# Stats

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```					Stats Facts

Mark Halloran
Diagnostic Stats
Disease   Disease   TOTALS
present   absent
Test         a         b         a+b
positive
Test         c        d         c+d
negative
TOTALS       a+c       b+d      a+b+c+d
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)
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
TB treatment RCT
Death from TB   total
Yes       No

Control group   14     38       52
(bed rest)

Experimental   4       51       55
Group
(streptomycin+
bed rest
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%)
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%
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
Number needed to harm (NNH)

 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
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
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
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
Formulae (23)
 Standard Deviation: σ2 = 1/n Σ(xi - μ)2
 Coefficient of Variation = (sd x 100) /
mean)
 Standard Error
Standard Deviation
Confidence Interval
 Single observation: 95% CI = mean ± 1.96sd
 Mean of new sample: 95% CI = mean ±
1.96se
Study Designs
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
Levels of Evidence

Ia: Systematic review / meta-analysis of RCTs
Ib: At least 1 RCT
IIa: At least one well-designed controlled study (not randomised)
IIb: At least one well-designed quasi-experimental study eg cohort
III: Well-designed non-experimental descriptive studies eg case-control
IV: Expert committee reports, opinions ± clinical experience of
respected authorities

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 views: 5 posted: 11/23/2011 language: English pages: 18
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