John P. Klein

Competing risks arise when a subject is exposed to many causes of failure. Data consist of the time the subject failed and an indicator of which risk caused the subject to fail. Examples in medicine include the analysis of cause to death data, the analysis of relapse and death in remission in cancer studies, or random right censoring. In engineering applications competing risks arise when analyzing series systems. Classical competing risks deal with the modeling of the probability of failure in the observed system (crude probabilities) or in systems with some causes of failure removed (net or partial crude probabilities). Modern competing risks theory, often based on counting process methodology, examines estimation techniques for competing risks probabilities, regression modeling for competing risks probabilities and comparing competing risks probabilities between treatment groups. Copyright © 2010 John Wiley & Sons, Inc.This article is categorized under: Statistical and Graphical Methods of Data Analysis > Reliability, Survivability, and Quality Control

Reporting transplant center-specific survival rates after hematopoietic cell transplantation is required in the United States. We describe a method to report 1-year survival outcomes by center, as well as to quantify center performance relative to the transplant center network average, which can be reliably used with censored data and for small center sizes. Each center’s observed 1-year survival outcome is compared to a predicted survival outcome adjusted for patient characteristics using a pseudovalue regression technique. A 95% prediction interval for 1-year survival assuming no center effect is computed for each center by bootstrapping the scaled residuals from the regression model, and the observed 1-year survival is compared to this prediction interval to determine center performance. We illustrate the technique using a recent center specific analysis performed by the Center for International Blood and Marrow Transplant Research, and study the performance of this method using simulation.

Donor lymphocyte infusion (DLI) for patients who relapse following an allogeneic stem cell transplant has proved remarkably durable. Because of the potential for second remissions with DLI, the current leukemia free survival (CLFS), which is the probability that a patient has not failed the entire course of the treatment, is becoming of interest to clinical investigators. Based on either a multistate Markov model or a linear combination of Kaplan-Meier estimators, we explore regression models for the CLFS. We focus on the two sample problem and we develop confidence bands for the CLFS or for differences in CLFS as well as a Kolmogorov type hypothesis test using a re-sampling technique. We also examine the use of pseudo-values to make inference on the direct effects of covariates on the CLFS function and we develop a score test for the equality of two CLFS. We illustrate these inference methods on a bone marrow transplant dataset.

A common problem encountered in many medical applications is the comparison of survival curves. Often, rather than comparison of the entire survival curves, interest is focused on the comparison at a fixed point in time. In most cases, the naive test based on a difference in the estimates of survival is used for this comparison. In this note, we examine the performance of alternatives to the naive test. These include tests based on a number of transformations of the survival function and a test based on a generalized linear model for pseudo‐observations. The type I errors and power of these tests for a variety of sample sizes are compared by a Monte Carlo study. We also discuss how these tests may be extended to situations where the data are stratified. The pseudo‐value approach is also applicable in more detailed regression analysis of the survival probability at a fixed point in time. The methods are illustrated on a study comparing survival for autologous and allogeneic bone marrow transplants. Copyright © 2007 John Wiley & Sons, Ltd.

Competing risks arise commonly in the analysis of cancer studies. Most common are the competing risks of relapse and death in remission. These two risks are the primary reason that patients fail treatment. In most medical papers the effects of covariates on the three outcomes (relapse, death in remission and treatment failure) are model by distinct proportional hazards regression models. Since the hazards of relapse and death in remission must add to that of treatment failure, we argue that this model leads to internal inconsistencies. We argue that additive models for either the hazard rates or the cumulative incidence functions are more natural and that these models properly partition the effect of a covariate on treatment failure into its component parts. We illustrate the use and interpretation of additive models for the hazard rate or for the cumulative incidence function using data from a study of the efficacy of two preparative regimes for hematopoietic stem cell transplantation. Copyright © 2006 John Wiley & Sons, Ltd.

Aalen's additive hazards regression model is a useful alternative to the proportional hazards model for censored data regression. When used to compare treatments this approach leads to weighted comparisons of the crude estimate of the hazard rate of each group as compared to a baseline group. This is contrasted to the weighted log rank test from the proportional hazards model which compares each treatment's rate to the pooled rate. We show in this brief note that Aalen's suggestion for weights in this test leads to inconsistent tests in the sense that the test statistic depends on which group we pick for a baseline group. We show that ‘consistent’ tests are obtained by using common weight functions for all comparisons and we make some suggestions. Copyright © 2005 John Wiley & Sons, Ltd.

SummaryTypically, regression models for competing risks outcomes are based on proportional hazards models for the crude hazard rates. These estimates often do not agree with impressions drawn from plots of cumulative incidence functions for each level of a risk factor. We present a technique which models the cumulative incidence functions directly. The method is based on the pseudovalues from a jackknife statistic constructed from the cumulative incidence curve. These pseudovalues are used in a generalized estimating equation to obtain estimates of model parameters. We study the properties of this estimator and apply the technique to a study of the effect of alternative donors on relapse for patients given a bone marrow transplant for leukemia.

Allogeneic hematopoietic stem cell transplantation is the only curative therapy for myelodysplasia (MDS). To identify factors influencing transplantation outcome, we studied 452 recipients of HLA-identical sibling transplants for MDS from 1989 to 1997, reported to the International Bone Marrow Transplant Registry. Patients with treatment-related MDS or unclassified MDS were excluded. Median age was 38 years (range, 2-64 years). Sixty percent had refractory anemia with excess blasts (n = 136) or with excess blasts in transformation (n = 136). Conditioning regimens included total body irradiation in 199 (44%) cases. Marrow was T-cell depleted for 58 (13%) transplants. Cumulative incidences of neutrophil engraftment, grades II-IV acute graft-versus-host disease (GVHD), and chronic GVHD were 91% (95% confidence interval [CI], 88%-93%), 36% (95% CI, 31%-40%), and 39% (95% CI, 33%-44%), respectively. Three-year transplantation-related mortality (TRM), relapse, disease-free survival, and overall survival rates were 37% (95% CI, 32%-42%), 23% (95% CI, 19%-27%), 40% (95% CI, 36%-45%), and 42% (95% CI, 37%-47%), respectively. Multivariate analyses showed that young age and platelet counts higher than 100 x 10(9)/L at transplantation were associated with lower TRM and higher disease-free and overall survival rates. Relapse incidence was higher in patients with high percentages of blasts in the marrow at transplantation or presentation, with high International Prognostic Scoring System scores at diagnosis, and with T-cell-depleted transplants. These findings indicate that transplantation from an HLA-identical sibling offers the possibility of long-term, disease-free survival to patients with MDS. Best candidates are younger patients with a low percentage of blasts and preserved platelet counts.