German Breast Cancer Study Group Research Articles

Sensitivity analysis for unmeasured confounding in estimating the difference in restricted mean survival time.

The difference in restricted mean survival time has been increasingly used as an alternative measure to the hazard ratio in survival analysis. Although some statistical methods have been developed for estimating the difference in restricted mean survival time adjusted for measured confounders in observational studies, the impact of unmeasured confounding on the estimate has rarely been assessed. We develop a novel sensitivity analysis for the estimate of the difference in restricted mean survival time with respect to unmeasured confounding. After formulating the sensitivity analysis problem as an optimization problem, we explain how to obtain the sensitivity range of the difference in restricted mean survival time efficiently and assess its uncertainty using the percentile bootstrap confidence interval. Analytic results are provided for some important survival settings. Simulation studies show that the proposed methods perform well in various settings. We illustrate the proposed sensitivity analysis method by analyzing data from the German Breast Cancer Study Group study.

Survival analysis in breast cancer: evaluating ensemble learning techniques for prediction.

Breast cancer is most commonly faced with form of cancer amongst women worldwide. In spite of the fact that the breast cancer research and awareness have gained considerable momentum, there is still no one treatment due to disease heterogeneity. Survival data may be of specific interest in breast cancer studies to understand its dynamic and complex trajectories. This study copes with the most important covariates affecting the disease progression. The study utilizes the German Breast Cancer Study Group 2 (GBSG2) and the Molecular Taxonomy of Breast Cancer International Consortium dataset (METABRIC) datasets. In both datasets, interests lie in relapse of the disease and the time when the relapse happens. The three models, namely the Cox proportional hazards (PH) model, random survival forest (RSF) and conditional inference forest (Cforest) were employed to analyse the breast cancer datasets. The goal of this study is to apply these methods in prediction of breast cancer progression and compare their performances based on two different estimation methods: the bootstrap estimation and the bootstrap .632 estimation. The model performance was evaluated in concordance index (C-index) and prediction error curves (pec) for discrimination. The Cox PH model has a lower C-index and bigger prediction error compared to the RSF and the Cforest approach for both datasets. The analysis results of GBSG2 and METABRIC datasets reveal that the RSF and the Cforest algorithms provide non-parametric alternatives to Cox PH model for estimation of the survival probability of breast cancer patients.

Multi-task banded regression model: A novel individual survival analysis model for breast cancer

PurposeTo reveal the hazard probability of individual breast cancer patients, a multi-task banded regression model is proposed for individual survival analysis of breast cancer. MethodsA banded verification matrix is designed to construct the response transform function of the proposed multi-task banded regression model, which can solve the repeated switching of survival rate. A martingale process is introduced to construct different nonlinear regressions for different survival subintervals. The concordance index (C-index) is used to compare the proposed model with Cox proportional hazards (CoxPH) models and previous multi-task regression models. ResultsTwo commonly-used breast cancer datasets are employed to validate the proposed model. Specifically, the Molecular Taxonomy of Breast Cancer International Consortium (METABRIC) includes 1981 breast cancer patients, of which 57.7% died of breast cancer. The Rotterdam & German Breast Cancer Study Group (GBSG) includes 1546 patients with lymph node-positive breast cancer in a randomized clinical trial, of which 44.4% died. Experimental results indicate that the proposed model is superior to some existing models for overall and individual survival analysis of breast cancer, with the C-index of 0.6786 for the GBSG and 0.6701 for the METABRIC. ConclusionThe superiority of the proposed model can be contributed to three novel ideas. One is that a banded verification matrix can band the response of the survival process. Second, the martingale process can construct different nonlinear regressions for different survival subintervals. Third, the novel loss can adapt the model to making the multi-task regression similar to the real survival process.

Multiple imputation for discrete data: Evaluation of the joint latent normal model.

Missing data are ubiquitous in clinical and social research, and multiple imputation (MI) is increasingly the methodology of choice for practitioners. Two principal strategies for imputation have been proposed in the literature: joint modelling multiple imputation (JM‐MI) and full conditional specification multiple imputation (FCS‐MI). While JM‐MI is arguably a preferable approach, because it involves specification of an explicit imputation model, FCS‐MI is pragmatically appealing, because of its flexibility in handling different types of variables. JM‐MI has developed from the multivariate normal model, and latent normal variables have been proposed as a natural way to extend this model to handle categorical variables. In this article, we evaluate the latent normal model through an extensive simulation study and an application on data from the German Breast Cancer Study Group, comparing the results with FCS‐MI. We divide our investigation in four sections, focusing on (i) binary, (ii) categorical, (iii) ordinal, and (iv) count data. Using data simulated from both the latent normal model and the general location model, we find that in all but one extreme general location model setting JM‐MI works very well, and sometimes outperforms FCS‐MI. We conclude the latent normal model, implemented in the R package jomo, can be used with confidence by researchers, both for single and multilevel multiple imputation.

Subgroup identification by recursive segmentation

ABSTRACTA new modeling approach called ‘recursive segmentation’ is proposed to support the supervised exploration and identification of subgroups or clusters. It is based on the frameworks of recursive partitioning and the Patient Rule Induction Method (PRIM). Through combining these methods, recursive segmentation aims to exploit their respective strengths while reducing their weaknesses. Consequently, recursive segmentation can be applied in a very general way, that is in any (multivariate) regression, classification or survival (time-to-event) problem, using conditional inference, evolutionary learning or the CART algorithm, with predictor variables of any scale and with missing values. Furthermore, results of a synthetic example and a benchmark application study that comprises 26 data sets suggest that recursive segmentation achieves a competitive prediction accuracy and provides more accurate definitions of subgroups by models of less complexity as compared to recursive partitioning and PRIM. An application to the German Breast Cancer Study Group data demonstrates the improved interpretability and reliability of results produced by the new approach. The method is made publicly available through the R-package rseg (http://rseg.r-forge.r-project.org/).

Information-Adaptive Clinical Trials: A Selective Recruitment Design

Summary We propose a novel adaptive design for clinical trials with time-to-event outcomes and covariates (which may consist of or include biomarkers). Our method is based on the expected entropy of the posterior distribution of a proportional hazards model. The expected entropy is evaluated as a function of a patient’s covariates, and the information gained due to a patient is defined as the decrease in the corresponding entropy. Candidate patients are only recruited onto the trial if they are likely to provide sufficient information. Patients with covariates that are deemed uninformative are filtered out. A special case is where all patients are recruited, and we determine the optimal treatment arm allocation. This adaptive design has the advantage of potentially elucidating the relationship between covariates, treatments and survival probabilities by using fewer patients, albeit at the cost of rejecting some candidates. We assess the performance of our adaptive design by using data from the German Breast Cancer Study Group and numerical simulations of a biomarker validation trial.

Adjusting Complex Heterogeneity in Treatment Assignment in Observational Studies

Treatment assignment in observational studies is complex and can be influenced by many factors that include patient characteristics, physician practices, and health care systems. These influences can present heterogeneity or clustering effects in the treatment assignment. If those heterogeneity or clustering effects are not appropriately adjusted, the estimated treatment effect may be severely biased. Through a series of models that mimic various level of heterogeneity in treatment assignment in observational studies, we evaluate, through simulation study, the performance of several estimators under the impact of different types of heterogeneity. These estimators include propensity score stratification, propensity score inverse probability weighting, propensity score regression and the partial least squares method. Our results suggest that the partial least squares method is most robust while the dummy variable adjustment method in propensity regression also performs fairly consistently. We use the proposed method to analyze a data set from the German Breast Cancer Study Group study.

Multi-state model for studying an intermediate event using time-dependent covariates: application to breast cancer

BackgroundThe aim of this article is to propose several methods that allow to investigate how and whether the shape of the hazard ratio after an intermediate event depends on the waiting time to occurrence of this event and/or the sojourn time in this state.MethodsA simple multi-state model, the illness-death model, is used as a framework to investigate the occurrence of this intermediate event. Several approaches are shown and their advantages and disadvantages are discussed. All these approaches are based on Cox regression. As different time-scales are used, these models go beyond Markov models. Different estimation methods for the transition hazards are presented. Additionally, time-varying covariates are included into the model using an approach based on fractional polynomials. The different methods of this article are then applied to a dataset consisting of four studies conducted by the German Breast Cancer Study Group (GBSG). The occurrence of the first isolated locoregional recurrence (ILRR) is studied. The results contribute to the debate on the role of the ILRR with respect to the course of the breast cancer disease and the resulting prognosis.ResultsWe have investigated different modelling strategies for the transition hazard after ILRR or in general after an intermediate event. Including time-dependent structures altered the resulting hazard functions considerably and it was shown that this time-dependent structure has to be taken into account in the case of our breast cancer dataset. The results indicate that an early recurrence increases the risk of death. A late ILRR increases the hazard function much less and after the successful removal of the second tumour the risk of death is almost the same as before the recurrence. With respect to distant disease, the appearance of the ILRR only slightly increases the risk of death if the recurrence was treated successfully.ConclusionsIt is important to realize that there are several modelling strategies for the intermediate event and that each of these strategies has restrictions and may lead to different results. Especially in the medical literature considering breast cancer development, the time-dependency is often neglected in the statistical analyses. We show that the time-varying variables cannot be neglected in the case of ILRR and that fractional polynomials are a useful tool for finding the functional form of these time-varying variables.

Evaluating Random Forests for Survival Analysis using Prediction Error Curves.

Prediction error curves are increasingly used to assess and compare predictions in survival analysis. This article surveys the R package pec which provides a set of functions for efficient computation of prediction error curves. The software implements inverse probability of censoring weights to deal with right censored data and several variants of cross-validation to deal with the apparent error problem. In principle, all kinds of prediction models can be assessed, and the package readily supports most traditional regression modeling strategies, like Cox regression or additive hazard regression, as well as state of the art machine learning methods such as random forests, a nonparametric method which provides promising alternatives to traditional strategies in low and high-dimensional settings. We show how the functionality of pec can be extended to yet unsupported prediction models. As an example, we implement support for random forest prediction models based on the R-packages randomSurvivalForest and party. Using data of the Copenhagen Stroke Study we use pec to compare random forests to a Cox regression model derived from stepwise variable selection. Reproducible results on the user level are given for publicly available data from the German breast cancer study group.

On a new NBUE property in multivariate sense: An application

Since multivariate lifetime data frequently occur in applications, various properties of multivariate distributions have been previously considered to model and describe the main concepts of aging commonly considered in the univariate setting. The generalization of univariate aging notions to the multivariate case involves, among other factors, appropriate definitions of multivariate quantiles and related notions, which are able to correctly describe the intrinsic characteristics of the concepts of aging that should be generalized, and which provide useful tools in the applications. A new multivariate version of the well-known New Better than Used in Expectation univariate aging notion is provided, by means of the concepts of the upper corrected orthant and multivariate excess-wealth function. Some of its properties are described, with particular attention paid to those that can be useful in the analysis of real data sets. Finally, through an example it is illustrated how the new multivariate aging notion influences the final results in the analysis of data on tumor growth from the Comprehensive Cohort Study performed by the German Breast Cancer Study Group.

Additive survival least‐squares support vector machines

This work studies a new survival modeling technique based on least-squares support vector machines. We propose the use of a least-squares support vector machine combining ranking and regression. The advantage of this kernel-based model is threefold: (i) the problem formulation is convex and can be solved conveniently by a linear system; (ii) non-linearity is introduced by using kernels, componentwise kernels in particular are useful to obtain interpretable results; and (iii) introduction of ranking constraints makes it possible to handle censored data. In an experimental setup, the model is used as a preprocessing step for the standard Cox proportional hazard regression by estimating the functional forms of the covariates. The proposed model was compared with different survival models from the literature on the clinical German Breast Cancer Study Group data and on the high-dimensional Norway/Stanford Breast Cancer Data set.

Radiation therapy and tamoxifen after breast-conserving surgery: Updated results of a 2 × 2 randomised clinical trial in patients with low risk of recurrence

To study the role of radiotherapy and tamoxifen after breast-conserving surgery (BCS) in patients with a favourable prognosis, a clinical trial was initiated by the German Breast Cancer Study Group (GBSG-V). Between 1991 and 1998, 361 patients (pT 1pN0M0, aged 45–75 years, receptor positive, grades I and II) were randomised to radiotherapy (yes/no) and tamoxifen for 2 years (yes/no) in a 2 × 2-factorial design; the exclusion of seven centres (14 patients) left 347 patients for the analysis. First results after a median follow-up of 5.9 years were published. Herein we present updated results after a median follow-up of about 10 years. Hundred and eleven events concerning event-free survival (EFS) have been observed. Since a strong interactive effect between radiotherapy and tamoxifen has been established, the results are presented in terms of the treatment effects for all four treatment groups separately. Mainly due to the presence of local recurrences, the event rate was much higher in the group with BCS only than in the other three groups. No significant difference could be established between the four treatment groups for distant disease-free survival rates (DDFS). Updated results give further evidence that even in patients with a favourable prognosis, the avoidance of radiotherapy and tamoxifen after BCS increases the rate of local recurrences substantially. Rates are about three times higher in the BCS only group. For the two outcomes EFS and DDFS, no important difference could be seen between the three groups with an additional treatment. However, because of the limited sample size with corresponding low power the strength of evidence for such a comparison is weak.

Assessment of Optimal Selected Prognostic Factors

AbstractThe identification and assessment of prognostic factors is one of the major tasks in clinical research. The assessment of one single prognostic factor can be done by recently established methods for using optimal cutpoints. Here, we suggest a method to consider an optimal selected prognostic factor from a set of prognostic factors of interest. This can be viewed as a variable selection method and is the underlying decision problem at each node of various tree building algorithms.We propose to use maximally selected statistics where the selection is defined over the set of prognostic factors and over all cutpoints in each prognostic factor. We demonstrate that it is feasible to compute the approximate null distribution. We illustrate the new variable selection test with data of the German Breast Cancer Study Group and of a small study on patients with diffuse large B‐cell lymphoma. Using the null distribution for a p‐value adjusted regression trees algorithm, we adjust for the number of variables analysed at each node as well. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Radiation therapy after breast-conserving surgery: first results of a randomised clinical trial in patients with low risk of recurrence

To study the role of radiotherapy and tamoxifen after breast-conserving surgery (BCS) in patients with a favourable prognosis, a clinical trial was initiated by the German Breast Cancer Study Group. Between 1991 and 1998, 361 patients (pT1pN0M0, aged 45–75 years, receptor positive, grade I–II) were randomised to radiotherapy (yes/no) and tamoxifen for 2 years (yes/no) in a 2×2 factorial design; the exclusion of seven centres (14 patients) left 347 patients in the analysis. After a median follow-up of 5.9 years, 77 events concerning event-free survival have been observed. Since a strong interactive effect between radiotherapy and tamoxifen has been established, the results are presented in terms of the treatment effects for all four treatment groups separately. Mainly due to the presence of local recurrences, the event rate was about three times higher in the group with BCS only than in the other three groups. No difference could be established between the four treatment groups for distant disease-free survival rates. It is concluded that even in patients with a favourable prognosis, the avoidance of radiotherapy and tamoxifen after BCS increases the rate of local recurrences substantially.

Long-Term Follow-Up of Patients in Four Prospective Studies of the German Breast Cancer Study Group (GBSG): A Summary of Key Results

Evaluation of treatment modalities and prognostic factors in early breast cancer requires a long-term follow-up of patients in prospective studies. The German Breast Cancer Study Group (GBSG) started four nationwide studies in 1983 in which a total of 2,746 patients have been enrolled and followed for about 10 years. Questions that have been addressed in these studies are still relevant today and comprise the role of breast-conserving therapy, the duration of adjuvant chemotherapy, and whether adjuvant radiotherapy is needed. The key results of these studies are highlighted including some important findings on prognosis, e.g., the role of isolated locoregional recurrence and the prognosis of patients with 10 or more positive lymph nodes. The data of all randomized patients were regularly included into the overviews of the Early Breast Cancer Trialists’ Collaborative Group; the data of the nonrandomized patients have been used to examine the external validity of treatment comparisons. Overall, it can be concluded that the GBSG studies have made valuable and internationally recognized contributions to the prognosis and treatment of patients with early breast cancer.

Long-term prognosis of breast cancer patients with 10 or more positive lymph nodes treated with CMF

The purpose of this investigation was to study the long-term prognosis of breast cancer patients with 10 or more positive lymph nodes after conventional chemotherapy treatment with cyclophosphamide, methotrexate and 5-fluorouracil (CMF). Between 1984 and 1989, 1048 node-positive patients were treated with CMF in two separate trials conducted by the German Breast Cancer Study Group (GBSG). Subgroups either received radiotherapy or tamoxifen in addition. In this study, long-term prognosis in the subgroup of 141 patients with 10 or more positive lymph nodes was investigated. Univariate and multivariate Cox models were used to evaluate the effect of prognostic factors on event-free survival (EFS) and overall survival (OS). Both univariate and multivariate analyses revealed the progesterone receptor (PR) status as the dominating prognostic factor for both EFS and OS, resulting in a strongly increased risk of more than 2-fold for receptor-negative patients. A large number of positive lymph nodes also affected the prognosis for EFS. In univariate analysis, the degree of lymph node involvement (i.e. percentage of positive nodes out of all examined nodes), oestrogen status (ER) status, and tumour grade also showed significant effects. To conclude, the prognosis in the subgroup of patients with 10 or more positive lymph nodes is heterogeneous. Some surprisingly high survival rates have been observed in case series of breast cancer patients treated with high-dose chemotherapy which may be explained by patient selection. From the usual factors investigated in this study, the PR status showed the strongest effect, and, at least this factor should be taken into account in the design and analysis of trials for breast cancer patients with a poor prognosis.

Role of isolated locoregional recurrence of breast cancer: results of four prospective studies.

We evaluated the effect on future prognosis of an isolated locoregional recurrence (ILRR) after the primary diagnosis of breast cancer. Using data from four prospective studies of the German Breast Cancer Study Group, we investigated factors influencing prognosis after ILRR and defined a simple classification of patients into groups with different prognoses. From 1983 to 1989, 2,746 patients were recruited into four studies comparing different treatments in primary breast cancer. After a median follow-up time of 8 years, 337 patients developed an ILRR as the first event. The influence of ILRRs on disease progression was examined. The effects of different prognostic factors on progression-free survival (PFS) and overall survival after ILRR were analyzed after a median follow-up time of 4.5 years. ILRRs increased the risk with respect to distant recurrence and death. After ILRR, 185 events occurred with respect to the PFS end point, and 171 patients died. Primary nodal status, tumor grade, estrogen receptor status of the primary tumor, and length of the disease-free interval (DFI) until the time of the ILRR had a significant prognostic impact. Determinants of prognosis after the ILRR should be taken into account for designing future risk-adapted clinical studies for these patients. Risk strata can be defined by a simple classification scheme based on primary nodal status and DFI.

Methodological arguments for the necessity of randomized trials in high-dose chemotherapy for breast cancer.

In the past ten years high-dose chemotherapy with autologous haematopoietic stem-cell support (HD-CT) has increasingly been used for breast cancer. But the vast majority of trials are small phase I/II studies showing until now not enough evidence that HD-CT is superior to conventional-dose chemotherapy (CD-CT). In contrast to this, the public perception of this treatment is different. Patients as well as physicians often uncritically believe in reports contrasting the positive results obtained in case series treated by HD-CT with those of historical control groups. This leads to the problem that many patients and also clinicians are not willing to participate in randomized trials on this topic. A critical assessment of current knowledge on the effectiveness of HD-CT in breast cancer is given. The problems related to the use of historical controls, in general, and especially in the setting of HD-CT are demonstrated. Using data of patients treated with CD-CT within trials of the German Breast Cancer Study Group (GBSG) it will be shown that results similarly favorable to those reported from patients treated with a high-dose regimen may be produced using quite simple selection mechanisms. Comparisons of patients treated with HD-CT with historical control groups of patients treated with CD-CT may be misleading. A valid treatment comparison is only possible by means of large randomized trials. Clinicians should participate in the ongoing trials and enter all eligible patients.

The effect of oral contraceptive use on the prognosis of node positive breast cancer patients. German Breast Cancer Study Group.

The effect of oral contraceptive (OC) use as a risk factor for breast cancer was recently assessed in a large meta-analysis, but currently available data on the prognostic effect are still insufficient. We investigated the relationship between OC use and standard prognostic factors and the effect of OC use on recurrence-free survival (RFS) and overall survival (OS) in 422 premenopausal pT1a-3aN + M0 patients from two trials of the German Breast Cancer Study Group (GBSG). 137 patients (32.5%) were OC users. They were younger on average (mean age 41.5 years versus 45 years for non-OC users) and the percentage of patients with smaller tumours was higher in the group of OC users. Based on 163 events for RFS and 103 events for OS, no significant effect of OC use on RFS and OS could be demonstrated in univariate and multivariate analyses. In our study of node positive breast cancer cases, OC users were younger and had smaller tumours. This may be an effect of earlier detection of breast cancer, but OC users did not have a better prognosis, both before and after adjustment for tumour size and other prognostic factors.

Validation of existing and development of new prognostic classification schemes in node negative breast cancer. German Breast Cancer Study Group.

Several prognostic classification schemes in node negative breast cancer are proposed, but only the Nottingham Prognostic Index (NPI) seems to be sufficiently validated. Validation, which is a prerequisite for a sensible assessment, is not published for two recent proposals according to Glick et al. [1] and Rubens [2]. The German Breast Cancer Study Group (GBSG) entered 662 eligible patients in a prospective observational study. 603 of them had complete data for seven 'standard' prognostic factors and median follow-up is about 5 years. As there is no accepted and informative measure of separation for classification schemes presently available, we propose a new one and use it additionally to the well known logrank-test and Kaplan-Meier estimates to investigate the predictive power of the three schemes. significant differences in survival and recurrence-free survival could be established for the NPI subgroups but not for others where even the ordering of the groups was different. With the Cox model and the classification and regression tree approach we develop two new proposals for the differentiation of subgroups of node negative patients. As in the NPI, tumor size and grade are the most important factors, but with a different weighting scheme. Young age (< or = 40 years) and very high estrogen receptor values (> 300 fmol) in a small subgroup of patients were associated with worse prognosis. The new proposals showed a better degree of separation, which demonstrates that an improvement seems possible using standard factors. Because the measures of separation give an overoptimistic impression for the new proposals, a validation with other studies is necessary before a general recommendation can be given.