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Step 3: Critically Appraising the Evidence: Statistics for Therapy
Clinical Statistics Calculator (Excel) Statistics for: Therapy Control Event Rate (CER) & Experimental Event Rate (EER) Number Needed to Treat (NNT) Absolute Risk Reduction (ARR) Relative Risk (RR) Odds Odds Ratio (OR) Practice Exercises Table of Contents
If available, find the best evidence in secondary sources where analysis has already occurred. If not pre-assessed, use critical appraisal worksheets to help you through the process. Making It Easier
Importance of Critically Appraising the Evidence • Understanding the Limitations of the Author’s Analyses and Interpretations of the Data • Assessing Internal Validity • Assessing External Validity • Identifying Potential Confounding Variables • Simpson’s Paradox
Critical Appraisal Basics • View movie as: • QuickTime (.mov) • Flash (.swf) • Double-click on video for full-screen mode.
Control Event Rate (CER) and Experimental Event Rate (EER) • Experimental Event Rate (EER) • The proportion of patients (in the intervention) who experienced the target disorder with the treatment • Control Event Rate (CER) • The proportion of patients (in the comparison group) who experienced the target disorder without the treatment
Calculating CER and EER • Experimental Event Rate (EER) • a/(a+b) • Control Event Rate (CER) • c/(c+d)
Number Needed to Treat (NNT) • The estimated number of patients needed to be treated for every patient benefiting from the treatment beyond baseline/control expectation • So small numbers indicate greater effectiveness
Calculating NNT: Starting Off • Essentially we want to know how many patients we must treat before we can expect one successful treatment beyond what we would normally expect without treatment. • First consider, what we already know: • We know both the proportions of how many patients still had the target disorder that were treated (EER) and that were not treated (CER).
Calculating NNT: Establish Baseline • With these two proportions we can find the proportion of successful treatment beyond the baseline expectation (control). • From there, we can determine how many we would need to treat to expect one success. • Now let’s start from the baseline: Find the proportion of untreated patients with the target disorder (CER).
Calculating NNT: Calculating Absolute Risk Reduction (ARR) • Now we want to know how much better the treatment did than no treatment at all. So we find the proportion of the treated patients that had the target disorder (EER) • Now we find their difference (CER-EER), which we call the Absolute Risk Reduction (ARR).
Calculating NNT: ARR Example • That is if 10% of the untreated patients had the disease and 3% of the treated patients had the disease, then the treatment helped 7% (=10%-3%) of the treated patients (which if left without treatment would still likely have the disease). So 0.07 would be the ARR. • Hence ARR is the probability that treatment will reduce the risk of a given patient beyond baseline expectation.
Calculating NNT: Using the ARR • Now we know that the treatment reduced the risk of a proportion of patients, which we call Absolute Risk Reduction and that ARR = CER – EER. • In other words, ARR is the number of successful treatments beyond baseline expectation divided by the number of treated patients. • Now we’re close. NNT is the number of treated patients per successful treatments beyond baseline expectation. Can you see the relationship yet?
Calculating NNT: Another way of looking at it • In this situation, we should look for a way to invert our number. • We know that we can divide any number by 1 without altering it. So ARR = ARR/1. So think of ARR as a fraction. • Now think of the number of successful treatments beyond baseline expectation as the unit on top of the fraction (i.e. ARR) and the number of treated patients as the unit on the bottom.
Calculating NNT: Final Touches • Now if we take the inverse (i.e. flip our fraction over) and calculate 1/ARR, we get a number where the units are flipped. Thereby, this number has the number of treated patients as the unit on top of the fraction (i.e. ARR) and the number of successful treatments beyond baseline expectation as the unit on the bottom. This is exactly how we defined NNT.
Calculating NNT: The Formula • NNT = 1/ARR = 1/|CER – EER| • Often rounded up to nearest whole number
NNT Question • View movie as: • QuickTime (.mov) • Flash (.swf) • Double-click on video for full-screen mode.
Answer to NNT Question • View movie as: • QuickTime (.mov) • Flash (.swf) • Double-click on video for full-screen mode.
Relative Risk (RR) • The number of treated/exposed patients with the target outcome for every patients in the control with the target outcome • (Also used in therapy articles) • RR = EER / CER = (a/(a+b)) / (c/(c+d))
Relative Risk Video • View movie as: • QuickTime (.mov) • Flash (.swf) • Double-click on video for full-screen mode.
Odds • The number of times the target outcome occurred in patients exposed to the risk for each time the target outcome occurred in patients not exposed to the risk.
Odds Ratio (OR) • OR = (a/b) / (c/d) • = a*d / b*c • A measure of association • When large, there is greater association
Try it on your own. • Critical Appraisal Practice Exercises • From CEBM
Links to Other Websitesand Hands-On Activities • EBM Glossary • From CEBM • Critical Appraisal Practice Exercises • From CEBM