IN THE late 1800s a New York doctor noticed that getting an infection after surgery helped some cancer patients. So he began to treat cancer using infections and had a little success. But many doctors were sceptical of his work, and other treatments such as radiation therapy and chemotherapy eventually took off. Today, however, the pharmaceutical industry understands how his treatments would have worked and has placed a sizeable bet that immuno-oncology—the treatment of cancer using the body’s immune system—will yield breakthrough drugs.

Earlier this month one of a promising new class of immuno-oncology drugs was approved for use in America by the Food and Drug Administration (FDA). Developed by Merck, pembrolizumab will be used to treat advanced melanoma, a skin cancer. Another American firm, Bristol-Myers Squibb, hopes to gain FDA approval soon for its melanoma treatment, nivolumab, which is already in use in Japan.

Cancer cells have defences that stop the immune system from attacking them, but pembrolizumab and nivolumab are among an emerging category of drugs called “checkpoint inhibitors”, which overcome these defences by interacting with proteins on the surface of either cancer cells or the immune system’s T-cells.

Four drugmakers in particular—AstraZeneca, Roche, Merck and Bristol-Myers Squibb—are chasing new immuno-oncology medicines. Evidence has grown that some checkpoint inhibitors may be effective in treating a wider range of malignancies than was first thought. Two years ago Bristol-Myers reported that nivolumab shrank tumours in 28% of melanoma patients, 27% of people with kidney cancer and 18% of those with advanced lung cancer. This news fired the starting pistol on large numbers of costly clinical trials with tens of thousands of patients.

Analysts are finding it hard to value the potential market for these treatments. Citigroup, a bank, thinks they will generate sales of up to $35 billion a year within the next ten years. Leerink Swan, an investment bank, says $29 billion by 2025. Sanford C. Bernstein, an equity-research firm, thinks around $16 billion, by 2020. Decision Resources Group, which analyses the health-care industry, is more cautious, reckoning $9 billion by 2022.

There are good reasons for the uncertainty. This is not a simple, predictable condition, like high cholesterol or diabetes. No one yet knows how many different cancers each drug will work on. Some patients may only need a few doses, which makes it especially hard to predict the market.

Tim Anderson, an analyst at Bernstein, notes that developing cancer drugs always involves a lot of trial and error—even more so in treatments like these that represent a paradigm shift in how to attack the disease. Another complication is that some checkpoint inhibitors may, alone, work on perhaps 20% of patients, but when combined with another could be far more successful.

Indeed, the industry is now in a frenzy of partnering, with companies speed-dating their rivals to form treatment alliances. For example, Pfizer, whose drug is called crizotinib, is collaborating on a trial with Merck and pembrolizumab to treat one form of lung cancer. Other collaborations will combine immuno-oncology with conventional cancer drugs, and even chemotherapy. With all these potential combinations of treatments, it is going to be quite a struggle for scientists, let alone stockmarket analysts, to keep up. But future cancer patients will have much to hope for, especially if lots of rival treatments emerge, since that should constrain their prices.