Chapter 14

Estimation with external information

14.1.10 Improving calibration with the adaptation method

To improve the calibration of the predictions resulting from applying the adaptation method, we considered two approaches.

  1. First, we shrunk the multivariable regression coefficients as estimated in the individual patient data. This approach was discarded since it led to better calibration (slope closer to 1), but a decrease in discriminative ability.
  2. The second approach was motivated by the observation that the miscalibration of the adapted estimates was approximately halfway that of shrunk estimates and the standard ML estimates. The proposed formula is
    βm | I+L = (1+shrinkage factor)/2 * [βu | L + (βm | I – βu | I )],
    where the shrinkage factor is the uniform shrinkage factor, either estimated with a heuristic formula, or by bootstrapping (see Chapter 13).

Evaluations of this correction with method 1 (c set to 1) or 2 (copt estimated by bootstrapping) showed an improvement in calibration. Discriminative ability was identical to that without shrinkage, since the shrinkage did not affect the ordering of predictions.

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