WASHINGTON — The federal Medicare program and private health insurers waste nearly $3 billion every year buying cancer medicines that are thrown out because many drug makers distribute the drugs only in vials that hold too much for most patients, a group of cancer researchers has found.

The expensive drugs are usually injected by nurses working in doctors’ offices and hospitals who carefully measure the amount needed for a particular patient and then, because of safety concerns, discard the rest.

If drug makers distributed vials containing smaller quantities, nurses could pick the right volume for a patient and minimize waste. Instead, many drug makers exclusively sell one-size-fits-all vials, ensuring that many smaller patients pay thousands of dollars for medicine they are never given, according to researchers at Memorial Sloan Kettering Cancer Center, who published a study on Tuesday in BMJ, formerly known as the British Medical Journal.

Some of these medicines are distributed in smaller vial sizes in Europe, where governments play a more active role than the United States does in drug pricing and distribution.