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VirSci Corporation, PO Box 760, Newtown, PA 18940 (215) 504- 4164 • (215) 504-5739 (fax) www.virsci.com • www.pharmamarketingnews.com We asked members of the PHARMA-MKTING online discussion forum to solve the following clinical trial “brain teaser”: Sometimes, not all the critical data from a trial are available and you need to do some math to calculate risk. Here’s an example: • There were 2,643 people in a study comparing naproxen to Celebrex. 702 took naproxen, 1057 • There were a total of 70 cardiovascular events among all the study participants. • The proportion of people having an event was 50% higher in the naproxen group compared to • There was no increased risk for people taking Celebrex compared to placebo. You can assume that the Celebrex risk was the same as the placebo risk. Using the above information, please answer the following questions. 1. Calculate the likely magnitude of the naproxen risk, i.e., what percent of people taking naproxen experienced a cardiovascular event compared to people taking placebo? A: Naproxen % Risk of CV event? B. Placebo % Risk of CV event? 2. What would these numbers be if no (0) people taking Celebrex in this trial experienced a A: Naproxen % Risk of CV event? B. Placebo % Risk of CV event? See the table below, which shows responses (each row represents the answers from a single respondent). Only 1 respondent got it right. See the next page for the math and correct answers. Q1A Q1B Q2A Q2B
0.0% 0.0% 0.0% 0.0% 0.3% 0.1% 0.3% 0.1% 1.7% 1.1% 6.5% 2.1% 2.0% 2.0% 2.0% 2.0% 3.0% 2.0% 5.0% 3.5% 3.7% 2.4% 3.7% 4.1% 3.7% 2.5% 5.0% 3.3% 3.9% 2.6% 5.4% 3.6% 4.4% 2.2% 5.7% 2.8% 4.9% 2.5% 0.0% 0.0% 5.0% 2.0% 5.0% 2.0% 5.0% 1.6% 0.0% 0.0% 5.0% 3.0% 4.0% 2.0% 20.0% 10.0% 42.0% 28.0% 50.0% 0.0% 50.0% 0.0% VirSci Corporation, PO Box 760, Newtown, PA 18940 (215) 504- 4164 • (215) 504-5739 (fax) www.virsci.com • www.pharmamarketingnews.com
The chart on the right—taken from the INPUT 1: There were a total of 2,463 people in the study.
naproxen
celebrex
for calculating the number of people experiencing a CV event in each arm of the study: Let X=number of people taking naproxen, INPUT 2: There were a total of 70 events in the 3 groups.
in naproxen group
in placebo group
in celebrex group
26 (X) people taking naproxen experienced a CV event; this represents 3.7% of the 704 people in the study taking naproxen. This is the correct answer for Q1A.
INPUT 3: The proportion of people having an “event” was 50% higher in the naproxen group
Y, which is the number of people taking placebo who experienced a CV event, is also 26. Since there were 1057 people in this group, the naproxen
percent experiencing a CV event is 26/1057 = 2.5%. This is the correct answer to Q1B. Note that 3.7% is 50% greater than 2.5%, which satisfies one of the initial conditions. Many respondents obviously did not check their math by confirming that their results satisfied this INPUT 4: There was no increased risk for people taking celecoxib compared to placebo.
For Q2, we assume no people taking Celebrex experienced a CV event. Therefore, Z=0 and celebrex
X+Y=70. X still equals 0.996Y to satisfy the 50% condition, which still applies. Therefore, substituting 0.996Y for X in the X+Y=70 equation gives us 1.996Y=70 and Y=70/1.996=35, which represents 5.0% of the people taking naproxen (35/704). Rounding off, X also equals 35, which represents 3.3% of the people taking placebo.
CALCULATION: Substituting into original equation and solving for Y
The correct answers, therefore, are as follows: Q1A: 3.7%
Q1B: 2.5%
Q2A: 5.0%
Q2B: 3.3%
We round the values as follows: X = 26 Y = 26 Z = 18

Source: http://pharma-mkting.com/surveys/CT-BrainTeaser.pdf