# My Life with the Geometric Series

I was off the Aimovig for a while because reasons, and now I’ve started back on it. My neurologist pointed out that most people find that it takes about three months to start working.

Did you know that when you pick up a new prescription in California that the pharmacist is required by law to ask if you have any questions? As an intellectually curious person, I always have questions! I am learning so much about pharmacokinetics!

When you take medicine, you are usually adding to the amount in your system linearly. You take one dose per fixed amount of time. Your body clears the medine from your body under an exponential model, removing half of it in a set amount of time.

THE CALCULATIONS ARE SO EASY WITH AIMOVIG BECAUSE YOU TAKE IT ONCE A MONTH AND THE HALFLIFE IS ONE MONTH.

Let’s say that you take a dose *d* of Aimovig. A month later, this initial dose has
decayed to \(\frac{d}{2}\), and you take another dose, bringing you to
\(d + \frac{d}{2}\). So we have a geometric series, and at the beginning of month *n*,
you’ll have \(\sum_{i=1}^{n} \left( \frac{1}{2} \right)^{n-1} d \) Aimovig in your
system.

It also means that at steady state that you will have *2d* Aimovig in your system.

At month 3, you’re already up to almost 90% of steady state.

Clearly I know nothing about how drug companies structure their studies, but if I were working for Amgen/Novartis, I would have structured the clinical trials a bit differently from how they did it. In the trials, one group of patients took a dose of 70 mg/ml once a month, and another group of patients took a dose of 140 mg/ml once a month. Both dosages are on the market. The 70 mg/ml is the standard dose and the one that my insurance company is willing to chip in towards. (I have a $300 copay.)

The thing about spendy drugs is that the insurance company tends to only want to pay for the drug if your situation matches exactly with that of the subjects in the trial. If the patients in the trial all had at least 15 headache days a month and you are only having 12 headache days a month, then your insurance company won’t pay for it. (And by “you” in this instance I mean “me.”) (Thanks, Allergan.)

The other thing about spendy drugs is that I have to make a lot of phone calls in order to take this medication. It is kind of inconvenient. And my insurance company says that I can’t get it at Walgreens (my usual pharmacy); I have to get it at CVS. Also, in order to pay less than $300 a month, I need to join “the program” that the drug company has, and I need to keep on top of when that needs to be renewed. So, yeah, inconvenient and potentially expensive. Also you need to stab yourself with the medicine. Not the sort of drug that you’ll just keep taking if it is not working.

If the study had instead had the subjects take the 140 mg/ml dose the first month and then 70 mg/ml thereafter, then they would have been at steady state from the beginning. Patients would have been at steady state from day one (and would have a better chance of seeing positive effects sooner). And everyone would need to buy TWO injectors the first month, which means more units sold.

But I am just a ~~mathematician~~ data scientist and not a drug company expert. So there
is probably a good reason why they did not go with the dosing schedule that could have
made them more money.