ties -------- - Available in: CoxPH - Hyperparameter: no Description ~~~~~~~~~~~ This option configures approximation method for handling ties in the partial likelihood. This can be either **efron** (default) or **breslow**). Of the two approximations, Efron's produces results closer to the exact combinatoric solution than Breslow's. Under this approximation, the partial likelihood and log partial likelihood are defined as: :math:PL(\beta) = \prod_{m=1}^M \frac{\exp(\sum_{j \in D_m} w_j\mathbf{x}_j^T\beta)}{\big[\prod_{k=1}^{d_m}(\sum_{j \in R_m} w_j \exp(\mathbf{x}_j^T\beta) - \frac{k-1}{d_m} \sum_{j \in D_m} w_j \exp(\mathbf{x}_j^T\beta))\big]^{(\sum_{j \in D_m} w_j)/d_m}} :math:pl(\beta) = \sum_{m=1}^M \big[\sum_{j \in D_m} w_j\mathbf{x}_j^T\beta - \frac{\sum_{j \in D_m} w_j}{d_m} \sum_{k=1}^{d_m} \log(\sum_{j \in R_m} w_j \exp(\mathbf{x}_j^T\beta) - \frac{k-1}{d_m} \sum_{j \in D_m} w_j \exp(\mathbf{x}_j^T\beta))\big] Under Breslow's approximation, the partial likelihood and log partial likelihood are defined as: :math:PL(\beta) = \prod_{m=1}^M \frac{\exp(\sum_{j \in D_m} w_j\mathbf{x}_j^T\beta)}{(\sum_{j \in R_m} w_j \exp(\mathbf{x}_j^T\beta))^{\sum_{j \in D_m} w_j}} :math:pl(\beta) = \sum_{m=1}^M \big[\sum_{j \in D_m} w_j\mathbf{x}_j^T\beta - (\sum_{j \in D_m} w_j)\log(\sum_{j \in R_m} w_j \exp(\mathbf{x}_j^T\beta))\big] Related Parameters ~~~~~~~~~~~~~~~~~~ - None Example ~~~~~~~ .. example-code:: .. code-block:: r library(h2o) h2o.init() # import the heart dataset heart <- h2o.importFile("http://s3.amazonaws.com/h2o-public-test-data/smalldata/coxph_test/heart.csv") # set the predictor name and response column x <- "age" y <- "event" # set the start and stop columns start <- "start" stop <- "stop" # train your model coxph.h2o <- h2o.coxph(x=x, event_column=y, start_column=start, stop_column=stop, ties="breslow", training_frame=heart.hex) # view the model details coxph.h2o Model Details: ============== H2OCoxPHModel: coxph Model ID: CoxPH_model_R_1527700369755_2 Call: "Surv(start, stop, event) ~ age" coef exp(coef) se(coef) z p age 0.0307 1.0312 0.0143 2.15 0.031 Likelihood ratio test=5.17 on 1 df, p=0.023 n= 172, number of events= 75 .. code-block:: python import h2o from h2o.estimators.coxph import H2OCoxProportionalHazardsEstimator h2o.init() # import the heart dataset heart = h2o.import_file("http://s3.amazonaws.com/h2o-public-test-data/smalldata/coxph_test/heart.csv") # set the parameters coxph = H2OCoxProportionalHazardsEstimator(start_column="start", stop_column="stop", ties="breslow") # train your model coxph.train(x="age", y="event", training_frame=heart) # view the model details coxph