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I want to develop a prognostic model from outcome data of patients treated in a randomized controlled trial where patients received radiotherapy in one arm and radiotherapy and concurrent chemotherapy in the other arm. The objective of the model is to develop a prognostic model whose score can then be used to inform patients about the benefit that can be obtained from chemoradiation. I have two ways to develop the model :

  1. Develop the model in the patients treated with radiation only and validate it in the patients receiving concurrent chemotherapy. The prognostic model should exhibit discrimination in the survival outcomes even in the cohort treated with concurrent chemotherapy. However in this method, the number of events per factor in the model is approximately 10 - 12. I can use a penalized model for this purpose and have used the hdnom package for this.

  2. The alternative method is to split the whole dataset randomly into two parts including patients in both arms so that my sample size is better and then use the model to predict outcomes. However in this method, I am unsure as to how to model the effect of treatment as for the patients with a particularly poor prognosis concurrent chemotherapy results in a significant improvement in outcomes.

My question is which of these methods is better.

One important point is that concurrent chemotherapy is not better as compared to radiation alone when the arms are compared to each other and it is only a particularly poor risk subgroup that benefit of concurrent chemotherapy becomes clinically meaningful.

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It will create bias or inefficiency not to use the entire dataset. Treatment must be in the statistical model, and for the ultimate purpose you describe set treatment to control to obtain predictions of outcomes for standard therapy. You can set treatment to each of the two values and subtract predicted risks or life expectancies to get estimates of absolute treatment benefit for individual patients.

Don't think of "poor risk groups". Risk is on a continuum.

Don't use split sample methods for validation of the prognostic model; use rigorous internal validation based on the optimism bootstrap.

Detailed examples are in Section 13.6 of Biostatistics for Biomedical Research available here.

When estimating absolute treatment benefit be clear that the estimates come from a single model; that model is evaluated at observed covariate values for all subjects, and with treatment set to a constant for all subjects, then the process is repeated with only the treatment changing to another constant. After suitable transformation of $X\hat{\beta}$, differences are formed and analyzed. For a linear model the estimated treatment benefit, when treatment doesn't interact with anything, comes from $\hat{\beta}_{treatment}$ without going to this trouble.

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  • $\begingroup$ Thanks Dr Harrell, had to take time to go through your course notes as well as the textbook to understand this. Just to make sure I have understood this: 1. Model 1 will have chemoradiation set as the "control" arm and 2. Model 2 will have radiation set as the "control" arm. We will obtain the linear predictors and predict outcomes at a defined time point for each patient from this ? The difference would be used to obtain the treatment benefit? $\endgroup$ – Santam Jul 19 '16 at 3:43
  • $\begingroup$ I expanded the answer $\endgroup$ – Frank Harrell Jul 19 '16 at 11:38

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