Time-dependent effects of fixed covariates in Cox regression

A nonparametric modification is proposed for Cox's proportional hazards model (Cox, 1972, Journal of the Royal Statistical Society, Series B 34, 187-220), where the covariates are fixed, but their effects are allowed to vary in time. Parameters are introduced for the covariate effects at the (uncensored) survival times. Estimates are obtained by maximizing the penalized partial log-likelihood that arises if a penalty function of the first order differences of consecutive parameters is subtracted from the partial log-likelihood. The choice of the smoothing parameter, which determines the weight of the penalty, is based on Akaike's Information Criterion. The methods are illustrated in a set of ovarian cancer data and in a set of kidney transplantation data.

Penalized likelihood in Cox regression

In a Cox regression model, instability of the estimated regression coefficients can be reduced by maximizing a penalized partial log-likelihood, where a penalty function of the regression coefficients is substracted from the partial log-likelihood. In this paper, we choose the optimal weight of the penalty function by maximizing the predictive value of the model, as measured by the crossvalidated partial log-likelihood. Our methods are illustrated by a study of ovarian cancer survival and by a study of centre-effects in kidney graft survival.

Persistence of host-type hematopoiesis after allogeneic bone marrow transplantation for leukemia is significantly related to the recipient's age and/or the conditioning regimen, but it is not associated with an increased risk of relapse

We investigated the chimerism pattern within flow-sorted peripheral blood- or bone marrow-derived cell populations after allogeneic bone marrow transplantation (BMT) for the treatment of leukemia in children. This study was performed to define the identity of persistent host-type cells, to identify prognostic variables for the persistence of host-type hematopoiesis, and to determine the prognostic significance of the chimerism pattern on the duration of the leukemia-free interval, the overall survival, and the leukemia-free survival. The patients received either HLA-identical non-T-cell-depleted (n = 46) or HLA nonidentical T-cell-depleted (n = 7) BMT. In the peripheral blood, the children showed either stable mixed chimerism (SMC; ie, persistent host-type hematopoiesis; n = 14), (transient) mixed T-lymphoid chimerism (MTLC; n = 9), or complete chimerism (CC; n = 30). In the bone marrow, only donor-type cells were found in children with either CC (n = 8) or MTLC (n = 2), and a mixture of donor- and recipient-type cells was found in children with SMC (n = 7). The persistence of host-type hematopoiesis (SMC) was significantly related to a lower age of the recipient, the type of conditioning regimen, a lower total body irradiation dose, T-cell depletion of the bone marrow graft, and the use of cyclosporine A for acute graft-versus-host disease prophylaxis. No significant differences were found between patients with (SMC) or without (CC/MTLC) persistent host-type hematopoiesis with respect to the duration of the leukemia-free interval, the overall survival, or the leukemia-free survival. We conclude that ablation of host-type hematopoiesis is not compulsory for long-term leukemia-free survival after allogeneic BMT for various hematologic malignancies.

Cross-validation in survival analysis

The predictive value of a statistical model is conceptually different from the explained variation. In this paper we construct a measure of the predictive value of the Cox proportional hazards model, computed from the leave-one-out regression coefficients. These coefficients can also be used to calculate a shrinkage factor which can be applied to improve the predictions and that can be used in R2-type measures of the proportion of explained variation. Our methods are illustrated by a study of chemotherapy for advanced ovarian cancer.