Inferring Heterogeneous Treatment Effects

People are different.  Different people have different cancers and those cancers require different treatments.  While most oncologists and cancer researchers understand this, it does not stop them from insisting that we must rely on statistical techniques that are not able to measure the effect of these differences on treatment outcomes.

Standard statistical analysis of randomized control trials provides unbiased estimates of the average treatment effect.  Standard statistical analysis of randomized control trials provides no information about the variation in the treatment effect across the patient population.  

To observe variation in treatment effect we would have to observe each patient's outcome with both the treatment that they received and the treatment that they did not receive.  Economists call this the "counter-factual" problem.  The treatment the patient did not receive is counter to the fact.  If in some imaginary world we were able to observe both the factual outcome and the counter-factual outcome then we would look at the difference between them and measure the distribution of the differences.  We would be able to measure the distribution of the treatment effect.  As we live in the real world we do not directly observe the distribution of the treatment effect.

While we cannot directly observe the variation in the treatment effect, we may be able to infer it.

The idea is that the heterogeneity in the treatment effect is being determined by some characteristic of the patient that is unobserved by the statistician.  Further, patients can be categorized into latent or hidden classes according to this unobserved characteristic.  These hidden classes can be inferred from observing certain characteristics of the patients that we know to be associated with the hidden classes.  It has been shown that if we observe a number patient characteristics that are all associated with the hidden classes then we may be able to uncover the hidden classes.  

Analysis based on these ideas have been successfully used in econometrics, psychometrics, biostatistics and computer science.

Here is my foray into the use of a technique called non-negative matrix factorization.  I use the technique to analyze heterogeneous treatment effects in adjuvant therapy for colon cancer.