A stratified adaptive two-stage design with co-primary endpoints for phase II clinical oncology trials.

BACKGROUND: Given the inherent challenges of conducting randomized phase III trials in older cancer patients, single-arm phase II trials which assess the feasibility of a treatment that has already been shown to be effective in a younger population may provide a compelling alternative. Such an approach would need to evaluate treatment feasibility based on a composite endpoint that combines multiple clinical dimensions and to stratify older patients as fit or frail to account for the heterogeneity of the study population to recommend an appropriate treatment approach. In this context, stratified adaptive two-stage designs for binary or composite endpoints, initially developed for biomarker studies, allow to include two subgroups whilst maintaining competitive statistical performances. In practice, heterogeneity may indeed affect more than one dimension and incorporating co-primary endpoints, which independently assess each individual clinical dimension, would therefore appear quite pertinent. The current paper presents a novel phase II design for co-primary endpoints which takes into account the heterogeneity of a population.  METHODS: We developed a stratified adaptive Bryant & Day design based on the Jones et al. and Parashar et al. algorithm. This two-stage design allows to jointly assess two dimensions (e.g. activity and toxicity) in two different subgroups. The operating characteristics of this new design were evaluated using examples and simulation comparisons with the Bryant & Day design in the context where the study population is stratified according to a pre-defined criterion. RESULTS: Simulation results demonstrated that the new design minimized the expected and maximum sample sizes as compared to parallel Bryant & Day designs (one in each subgroup), whilst controlling type I error rates and maintaining a competitive statistical power as well as a high probability of detecting heterogeneity. CONCLUSIONS: In a heterogeneous population, this two-stage stratified adaptive phase II design provides a useful alternative to classical one and allows to identify a subgroup of interest without dramatically increasing sample size. As heterogeneity is not limited to older populations, this new design may also be relevant to other study populations such as children or adolescents and young adults or the development of targeted therapies based on a biomarker.

Comparison of Variable Selection Methods for Time-to-Event Data in High-Dimensional Settings.

Over the last decades, molecular signatures have become increasingly important in oncology and are opening up a new area of personalized medicine. Nevertheless, biological relevance and statistical tools necessary for the development of these signatures have been called into question in the literature. Here, we investigate six typical selection methods for high-dimensional settings and survival endpoints, including LASSO and some of its extensions, component-wise boosting, and random survival forests (RSF). A resampling algorithm based on data splitting was used on nine high-dimensional simulated datasets to assess selection stability on training sets and the intersection between selection methods. Prognostic performances were evaluated on respective validation sets. Finally, one application on a real breast cancer dataset has been proposed. The false discovery rate (FDR) was high for each selection method, and the intersection between lists of predictors was very poor. RSF selects many more variables than the other methods and thus becomes less efficient on validation sets. Due to the complex correlation structure in genomic data, stability in the selection procedure is generally poor for selected predictors, but can be improved with a higher training sample size. In a very high-dimensional setting, we recommend the LASSO-pcvl method since it outperforms other methods by reducing the number of selected genes and minimizing FDR in most scenarios. Nevertheless, this method still gives a high rate of false positives. Further work is thus necessary to propose new methods to overcome this issue where numerous predictors are present. Pluridisciplinary discussion between clinicians and statisticians is necessary to ensure both statistical and biological relevance of the predictors included in molecular signatures.

Addressing heterogeneity in the design of phase II clinical trials in geriatric oncology.

INTRODUCTION: Cancer in the elderly is a major public issue. However, older patients have long been debarred from clinical trials. There is a high unmet medical need for specific trials addressing oncology strategies adapted to older patients' conditions. While randomised phase III trials remain the gold standard, they usually require large numbers of patients. In this perspective, late single-arm phase II trials assessing treatment feasibility might prove a good alternative. However, it is essential to take into account the heterogeneity in an ageing population characterised by frailty. Standard parallel phase II studies in defined frail and non-frail populations also require a high number of patients. Used in molecular subtyping and treatment effect heterogeneity, stratified adaptive designs can improve statistical performance, but they have never been used in geriatric oncology. This report describes their potential benefits and useful applications as compared with standard designs. METHODS: In a heterogeneous population, stratified adaptive designs allowed us to select subgroups of interest in two stages. Operational characteristics were evaluated through simulations of clinical trials under different scenarios. RESULTS: Simulations showed that the use of stratified adaptive designs can efficiently minimise both the number of patients to be included and accrual duration with competitive statistical power and high heterogeneity detection rate at interim analysis. CONCLUSION: Compared with classical phase II designs, stratified adaptive phase II trial methodology offers a promising approach to improve clinical research in geriatric oncology. These designs may also be efficient in other populations such as children or adolescents and young adults.

Focus on an infrequently used quantity in the context of competing risks: The conditional probability function.

In clinical studies of hematologic and oncologic diseases, the outcomes of interest are generally composite time to event endpoints which are usually defined by occurrence of different event types. Nonetheless, clinicians are interested in studying only one event type, which leads to a competing risks situation. In this context, Pepe and Mori presented a quantity directly derived from the cumulative incidence: the conditional probability. This function defines the probability that a given event occurs, conditionally on not having had a competing event by that time. The objective of this paper is to present this conditional cumulative incidence function and to compare its use to the cumulative incidence in different data sets. Different scenarios highlight the importance of the competing event on the interpretation of the conditional probability. Conditional probability needs to be interpreted jointly with the cumulative incidence. This quantity can be of interest especially when the risk of the competing event is large, strongly precludes the risk of the event of interest and provides useful additional information.

Comparison of variable selection methods for high-dimensional survival data with competing events.

BACKGROUND: In the era of personalized medicine, it's primordial to identify gene signatures for each event type in the context of competing risks in order to improve risk stratification and treatment strategy. Until recently, little attention was paid to the performance of high-dimensional selection in deriving molecular signatures in this context. In this paper, we investigate the performance of two selection methods developed in the framework of high-dimensional data and competing risks: Random survival forest and a boosting approach for fitting proportional subdistribution hazards models. METHODS: Using data from bladder cancer patients (GSE5479) and simulated datasets, stability and prognosis performance of the two methods were evaluated using a resampling strategy. For each sample, the data set was split into 100 training and validation sets. Molecular signatures were developed in the training sets by the two selection methods and then applied on the corresponding validation sets. RESULTS: Random survival forest and boosting approach have comparable performance for the prediction of survival data, with few selected genes in common. Nevertheless, many different sets of genes are identified by the resampling approach, with a very small frequency of genes occurrence among the signatures. Also, the smaller the training sample size, the lower is the stability of the signatures. CONCLUSION: Random survival forest and boosting approach give good predictive performance but gene signatures are very unstable. Further works are needed to propose adequate strategies for the analysis of high-dimensional data in the context of competing risks.

A Statistical Approach to Determine the Optimal Duration of Post-Treatment Follow-Up: Application to Metastatic Nonseminomatous Germ Cell Tumors.

BACKGROUND: The objective of this study was to present a statistical method to define an optimal duration of follow-up for patients in remission after treatment for cancer, for detection of recurrences. PATIENTS AND METHODS: Surveillance duration was estimated using the 2-step approach proposed by Mould et al. Relapse-free interval was modeled using the parametric cure model proposed by Boag. The optimal length of follow-up was then estimated as the minimal elapsed time after which the probability of a patient to relapse and to be cured with success is below a given threshold value. The method is applied to 2 real data sets of patients treated for metastatic non seminomatous germ-cell tumors: T93BP and T93MP. RESULTS: For the T93BP, cure rate was estimated at 91.3% and proportions of patients who relapsed after 3 and 5 years were estimated at 0.5% and 0.2%. With a probability of success of salvage treatment equal to 80% and 50%, numbers of delayed cases after 5 years were 2 and 1. For T93MP, the proportion of patients who presented relapse after 5 and 10 years were estimated at 5.2% and 2.6%. Considering a probability of salvage treatment equal to 20%, the number of delayed cases after 5 and 10 years were 10 and 5. CONCLUSION: Using this methodology, duration of post-therapeutic follow-up might be tailored according to an objective criteria: the number of patients who present relapse after the end of follow-up and who could have been treated with success in case of early detection.

Optimal scheduling of post-therapeutic follow-up of patients treated for cancer for early detection of relapses.

Post-therapeutic surveillance is one important component of cancer care. However, there still is no evidence-based strategies to schedule patients' follow-up examinations. Our approach is based on the modeling of the probability of the onset of relapse at an early asymptotic or preclinical stage and its transition to a clinical stage. For that we consider a multistate homogeneous Markov model, which includes the natural history of relapse. The model also handles separately the different types of possible relapses. The optimal schedule is provided by the calendar visit that maximizes a utility function. The methodology has been applied to laryngeal cancer. The different follow-up strategies revealed to be more efficient than those proposed by different scientific societies.

Determining the length of posttherapeutic follow-up for cancer patients using competing risks modeling.

BACKGROUND/OBJECTIVE: After a curative treatment for cancer, patients enter into a posttherapeutic surveillance phase. This phase aims to detect relapses as soon as possible to improve the outcome. Mould and others predicted with a simple formula, using a parametric mixture cure model, how long early-stage breast cancer patients should be followed after treatment. However, patients in posttherapeutic surveillance phase are at risk of different events types with different responses according to their prognostic factors and different probabilities to be cured. This paper presents an adaptation of the method proposed by Mould and others, taking into account competing risks. Our loss function estimates, when follow-up is stopped at a given time, the proportion of patients who will fail after this time and who could have been treated successfully. METHOD: We use the direct approach for cumulative incidence modeling in the presence of competing risks with an improper Gompertz probability distribution as proposed by Jeong and Fine. Prognostic factors can be taken into account, leading to a proportional hazards model. In a second step, the estimates of the Gompertz model are combined with the probability for a patient to be treated successfully in case of relapse for each event type. The method is applied to 2 examples, a numeric fictive example and a real data set on soft tissue sarcoma. RESULTS: and CONCLUSION: The model presented is a good tool for decision making to determine the total length of posttherapeutic surveillance. It can be applied to all cancers regardless of the localizations.

Smooth conditional distribution function and quantiles under random censorship.

We consider a nonparametric random design regression model in which the response variable is possibly right censored. The aim of this paper is to estimate the conditional distribution function and the conditional alpha-quantile of the response variable. We restrict attention to the case where the response variable as well as the explanatory variable are unidimensional and continuous. We propose and discuss two classes of estimators which are smooth with respect to the response variable as well as to the covariate. Some simulations demonstrate that the new methods have better mean square error performances than the generalized Kaplan-Meier estimator introduced by Beran (1981) and considered in the literature by Dabrowska (1989, 1992) and Gonzalez-Manteiga and Cadarso-Suarez (1994).