Here’s another post in Our Milestones series – looking at some of the most significant discoveries made by Cancer Research UK-funded scientists over the years. This time, we take a look at the history of the Calvert formula – a mathematical equation used by doctors all over the world to calculate the required dose of the life-saving cancer drug carboplatin.
One way to gain immortality – at least as a scientist – is to have something named after you.
That’s exactly the honour bestowed on Cancer Research UK’s drug discovery expert Professor Hilary Calvert, Director of Cancer Drug Discovery and Development at the UCL Cancer Institute.
Professor Calvert is the chief architect of the “Calvert formula”, a simple calculation that allows doctors to calculate the correct dose of carboplatin (also known as Paraplatin) – a drug mainly used to treat lung and ovarian cancers, as well as several others.
Professor Calvert and his colleagues developed the formula in 1989, and the impact of this humble equation has been huge. As we previously wrote about, ovarian cancer survival rates have almost doubled over the part thirty years, thanks in part to the use of carboplatin to treat the disease.
But it’s not only the sums that have made a difference – Professor Calvert and his Cancer Research UK-funded colleagues are behind the development of carboplatin itself – a drug that has been used to treat thousands upon thousands of patients in the UK, and many more around the world.
In this post, we’ll look at the birth of carboplatin and the origins of the Calvert formula.
Background: From cisplatin to carboplatin
At the start of the 1980s, the new kid on the chemotherapy block was a drug called cisplatin – a small molecule containing a single atom of the metal platinum. In the early 1970s, our researchers were among the first to show that the cisplatin had the potential to treat cancer.
Over subsequent years, the drug has produced impressive results in patients with testicular, ovarian and head and neck cancers, as well as some lymphomas. It continues to be a valuable part of treatment for some cancer today, but it also causes unpleasant side effects including sickness, kidney damage and an increased risk of infections.
The hunt was on for platinum-based cancer drugs that were just as effective as cisplatin, but caused fewer side effects. Leading the way were our scientists: Professor Tom Connors – one of the first people to look at the anti-cancer properties of cisplatin – Hilary Calvert, Ken Harrap and their colleagues at The Institute of Cancer Research in Sutton, working together with the pharmaceutical company Johnson Matthey.
Their approach was to take the basic chemical structure of cisplatin, with platinum at its heart, and start swapping its atoms around – a bit like a molecular version of Mr Potato Head.
In total, the scientists came up with around 300 new compounds, of which 40 showed some kind of anti-cancer activity in lab tests. Two of these, at that stage called JM8 and JM9, finally made it into early-stage clinical trials in 1981. The results were striking – JM8 (which subsequently became known as carboplatin) was just as effective as cisplatin, but significantly less toxic to patients. And it also beat JM9 (now known as iproplatin).
Further trials followed throughout the 80s, testing carboplatin against different cancer types and in larger groups of patients. It was finally licensed for use across the UK in 1986, and has gone on to become the ‘gold standard’ treatment for ovarian cancer, as well as being used to treat many other cancers. And the Calvert formula goes hand-in-hand with its clinical usefulness.
Doing the maths – the Calvert formula
Choosing the correct dose of a drug to give a particular patient is a bit of a dark art. Too low, and there’s a greater chance that the treatment won’t be effective – too high, and there’s a greater risk of causing serious side effects. This is particularly true of chemotherapy drugs, which, by their very nature, are pretty toxic.
Many things affect the size of dose of a drug an individual person needs, from their weight and height to the speed of their metabolism. While working on the early clinical trials of carboplatin, Calvert and the team worked out that a dose of 400 milligrams per square metre of body surface area was enough to treat the patient’s cancer while avoiding serious side effects. But they also noticed that some patients still had side effects, even though they were proportionally getting the same dose as other people.
Looking further into this, the scientists realised that people whose kidneys were slower at filtering their blood were more likely to have side effects, so they needed a lower dose of the drug. Medically speaking, this is known as the glomerular filtration rate (GFR) – how fast an individual’s kidneys can remove waste products from the blood and pass them out in their urine. Next, Professor Calvert’s team needed to work out the precise relationship between GFR and carboplatin dose.
In research published in 1989 in the Journal of Clinical Oncology, Professor Calvert and his team looked back over data that had been collected in previous trials of carboplatin in 18 patients, looking at the doses of the drug they had been given, their GFRs, and the changes in the levels of the drug in their bloodstream.
The researchers used this information to create a ‘dosage formula’, allowing them to calculate the dose of carboplatin needed to achieve a specific level of the drug in the blood – i.e. enough to treat the cancer without causing side effects , while taking into account how fast the patient’s kidneys were removing it.
Calvert and his team then tested their formula in a further 31 patients, to see how well it held up in ‘real life’. To do this, they measured GFR in the patients then gave them doses of carboplatin. Using the formula, the researchers were able to predict the level of carboplatin that they would expect to see in the patients, and compare these predictions to actual measurements of the drug in the blood.
Satisfyingly, the team found a good match between their predictions and observations, suggesting that the formula was holding up well. But there was still room for improvement. After a bit more number crunching, they came up with what is now known as the Calvert formula – a calculation that’s still used to this day to calculate the correct dose of carboplatin.
For any maths fans reading, here’s the formula in full:
Dose in milligrams = AUC x (A x GFR + B)
AUC is the “area under the curve” – a figure that reflects the concentration of drug in the body that doctors want to achieve; GFR is the glomerular filtration rate – the rate at which an individual patient’s kidneys work; A is the ratio of this glomerular filtration rate to how quickly the kidneys get rid of carboplatin; and B is the rate at which the body gets rid of carboplatin in other ways than through the kidneys.
What’s the impact?
Today carboplatin, together with the Calvert formula, is used to treat many thousands of cancer patients around the world. The drug has contributed to an impressive increase in survival from ovarian cancer, as we discussed previously on the blog, as well as helping to boost short-term survival from small cell lung cancer.
Clinical trials involving carboplatin are still going on today, testing it in combination with other drugs and in different cancer types. It is arguably one of our most powerful weapons against cancer, and its story far from over.
- Calvert AH et al (1989). Carboplatin dosage: prospective evaluation of a simple formula based on renal function. Journal of clinical oncology : official journal of the American Society of Clinical Oncology, 7 (11), 1748-56 PMID: 2681557