Accommodating Time-Varying Heterogeneity in Risk Estimation under the Cox Model: A Transfer Learning Approach

Transfer learning under the Cox model with interval‐censored data

“…The proposed method can be extended in several ways. First, similar to several existing methods [10,26], we presuppose the presence of pertinent covariates in both datasets. Nonetheless, practical challenges can arise when medical institutions or clinical trials collect divergent covariate sets [36].…”

“…When addressing information discrepancy, much of the literature uses $$$ {L}_1 $$$ penalties [8, 12, 26]. Specifically, Li et al [26] imposed the $$$ {L}_1 $$$ penalty on the divergence in regression coefficients and baseline hazard functions to address heterogeneity between the target and the source when dealing with right‐censored failure time data. However, their methodology requires a meticulous tuning parameter selection procedure.…”

“…The Trans-Cox-Lasso formulation is addressed using the TensorFlow [11] solver from Python and the tfp.math.minimize function from TensorFlow probability [13] for core optimization. The choice of learning rate, iteration steps, and tuning parameters aligns with the approach in Li et al [26], and takes about 2-3 min.…”

“…In our assessment, we contrast the proposed Trans‐Cox‐MIC method with two direct implementations of Cox regression: one exclusively employing the target data ( Cox‐Tonly ), and the other utilizing the combined datasets ( Cox‐Both ), as well as a Lasso‐based transfer learning method ( Trans‐Cox‐Lasso ), which replaces the $$$ {L}_0 $$$ norms with $$$ {L}_1 $$$ penalties in (). Trans‐Cox‐Lasso can be viewed as a generalized adaptation of the transfer learning approach presented in Li et al [26], originally designed for right‐censored data. The Trans‐Cox‐Lasso formulation is addressed using the TensorFlow [11] solver from Python and the tfp.math.minimize function from TensorFlow probability [13] for core optimization.…”

“…Additionally, as pointed out by Li et al [26], Cox models would be represented by different baseline hazards when the target and the source have time-varying risk shifts, and one should not discount the interactive relationship between the regression coefficients and the baseline hazards. As an alternative, Li et al [26] allowed different levels of information borrowing in both the regression coefficients and baseline hazard functions under Cox models but only required summary statistics from the source. They first estimated the source regression coefficients by maximizing the partial likelihood, and then estimated the source cumulative baseline hazards using the Breslow estimator.…”