How to turn “Stats” into something useful: Diagnosis and Interventions

How to turn “Stats” into something useful 1: Diagnosis

Understanding diagnostic utility

If you have data for diagnostic utility studies, you can use a 2×2 contingency table to calculate the following information (this should have been reported anyway in the study, but often isn’t):


     Gold standard
Clinical test +
+ aTP bFP




Sensitivity (“TP rate”) = a/(a+c)

Specificity (“TN rate”)= d/(b+d)

Likelihood ratio + = sensitivity/(1-specificity)

Likelihood ratio – = (1-sensitivity)/specificity

You can then use something like a nomogram to calculat post-test probability. You will need to have an estimate of pre-test probability. Ideally, this will be the known prevalence of the condition

Or, get yourself on app on your ‘phone like MedCalc3000

How to turn “Stats” into something useful 2: Interventions  

If a trial or systematic review is reporting DICHOTOMOUS outcomes, we can bring the “research” findings a little bit closer to clinical decision making… “Do you know HOW MANY subjects responded, and HOW they responded? e.g.  how many people in the TREATMENT group got better/worse, and the same for the control/placebo group?”

NO: then you can’t clinically apply findings. Doh.


YES: then go and do some evidence based decision making! Yipee.




Wow, how do we do that? Like this: 1)   Use a 2×2 table (again)

+ve -ve
Control/Placebo group  a  b
Rx group  c  d




2)   And some simple formulae…

CONTROL EVENT RATE (CER) number of Control Group people with +ve outcome divided by total number of Control Group people. In other words: i.e.: a/(a+b)

EXPERIMENTAL EVENT RATE (EER) = same as above for Rx Group c/(c+d) Now that we know the CER and EER, we can do loads of other useful things…

RELATIVE RISK, or RISK RATIO (RR): RR = EER/CER (a RR of 1 means there is no difference between groups; >1 means increased rate of outcome in Rx group, and <1 means less chance of outcome)



NUMBER NEEDED TO TREAT (NNT): NNT = 1/ARR Some other stats more USEFUL than “p-values”…



“What are the odds of getting this person better with this treatment?”


The greater above 1, the better.


This is a standardised, scale-free measure of the relative size of the effect of an intervention. It is particularly useful for quantifying effects measured on unfamiliar or arbitrary scales and for comparing the relative sizes of effects from different studies.

EFFECT SIZE = (mean score of group 1) – (mean score of group 2) / SD (of either group, or even pooled data)


EXAMPLE: A study into effects of manual therapy on neck pain measured a Rx group (n=23) and a Control group (n=21), and considered a “cut-off” point for improved ROM as being an increase in at least 20deg rotation (so results can be dichotomised). Mean Rx score = 28deg (SD 4) Mean Control score = 16deg (SD 4) Results were:


+ve -ve Total
Control/Placebo group a9 b12 a+b21
Rx group c18 d5 c+d23
Total a+c       27 b+d17 a+b+c+d44

CER a/(a+b): 0.43 or 43%

EER c/(c+d): 0.78 or 78%

RR = EER/CER: 1.83

ARR = CER – EER: -0.35 or 35%

RRR = (CER-EER)/CER: -0.83 or 83% (a minus figure, so this would be RR Increase)

NNT = 1/ARR: 2.86, so say 3.

EEO: c/d = 3.6 CEO: a/b = 0.75

OR: EOR/CEO = 4.8

EFFECT SIZE =  28– 16   = 3 4


The clinical  story then…

“So, if untreated, my patient would have a 43% chance of getting better anyway.  But if treated, his chance of improvement would be 78%.  He is 1.83 times more likely to improve if I treat him. The absolute benefit of being treated would be 35%.  The treatment would increase the chance of improvement by 83%. I would need to treat 3 people (in the period of time relevant to the study) to achieve 1 positive outcome. The odds of him getting better with no treatment are 0.75, whereas if I treat him, the odds are much better, at 3.6. the odds are 3.6:0.75 (i.e. 4.8) of him improving with treatment. “

However… From a clinical reasoning perspective, we still need to understand what “43%, 78%, 35%, etc etc” MEANS… and that’s where the real fun starts:-)

Here’s a little video for y’all:


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