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Medical Statistics Pt 1

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Fastbleep Academic Masterclass - 31 May 2011
Overview of the use of statistics and statistical error.

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Medical Statistics Pt 1

  1. 1. Medical Statistics MasterclassFastbleep Academic Masterclass #4 University Place 31 May 2011
  2. 2. About us James Giles Richard Salisbury MB PhD Student F1 & MRes Graduate PAL & Fastbleep Director Cochrane AuthorLove stats, hated contextless Bioscience geek
  3. 3. 1. Use of statistics2. Statistical errors3. Common statistical tests
  4. 4. 1. Use of statisticsWhat is your question?What do you want to do?
  5. 5. Descriptive statistics• Averages - mean/median/mode• Frequency• Range (measures of spread)• Box-and-whisker plot• Bar chart• Pie chart
  6. 6. Scales of measurementNominalOrdinalNumerical
  7. 7. Scales of measurementNominal Name: red, blue, greenOrdinalNumerical
  8. 8. Scales of measurementNominal Name: red, blue, greenOrdinal Order: tumour stageNumerical
  9. 9. Scales of measurementNominal Name: red, blue, greenOrdinal Order: tumour stageNumerical Continuous: height Discrete: number of teeth
  10. 10. Nominal VariableDescription: Frequency/proportion Illustration: Bar chart/pie chart
  11. 11. AveragesMeanMedian - middle numberMode - most frequent
  12. 12. Distributions
  13. 13. Distributions
  14. 14. Distributions
  15. 15. Distributions
  16. 16. Distributions
  17. 17. AveragesMean - numerical & unskewedMedian - ordinal & skewedMode - nominal & bimodal
  18. 18. Measures of spreadStandard deviation (sd)Standard error of the mean (SEM)
  19. 19. Measures of spreadStandard deviation (sd)mean distance from the mean
  20. 20. Measures of spreadStandard deviation (sd)Standard error of the mean (SEM)
  21. 21. Measures of spreadStandard error (SEM)estimate of spread of your sample meanfrom a true population meanSEM = sd/ n 20 Neutrophil Count / 105/ml 15 10 5 0 A ac C ad B bc D bd
  22. 22. feltron.com
  23. 23. Analytical statistics Compare - difference, higher/lower Relate - correlation, regression, agreement
  24. 24. Comparisons1) One variable against a constant2) One variable across 2 dependant groups3) One variable across 2 independent groups4) One variable across pairs
  25. 25. Comparsion one variable against a constantIs Hb level in heavy smokers higher than the average of 14?Variable: Hb levelConstant: 14
  26. 26. Groups 2 types of groups• Dependent: one group a subset of the other• Independent: different sets
  27. 27. Comparison Example: one variable across 2 dependent(overlapping) groups Is serum PTH higher in severe renal failure than the average value in renal failure patients?Variable: serum PTHGroups: severe renal failure patients, all renal failure patients Is mortality rate in neck of femur fracture higher in case of cardiorespiratory co morbidity than average?Variable: mortality rateGroups: patients with neck of femur fracture and co morbidity, all patients with neck of femur fracture
  28. 28. Comparison Examples: One variable across 2 independent(non-overlaping) groupsIs Trop T higher in patients with STE-ACS than NSTE-ACS?Variable: Trop TGroups: STE-ACS and NSTE-ACSIs success rate to control variceal haemorrhage higher in SCLEROTHERAPY than BALLOON TAMPONADE?Variable: success rateGroups: sclerotherapy and balloon tamponade
  29. 29. Comparison Examples (pairs):Pairs = repeated measurements:t wo measurements of a variable on one patient at different time points
  30. 30. Comparison Is the PEF higher after Salbutamol nebuliser in asthma patients?Variable: PEFPairs: prior and after nebuliserIs the second-day serum lactate level higher than the third-day lactate level following antibiotic therapy in sepsis?Variable: lactate levelPairs: second and third day
  31. 31. Relation AssociationPrediction/regression Agreement
  32. 32. AssociationAssociation = correlation of t wo variables if one variable changes the other changes as well (in the same or opposite direction) No association = independence NOT CAUSATION
  33. 33. AssociationAssociation = correlation of t wo variables if one variable changes the other changes as well (in the same or opposite direction) No association = independence NOT CAUSATION
  34. 34. Association Two variablesExamples1. Is serum GENTAMICIN level dependent on serum CREATININE?Variables: serum Gentamicin, serum Creatinine2. Is THROMBOLYTIC THERAPY related to the number of in- hospital DEATHS in stroke?Variables: thrombolytic therapy, number of deaths
  35. 35. Prediction/regression A Formula Knowing the value of one variable(s)Calculating the value of the other variable
  36. 36. Prediction/regression Usage: To describe the relationship Y = aX + b Y= aX2 + b Z = aX + bY + c Z = a X2 + bY3 + c Framingham CHD Risk Calculator
  37. 37. Prediction/regression the predicted and predictor (s) Examples:The TIMI risk score to predict odds of death in STEMI The APACHE III system to predict mortality in ICUThe IMPACT models to predict 6-month disability in severe traumatic brain injury
  38. 38. 2. Statistical errorWhat do my findings mean?How likely are my findings to be true?
  39. 39. Types of errorTwo types: Type I ( ) error Type II ( ) error
  40. 40. Hypothesis synthesisResearch question/objectiveAnd the answer to three questions: What are the variables? What are the groups/pairs? What is the statistical analysis?
  41. 41. Example 1• Objective: to assess the effect of oral glucocorticoid on serum IL-8 in COPD patients• Variable: serum IL-8• Groups/Pairs: prior and following glucocorticoid oral therapy• Statistical analysis: comparison• Alternative hypothesis: there is a difference bet ween serum IL-8 prior and after glucocorticoid therapy• Null hypothesis: there is no difference bet ween serum IL-8 prior and after glucocorticoid therapy
  42. 42. Example 2• Objective: to assess whether or not high levels of serum Neuron Specific Endolase (NSE) is associated with CT abnormality in head injury• Variable: serum NSE• Groups: patients with CT abnormality, patients with no CT abnormality• Statistical analysis: comparison• Alternative hypothesis: there is a difference bet ween serum NSE levels in head-injury patients with and without CT abnormality• Null hypothesis: there is no difference bet ween serum NSE levels in head-injury patients with and without CT abnormality
  43. 43. Example 3• Objective: to describe the relationship of ISS and ED length of stay• Variables: ISS and ED length of stay• Groups/pairs: NIL• Statistical analysis: regression• Alternate hypothesis: the coefficient is not zero.
  44. 44. Sample vs. PopulationPopulation = everyoneSample = in your study
  45. 45. Probability of error is the following question:How certain are we that what is observed in the sample can be inferred on the actual population?
  46. 46. Belonje et al. (Circulation. 2010;121:245-251.)Increased Erythropoietin level is associated with increased mortality in 605 heart failure patients ( p < 0.05).Question: how true is this in the population of all heart failure patients?
  47. 47. Bloom et al. (Aliment Pharmacol Ther. 2004 Apr 15;19(8):871-8.)No difference in colitis activity of 48 ulcerative colitis patients who receive Tinzaparin with 52 patients who receive placebo (p = 0.84)Question: How true is this in the population of all ulcerative colitis patients?
  48. 48. Type I error orDefinition:When the null hypothesis is rejected in the sample but is true in the populationRejecting null hypothesis, when it is trueFalse positive result Sample Population difference no difference association no association
  49. 49. Type II error orDefinition:When the null hypothesis is true in the sample but is false in the populationAccepting null hypothesis, when it is falseFalse negative result Sample Population no difference difference no association association
  50. 50. Population Sample + - outcome + c areject null type 1 error - b daccept null type 2 error
  51. 51. Belonje et al. (Circulation. 2010;121:245-251.)Increased Erythropoietin level is associated with increased mortality in 605 heart failure patients ( p < 0.05).Null hypothesis: no association bet ween Erythropoietin and mortalityResult: reject null hypothesis - positive finding
  52. 52. RealityTest outcome + - + = 0.04 -
  53. 53. Belonje et al. (Circulation. 2010;121:245-251.) p < 0.05 Probability of type I error < 0.05 Probability of no association in the population <0.05Probability of no association bet ween increased erythropoietin and mortality in all heart failure patients < 0.05
  54. 54. Bloom et al. (Aliment Pharmacol Ther. 2004 Apr 15;19(8):871-8.)No difference in colitis activity of 48 ulcerative colitis patients who receive tinzaparin with 52 patients who receive placebo (p = 0.84)• Null hypothesis: no effect for tinzaparin Probability
of
• Result: true null hypothesis Type
II
error
?
  55. 55. RealityTest outcome + - + = 0.84 - =?
  56. 56. Bloom et al. (Aliment Pharmacol Ther. 2004 Apr 15;19(8):871-8.)Power calculation: 42 subjects in each group(treatment and placebo)Sample size: 48 patients in treatment group 52 patients in placebo group Large enough sample
  57. 57. Bloom et al. (Aliment Pharmacol Ther. 2004 Apr 15;19(8):871-8.) Low probability of type II error High probability of true null hypothesis in the populationHigh probability of no effect for tinzaparin in all ulcerative colitis patients
  58. 58. RealityFaecal Occult Blood Test + - + 20 180 200 - 10 1820 1830 30 2000 2030 Sensitivity = 1 - beta = 1 - (10/30) = 0.66 Probability you’ll detect a real cancer
  59. 59. RealityFaecal Occult Blood Test + - + 20 180 200 - 10 1820 1830 30 2000 2030 Specificity = 1 - alpha = 1 - (180/2000) = 0.91 Probability you’ll reassure a healthy person
  60. 60. RealityFaecal Occult Blood Test + - + 20 180 200 - 10 1820 1830 30 2000 2030 Positive predictive value = 20/200 = 0.1 Probability a positive result means cancer
  61. 61. RealityFaecal Occult Blood Test + - + 20 180 200 - 10 1820 1830 30 2000 2030 Negative predictive value = 1820/1830 = 0.995 Probability a negative result means all clear

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