In the study published in the journal Science, researchers treated the lab-grown 'mini tumours' with a range of drugs.
They then looked to see how this compared to how successful treatment was in those patients.
The approach found a drug that had a chance of shrinking a patient's tumour in almost nine in 10 cases.
Drugs that did not work in patients also had no effect on the mini tumours. This suggests they could help predict when drugs would not work, researchers said.
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The results of the study did not change how patients were treated. However, the approach could be used in the future to help choose treatment.
According to Nicola Valeri, who led the study, the technique needed to be tested in large clinical trials, but that it "has the potential to help deliver truly personalised treatment."
Mini tumours, also called organoids, are tiny balls of cancer cells grown in the lab.
Researchers believe that growing the cancer cells in this way can more closely mirror how they behave inside the body.
They grew mini tumours from biopsies taken from 71 patients with advanced bowel, stomach or bile duct cancer that had spread to other parts of the body.
The researchers tested 55 cancer drugs on the mini tumours, allowing them to compare the results to how each patient's cancer responded to the treatment they were given.
The study focused on stomach and bowel cancer, but Valeri said that "the technique could be applied to a wide variety of cancer types".
Organoids have already been grown from a variety of different cancers, including liver, pancreatic and oesophageal.