Proportional hazards regression — details_proportional_hazards

survival::coxph() fits a Cox proportional hazards model.

Details

For this engine, there is a single mode: censored regression

Tuning Parameters

This model has no tuning parameters.

Translation from parsnip to the original package

The censored extension package is required to fit this model.

library(censored)

proportional_hazards() %>%
  set_engine("survival") %>%
  set_mode("censored regression") %>%
  translate()

## Proportional Hazards Model Specification (censored regression)
##
## Computational engine: survival
##
## Model fit template:
## survival::coxph(formula = missing_arg(), data = missing_arg(),
##     weights = missing_arg(), x = TRUE, model = TRUE)

Other details

The model does not fit an intercept.

The main interface for this model uses the formula method since the model specification typically involved the use of survival::Surv().

The model formula can include special terms, such as survival::strata(). The allows the baseline hazard to differ between groups contained in the function. The column used inside strata() is treated as qualitative no matter its type. To learn more about using special terms in formulas with tidymodels, see ?model_formula.

For example, in this model, the numeric column rx is used to estimate two different baseline hazards for each value of the column:

library(survival)

proportional_hazards() %>%
  fit(Surv(futime, fustat) ~ age + strata(rx), data = ovarian) %>%
  extract_fit_engine() %>%
  # Two different hazards for each value of 'rx'
  basehaz()

##        hazard time strata
## 1  0.02250134   59   rx=1
## 2  0.05088586  115   rx=1
## 3  0.09467873  156   rx=1
## 4  0.14809975  268   rx=1
## 5  0.30670509  329   rx=1
## 6  0.46962698  431   rx=1
## 7  0.46962698  448   rx=1
## 8  0.46962698  477   rx=1
## 9  1.07680229  638   rx=1
## 10 1.07680229  803   rx=1
## 11 1.07680229  855   rx=1
## 12 1.07680229 1040   rx=1
## 13 1.07680229 1106   rx=1
## 14 0.05843331  353   rx=2
## 15 0.12750063  365   rx=2
## 16 0.12750063  377   rx=2
## 17 0.12750063  421   rx=2
## 18 0.23449656  464   rx=2
## 19 0.35593895  475   rx=2
## 20 0.50804209  563   rx=2
## 21 0.50804209  744   rx=2
## 22 0.50804209  769   rx=2
## 23 0.50804209  770   rx=2
## 24 0.50804209 1129   rx=2
## 25 0.50804209 1206   rx=2
## 26 0.50804209 1227   rx=2

Note that columns used in the strata() function will not be estimated in the regular portion of the model (i.e., within the linear predictor).

Predictions of type "time" are predictions of the mean survival time.

Linear predictor values

Since risk regression and parametric survival models are modeling different characteristics (e.g. relative hazard versus event time), their linear predictors will be going in opposite directions.

For example, for parametric models, the linear predictor increases with time. For proportional hazards models the linear predictor decreases with time (since hazard is increasing). As such, the linear predictors for these two quantities will have opposite signs.

tidymodels does not treat different models differently when computing performance metrics. To standardize across model types, the default for proportional hazards models is to have increasing values with time. As a result, the sign of the linear predictor will be the opposite of the value produced by the predict() method in the engine package.

This behavior can be changed by using the increasing argument when calling predict() on a model object.

Case weights

This model can utilize case weights during model fitting. To use them, see the documentation in case_weights and the examples on tidymodels.org.

The fit() and fit_xy() arguments have arguments called case_weights that expect vectors of case weights.

References

Andersen P, Gill R. 1982. Cox’s regression model for counting processes, a large sample study. Annals of Statistics 10, 1100-1120.