Spot the Error

Would you trust this doctor?

I’m researching drugs that are being developed to treat non-muscle invasive bladder cancer (NMIBC). One company developing a drug for NMIBC is GC Oncology.

The old tuberculosis vaccine, Bacillus Calmette-Guérin (BCG), containing a weakened version of tuberculosis bacterium, is often used to treat high-risk NMIBC cases. Unfortunately, BCG is hard to make and there have been persistent shortages. Merck & Co. is the only company making a BCG product that’s approved for use in the United States.

If bladder cancer isn’t treated effectively patients face the prospect of a radical cystectomy (surgical removal of the bladder).

CG Oncology made a short video of a physician, Ashish M. Kamat, from the University of Texas MD Anderson Cancer Center, describing how this shortage has negatively affected bladder cancer patients.

He made one big mistake and probably an additional small mistake.

The likely small mistake

Kamat said that in areas with BCG shortages the incidence of radical cystectomies went up almost 300%. I’m virtually certain he really meant to say it went up almost 200%.

Consider this mathematical example. Perhaps the rate of radical cystectomies in regions with BCG was 5% (one out of every 20 patients got one). If the rate in regions without BCG was 15%, we would say that the rate was three times, or 300% of the rate with BCG. This reflects an increase of 200% over the BCG rate and a rate three times as high (300%) as the BCG rate.

• The overall ratio is 300% = 15% divided by 5%. We would say the rate is three times as high.

• The increase, or step, is 200% = (15% minus 5%) divided by 5%. We would say the rate increased 200%.

This is a subtle mathematical mistake that is commonly made. I sometimes make this mistake when I want to describe the mathematical relationship (the 300% in the first equation) and I want to emphasize that it is an increase. But as soon as I add the word “increase” to my statement I’m looking at the step from the BCG rate to the non-BCG rate and I must use the second equation.

The big mistake

Kamat went on to say that these results meant that patients where BCG was limited were undergoing radical cystectomies 300 times more often than patients in regions where BCG was available. He not only said it orally but it was spelled out on a slide.

This mistake is a whopper. He’s taking the 300% and saying it is 300 times, when it really means three times! Three times as many patients were getting radical cystectomies, not 300 times as many. Three hundred times as many would equal 30,000%.

If the BCG rate was 5%, 300 times as many patients would mean that 1,500% of all patients would get a radical cystectomy, which is clearly impossible. At most, 100% of patients could get one.

Would you trust a doctor who makes such an egregious mistake?

[Note: I haven’t been able to find any study with the results Kamat described and some other studies seem to contradict his conclusion. So he might be wrong on the fundamental facts.]