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

1. Medical Statistics
Masterclass
Fastbleep Academic Masterclass #4
University Place
31 May 2011

2. About us
James Giles Richard Salisbury
MB PhD Student F1 & MRes Graduate
PAL & Fastbleep Director Cochrane Author
Love stats, hated contextless Bioscience geek

4. 1. Use of statistics
2. Statistical errors
3. Common statistical tests

5. 1. Use of statistics
What is your question?
What do you want to do?

6. Descriptive statistics
• Averages - mean/median/mode
• Frequency
• Range (measures of spread)
• Box-and-whisker plot
• Bar chart
• Pie chart

7. Scales of measurement
Nominal
Ordinal
Numerical

8. Scales of measurement
Nominal Name: red, blue, green
Ordinal
Numerical

9. Scales of measurement
Nominal Name: red, blue, green
Ordinal Order: tumour stage
Numerical

10. Scales of measurement
Nominal Name: red, blue, green
Ordinal Order: tumour stage
Numerical Continuous: height
Discrete: number of teeth

11. Nominal Variable
Description: Frequency/proportion
Illustration: Bar chart/pie chart

12. Averages
Mean
Median - middle number
Mode - most frequent

13. Distributions

14. Distributions

15. Distributions

16. Distributions

17. Distributions

18. Averages
Mean - numerical & unskewed
Median - ordinal & skewed
Mode - nominal & bimodal

19. Measures of spread
Standard deviation (sd)
Standard error of the mean (SEM)

20. Measures of spread
Standard deviation (sd)
mean distance from the mean

21. Measures of spread
Standard deviation (sd)
Standard error of the mean (SEM)

22. Measures of spread
Standard error (SEM)
estimate of spread of your sample mean
from a true population mean
SEM = sd/ n 20
Neutrophil Count / 105/ml
15
10
5
0
A ac C ad B bc D bd

23. feltron.com

25. Analytical statistics
Compare - difference, higher/lower
Relate - correlation, regression,
agreement

26. Comparisons
1) One variable against a constant
2) One variable across 2 dependant groups
3) One variable across 2 independent groups
4) One variable across pairs

27. Comparsion
one variable against a constant
Is Hb level in heavy smokers higher than the
average of 14?
Variable: Hb level
Constant: 14

28. Groups
2 types of groups
• Dependent: one group a subset of the other
• Independent: different sets

29. 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 PTH
Groups: 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 rate
Groups: patients with neck of femur fracture and co morbidity,
all patients with neck of femur fracture

30. Comparison
Examples: One variable across 2
independent(non-overlaping) groups
Is Trop T higher in patients with STE-ACS than NSTE-ACS?
Variable: Trop T
Groups: STE-ACS and NSTE-ACS
Is success rate to control variceal haemorrhage higher in
SCLEROTHERAPY than BALLOON TAMPONADE?
Variable: success rate
Groups: sclerotherapy and balloon tamponade

31. Comparison
Examples (pairs):
Pairs = repeated measurements:
t wo measurements of a variable on one patient at
different time points

32. Comparison
Is the PEF higher after Salbutamol nebuliser in asthma
patients?
Variable: PEF
Pairs: prior and after nebuliser
Is the second-day serum lactate level higher than the
third-day lactate level following antibiotic therapy in
sepsis?
Variable: lactate level
Pairs: second and third day

33. Relation
Association
Prediction/regression
Agreement

34. Association
Association = 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

35. Association
Association = 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

36. Association
Two variables
Examples
1. Is serum GENTAMICIN level dependent on serum
CREATININE?
Variables: serum Gentamicin, serum Creatinine
2. Is THROMBOLYTIC THERAPY related to the number of in-
hospital DEATHS in stroke?
Variables: thrombolytic therapy, number of deaths

37. Prediction/regression
A Formula
Knowing the value of one variable(s)
Calculating the value of the other variable

38. 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

39. 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 ICU
The IMPACT models to predict 6-month disability in
severe traumatic brain injury

41. 2. Statistical error
What do my findings mean?
How likely are my findings to
be true?

42. Types of error
Two types:
Type I ( ) error
Type II ( ) error

43. Hypothesis synthesis
Research question/objective
And the answer to three questions:
What are the variables?
What are the groups/pairs?
What is the statistical analysis?

44. 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

45. 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

46. 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.

47. Sample vs. Population
Population = everyone
Sample = in your study

48. 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?

49. 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?

50. 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?

51. Type I error or
Definition:
When the null hypothesis is rejected in the
sample but is true in the population
Rejecting null hypothesis, when it is true
False positive result
Sample Population
difference no difference
association no association

52. Type II error or
Definition:
When the null hypothesis is true in the
sample but is false in the population
Accepting null hypothesis, when it is false
False negative result
Sample Population
no difference difference
no association association

53. Population
Sample
+ -
outcome
+ c
a
reject null type 1 error
- b
d
accept null type 2 error

54. 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 mortality
Result: reject null hypothesis - positive finding

55. Reality
Test outcome + -
+ = 0.04
-

56. 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
<0.05
Probability of no association bet ween increased
erythropoietin and mortality in all heart failure
patients < 0.05

61. 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 ?

62. Reality
Test outcome + -
+ = 0.84
- =?

63. 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

64. 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 population
High probability of no effect for tinzaparin
in all ulcerative colitis patients

66. Reality
Faecal 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

67. Reality
Faecal 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

68. Reality
Faecal 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

69. Reality
Faecal 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