: At least one well-designed quasi-experimental study eg cohortIII: Well-designed non-experimental descriptive studies eg case-controlIV: Expert committee reports, opinions ± clinical experience of respected authorities

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