Results from EMILIA Trial for T-DM1. |

My previous post suggests that it is not possible to learn anything about the survival benefit of new treatments for cancer from randomized clinic trials. This is not true.

It is possible to learn some

It is possible to learn some

*limited*information about relative survival benefits from randomized control trials.
It is possible to "bound" the proportion of patients who would live longer on the new treatment from the data. We can use a mathematical relationship known as the "Frechet-Hoeffding bounds''.

These bounds imply that

For example, in the figure we see that at the 12-month mark, the survival difference is 6.8 percentage points, while at the 24-month mark the difference is 12.9 percentage points. From this we know that at least 12.9% of the population sampled would live longer on T-DM1 versus capecitabine and lapatinib.

From the EMILIA trail we learn that between 12.9% and 100% of the population of metastatic breast cancer patients sampled would live longer on T-DM1 versus the alternative. Another way to say this, is that we know between 0% and 77.1% of patients would live longer on capecitabine and lapatinib than on T-DM1.

Note that bounds may be even wider than suggested above. Firstly, our estimate of the bounds may be wider due to sampling variation (which I have not calculated). Second, the Frechet-Hoeffding bounds result is reliant on the fact that there is no biases in the trial data. Information reported on ClinicalTrials.gov suggests that 72 patients left the trial of their own decision, 28 from the T-DM1 arm and 48 from the X+L arm. This unbalanced attrition may cause the results at the 2-year mark to be biased. I discuss the effect of this bias in this unpublished working paper.

*minimum*proportion of the population sampled by the randomized control trial who would benefit from the new treatment is equal to the*maximum*difference in the survival curves at each point in time.For example, in the figure we see that at the 12-month mark, the survival difference is 6.8 percentage points, while at the 24-month mark the difference is 12.9 percentage points. From this we know that at least 12.9% of the population sampled would live longer on T-DM1 versus capecitabine and lapatinib.

From the EMILIA trail we learn that between 12.9% and 100% of the population of metastatic breast cancer patients sampled would live longer on T-DM1 versus the alternative. Another way to say this, is that we know between 0% and 77.1% of patients would live longer on capecitabine and lapatinib than on T-DM1.

Note that bounds may be even wider than suggested above. Firstly, our estimate of the bounds may be wider due to sampling variation (which I have not calculated). Second, the Frechet-Hoeffding bounds result is reliant on the fact that there is no biases in the trial data. Information reported on ClinicalTrials.gov suggests that 72 patients left the trial of their own decision, 28 from the T-DM1 arm and 48 from the X+L arm. This unbalanced attrition may cause the results at the 2-year mark to be biased. I discuss the effect of this bias in this unpublished working paper.

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