1.4.8 A Cox fit🔗ℹ

With #:family 'cox, the response is (surv time status). A Cox model has no intercept, so its coefficients are the predictors’ alone, and #:type 'response predicts the relative risk:

> (define survival-cv     (formula-cv (~ (surv time status) age dose marker) patients                 #:family 'cox))

> survival-cv

#<glmnet-cv:cox (~ (surv time status) age dose marker) Partial Likelihood Deviance         Lambda  Index  Measure      SE  Nonzero   min  0.04704     24    5.425  0.4747        2   1se   0.3997      1    5.868  0.4361        1>

> (coef survival-cv)

'(("age" . 0.0) ("dose" . 0.0) ("marker" . 0.142722357683114))

> (coef survival-cv #:lambda 'lambda-min)

'(("age" . 0.03435201616582482) ("dose" . 0.0) ("marker" . 1.691711581027472))

> (predict survival-cv new-patients #:type 'response #:lambda 'lambda-min)

'(9.206745640260905 4.7530444096829685)

At lambda-1se, the model keeps only the marker, the stronger of the two predictors that the survival time depends on; at lambda-min it adds age. Both drop the dose.