1. An Idiots Guide to Statistics Curriculum 3.6
Daisy de Ferranti
Stephanie de Giorgio
Lindo Van der Merwe

3. Overview Why bore you with Statistics Definitions
How to work through the stats questions

4. Why bore you with Statistics
AKT- Definitions, interpretation of terms, 2 by 2 table (and forest plot for statisticians!)

5. Present
Absent
Positive a b
Negative c d

6. Present
Absent
Positive
True positive
False positive
Negative
False negative
True negative

7. Definitions
Sensitivity: (True positive rate) How good is this test at picking up people who have the condition?
a/a+c

8. Specificity True negative rate
How good is this test at correctly excuding people without the condition
d/b+d

9. Positive Predictive value
Post test probability of a positive test
If a person tests positive, what is the probability that he has the condition
a/a+b

10. Negative predictive value
Post test probability of a negative test
If a person tests negative what is the probabilty that he does not have the condition
d/c+d

11. How to remember this!
SnNOUT – with high sensitivity a negative result rules OUT the diagnosis
SpPin – with high specificity, a positive result rules IN the diagnosis

12. An example Gastric cancer Blood result Present Absent Positive 20 30
Negative 5 45

13. Sensitivity
20/25 = 0.8
Specificity
45/75 = 0.6
PPV
20/50 = 0.4
NPV
45/50 = 0.9

14. Accuracy
What proportion of all tests have given the correct result (ie true positives and true negatives as a proportion of all the results)
a+d/a+b+c+d

15. Likelihood ratio of a positive test
How much more likely is positive test to be found in a person with, as opposed to without, the condition
Sensitivity/1-specificity

16. Interventions Dead Alive Total no Control 404 a 921 b 1324 a+b
Surgical
350 c
974 d
1325
c+d

17. Risk Chance of being dead in control group X
Chance of being dead in surgical group Y

18. Relative Risk
RR of death is the risk in surgical pts compared with controls.
y/x

19. Relative risk reduction
Amount by which the risk of death is reduced by surgery

20. Another practical example – treatment of candida
Improved
Not improved
Total no
Antifungal 80 20
100
Placebo 60 40

21. Risk in placebo group = 40/100=0.4=40%
Risk in treatment group = 20/100=0.2=20%
Absolute risk reduction (ARR) =
80/100 – 60/100 = 20%
Relative risk reduction =
Risk in placebo (40)– risk in treatment(20) = 0.5
Risk in placebo (40)

22. Glossary Index

23. Hierarchy of Evidence Systematic review & meta-analysis RCT
Cohort studies
Case-control studies
Cross-sectional surveys
Case reports

24. Types of Study Case control: Retrospective
Group of cases with condition & group of controls without are studied to determine relative frequency of particular exposures of interest in 2 groups
Concerned with aetiology of disease rather than Rx
Cohort:
Prospective
Two groups of people are selected on basis of differences in their exposure to particular agent & followed up to establish how many in each group develop a particular disease
Follow up period generally years
Concerned with aetiology of disease

25. Types of Study 1. Case reports:
Describes medical hx of single pt in form of story.
2. Cross-sectional surveys:
Population or sample of population examined to determine prevalence of certain condition

26. Types of Study
5. RCT
Participants in trial are randomly allocated to either one intervention (ie drug) or another (ie placebo)
Both groups followed up for specified time & analysed in terms of specific outcomes defined at onset (ie death, MI)
Often short follow up due to costs & pressure to produce timely evidence
6. Systematic Reviews & Meta-analysis
Systematic review: Summary of medical literature that uses explicit methods to perform a thorough search & critical appraisal of individual studies
Meta-analysis: A systematic review that uses quantitative methods to summarise results – pooling all information from number of different (but similar) studies

27. Statistics which describe Data
Mean
Median
Mode
Standard Deviation

28. Mean Sum of all values, divided by the number of values
Used in “normal distribution” – spread of data is fairly similar on each side of mid point

29. Median
It is the point which has half the values above & half below
Used to represent average when data not symmetrical - “skewed distribution”
Mean=median in symmetrical distribution but not in skew distribution
Mode
Most common set of events

30. Standard Deviation
Good news – not necessary to know how to calculate the SD!
Used for data which is “normally distributed”
SD indicates how much a set of values is spread around the mean
+/- 1 SD (range of one SD above & below the mean) includes 68.2% of the values
+/- 2 SD includes 95.4% of values
+/- 3 SD includes 99.7%

31. Statistics which test confidence
P value
Confidence interval

32. P value
Test of probability ie any observed difference having happened by chance
Used to determine whether a hypothesis is true
“Null hypothesis” – no difference between two groups/treatments
P value <0.05 “statistically significant” ie unlikely to have happened by chance, hence important
The lower the p value, the less likely the difference happened by chance & thus the higher the significance
Significant p rejects Null hypothesis

33. Confidence interval When is it used? What does it mean?
Typically when, instead of simply wanting mean value of sample, we want a range that is likely to contain the “true population value”
“True value” is mean value that we would get if we had data for the whole population
What does it mean?
CI gives the range in which the true value is likely to be (usually with level of 95% certainty)
Provides same information as p value, but more useful
Size of CI related to sample size of study – larger studies have narrower CI
If CI crosses 0 – Null hypothesis true

34. Forest Plot/”blobbogram”

35. Forest Plot
Allows readers to see information from individual studies that went into the meta-analysis at a glance
Results of component studies are shown as squares centred on point estimate of result of each study
Horizontal line runs through to show its CI
Diamond symbol represents the overall estimate from meta-analysis and its CI
Significance is achieved if the diamond is clear of the “line of no effect”

36. Interpretation i. Wide CI, crosses 0
ii. Does not cross 0, intervention works but weak evidence
iii. Narrow CI, crosses 0, intervention no benefit
iv. Narrow CI, intervention works
v. Intervention detrimental
vi. Meta-analysis: intervention works

37. Key definitions
Incidence: proportion of a defined group developing a disease within a stated period
Prevalence: proportion of a defined group having a disease at any one time
Single blinded: subjects did not know which treatment they were receiving
Double blinded: neither investigators nor subjects knew who was receiving which treatment
Unblinded: all participants were aware of who received which intervention
Power: ability of a study to minimise uncertainties that arise because of chance variation between samples - ie larger samples
Type II error: common – accept null when alternative is true
Type I error: less common – accept alternative when null is true

38. Enough of the theory – here’s the practical bit!!
What do we need to be able to do?
1. Interpret drug rep data
2. Explain risk/benefits to our patients
3. Understand evidenced based medicine

39. Survival analysis and risk reduction
Use of ramipril in preventing stroke: double blind randomised trial. BMJ 324:
To determine the effect of ramipril on secondary prevention of stroke.
267 hospitals in 19 countries
9297 patients with vascular disease or diabetes followed for 4.5 yrs (HOPE study)

40. Outcome: stroke, TIA and cognitive function measured
Outcome: stroke, TIA and cognitive function measured. Blood pressure recorded at entry to study, after 2 years and at end.
Results:
Reduction in BP modest
Relative risk of stroke reduced by 31% in ramipril group compared to placebo, relative risk of fatal stroke reduced by 61%

41. Summary of results Stroke No-stroke Total Ramipril 156 (Fatal 17) 4479
4635
Placebo
226
(Fatal 44)
4426
4652

42. Risk of stroke in ramipril group
156/4635= = 3.36%
Risk of stroke in placebo group
226/4652= = 4.48%
Relative risk reduction = (4.86 – 3.36)/4.86
= 0.31
= 31%

43. Absolute risk reduction (ARR)
Risk in placebo – risk in rampril
= 4.86 – 3.36 = 1.5%
NNT = = 100 = 67
ARR 1.5

44. For fatal stroke
Risk in ramipril group = 17/4635=
Risk in placebo group - 44/4652 =
RRR = = = 61%
0.0094

45. Rampril reduced risk of stroke in high risk patients by 31%, which seems good.
However, have to treat 67 people for 4 ½ years in order to benefit 1 patient by preventing 1 stroke

46. Odds ratios and CI
Systematic r/v of long term anticoagulation or antiplatelet treatment in pts with atrial fibrillation BMJ 322:
Objective - to examine benefits/risks of warfarin compared to aspirin/indomethacin
Methods - meta-analysis of RCT. Odds ratios (95% CI) calculated to estimate treatment effects

48. Results for one of the trials
Odds of vascular death in patients on warfarin
number of times an event happens = = 0.088
number of times it does not happen
Odds of vascular death in aspirin pts = = 0.080
Odds ratio = odds in warfarin pts = = 1.10
odds in aspirin pts
Odds ratio of >1 indicates that rate of vasc death increased in warfarin pts over those in aspirin pts.

49. If the confidence interval for the Odds Ratio containes 1 ie no difference, then the difference in results is NOT statistically significant
Seen by CI plot line crossing the line at 1.
Overall the study did not show any benefit of long term anticoagulation and an increased risk of bleeding

50. In summary Important to understand for career, not just for exam.
Try to understand basic concepts well as can then apply to most questions.