Federico Rotolo

Empirical extensions of the lasso penalty to reduce the false discovery rate in high-dimensional Cox regression models.

Correct selection of prognostic biomarkers among multiple candidates is becoming increasingly challenging as the dimensionality of biological data becomes higher. Therefore, minimizing the false discovery rate (FDR) is of primary importance, while a low false negative rate (FNR) is a complementary measure. The lasso is a popular selection method in Cox regression, but its results depend heavily on the penalty parameter λ. Usually, λ is chosen using maximum cross-validated log-likelihood (max-cvl). However, this method has often a very high FDR. We review methods for a more conservative choice of λ. We propose an empirical extension of the cvl by adding a penalization term, which trades off between the goodness-of-fit and the parsimony of the model, leading to the selection of fewer biomarkers and, as we show, to the reduction of the FDR without large increase in FNR. We conducted a simulation study considering null and moderately sparse alternative scenarios and compared our approach with the standard lasso and 10 other competitors: Akaike information criterion (AIC), corrected AIC, Bayesian information criterion (BIC), extended BIC, Hannan and Quinn information criterion (HQIC), risk information criterion (RIC), one-standard-error rule, adaptive lasso, stability selection, and percentile lasso. Our extension achieved the best compromise across all the scenarios between a reduction of the FDR and a limited raise of the FNR, followed by the AIC, the RIC, and the adaptive lasso, which performed well in some settings. We illustrate the methods using gene expression data of 523 breast cancer patients. In conclusion, we propose to apply our extension to the lasso whenever a stringent FDR with a limited FNR is targeted. Copyright

Statistical controversies in clinical research: prognostic gene signatures are not (yet) useful in clinical practice

With the genomic revolution and the era of targeted therapy, prognostic and predictive gene signatures are becoming increasingly important in clinical research. They are expected to assist prognosis assessment and therapeutic decision making. Notwithstanding, an evidence-based approach is needed to bring gene signatures from the laboratory to clinical practice. In early breast cancer, multiple prognostic gene signatures are commercially available without having formally reached the highest levels of evidence-based criteria. We discuss specific concepts for developing and validating a prognostic signature and illustrate them with contemporary examples in breast cancer. When a prognostic signature has not been developed for predicting the magnitude of relative treatment benefit through an interaction effect, it may be wishful thinking to test its predictive value. We propose that new gene signatures be built specifically for predicting treatment effects for future patients and outline an approach for this using a cross-validation scheme in a standard phase III trial. Replication in an independent trial remains essential.

A simulation procedure based on copulas to generate clustered multi-state survival data

Generating survival data with a clustered and multi-state structure is useful to study finite sample properties of multi-state models, competing risks models and frailty models. We propose a simulation procedure based on a copula model for each competing events block, allowing to introduce dependence between times of different transitions and between those of grouped subjects. The effect of simulated frailties and covariates can be added in a proportional hazards way. In order to mimic information from real data, we also propose a method for the tuning of parameters via numerical minimization of a criterion function based on the ratios of target and observed values of median times and of probabilities of competing events. An example is provided on simulation of data mimicking those from a multicenter study on head and neck cancer, where the interest is in studying both time to local relapses and to distant metastases before death. The results demonstrated that data simulated according to our proposed method have characteristics very close to the target values.

Identification of biomarker‐by‐treatment interactions in randomized clinical trials with survival outcomes and high‐dimensional spaces

Stratified medicine seeks to identify biomarkers or parsimonious gene signatures distinguishing patients that will benefit most from a targeted treatment. We evaluated 12 approaches in high‐dimensional Cox models in randomized clinical trials: penalization of the biomarker main effects and biomarker‐by‐treatment interactions (full‐lasso, three kinds of adaptive lasso, ridge+lasso and group‐lasso); dimensionality reduction of the main effect matrix via linear combinations (PCA+lasso (where PCA is principal components analysis) or PLS+lasso (where PLS is partial least squares)); penalization of modified covariates or of the arm‐specific biomarker effects (two‐I model); gradient boosting; and univariate approach with control of multiple testing. We compared these methods via simulations, evaluating their selection abilities in null and alternative scenarios. We varied the number of biomarkers, of nonnull main effects and true biomarker‐by‐treatment interactions. We also proposed a novel measure evaluating the interaction strength of the developed gene signatures. In the null scenarios, the group‐lasso, two‐I model, and gradient boosting performed poorly in the presence of nonnull main effects, and performed well in alternative scenarios with also high interaction strength. The adaptive lasso with grouped weights was too conservative. The modified covariates, PCA+lasso, PLS+lasso, and ridge+lasso performed moderately. The full‐lasso and adaptive lassos performed well, with the exception of the full‐lasso in the presence of only nonnull main effects. The univariate approach performed poorly in alternative scenarios. We also illustrate the methods using gene expression data from 614 breast cancer patients treated with adjuvant chemotherapy.

Adjuvant cisplatin-based chemotherapy in nonsmall-cell lung cancer: new insights into the effect on failure type via a multistate approach

BACKGROUND Adjuvant cisplatin-based chemotherapy has become the standard therapy against resected nonsmall-cell lung cancer (NSCLC). Because of variable results on its late effect, we reanalyze the long-term data of the International Adjuvant Lung Cancer Trial (IALT) to describe in details the role of adjuvant chemotherapy. PATIENTS AND METHODS In the IALT, 1867 patients were randomized between adjuvant cisplatin-based chemotherapy and control, who were followed up for a median of 7.5 years. Of these, 1687 patients were enrolled from 132 centers accepting to report the times to cancer events. We used event history methodology to estimate the effects of adjuvant chemotherapy on the risks of local relapse, distant metastasis, and death. RESULTS Adjuvant chemotherapy was highly effective against local relapses [HR = 0.73; 95% confidence interval (CI) 0.60-0.90; P = 0.003] and nonbrain metastases (HR = 0.79; 95% CI 0.66-0.94; P = 0.008) but not against brain metastases (HR = 1.1; 95% CI 0.82-1.4; P = 0.61). The effect on noncancer mortality was nonsignificant during the first 5 years (HR = 1.1; 95% CI 0.81-1.5; P = 0.29), whereas the risk of noncancer mortality was subsequently higher with treatment (HR = 3.6; 95% CI 2.2-5.9; P < 0.001). This harmful effect, however, potentially concerned only about 2% of the patients at 8 years. CONCLUSION Adjuvant cisplatin-based chemotherapy reduced the risk of local relapse and of nonbrain metastasis, thereby improving survival. This treatment exerted no residual effect on mortality during the first 5 years, but a higher risk of noncancer mortality was found thereafter. Detailed long-term follow-up is strongly recommended for all patients in randomized trials evaluating adjuvant treatments in NSCLC.

Evaluation of Treatment Effect with Paired Failure Times in a Single-Arm Phase II Trial in Oncology

In early phase clinical trials of cytotoxic drugs in oncology, the efficacy is typically evaluated based on the tumor shrinkage. However, this criterion is not always appropriate for more recent cytostatic agents, and alternative endpoints have been proposed. The growth modulation index (GMI), defined as the ratio between the times to progression in two successive treatment lines, has been proposed for a single-arm phase II trials. The treatment effect is evaluated by estimating the rate of patients having a GMI superior to a given threshold. To estimate this rate, we investigated a parametric method based on the distribution of the times to progression and a nonparametric one based on a midrank estimator. Through simulations, we studied their operating characteristics and the impact of different design parameters (censoring, dependence, and distribution) on them. In these simulations, the nonparametric estimator slightly underestimated the rate and had slightly overconservative confidence intervals in some cases. Conversely, the parametric estimator overestimated the rate and had anticonservative confidence intervals in some cases. The nonparametric method appeared to be more robust to censoring than the parametric one. In conclusion, we recommend the nonparametric method, but the parametric method can be used as a supplementary tool.

biospear: an R package for biomarker selection in penalized Cox regression

Summary The R package biospear allows selecting the biomarkers with the strongest impact on survival and on the treatment effect in high-dimensional Cox models, and estimating expected survival probabilities. Most of the implemented approaches are based on penalized regression techniques. Availability and implementation The package is available on the CRAN. (https://CRAN.R-project.org/package=biospear). Contact stefan.michiels@gustaveroussy.fr. Supplementary information Supplementary data are available at Bioinformatics online.

A Poisson approach to the validation of failure time surrogate endpoints in individual patient data meta-analyses:

Surrogate endpoints are often used in clinical trials instead of well-established hard endpoints for practical convenience. The meta-analytic approach relies on two measures of surrogacy: one at the individual level and one at the trial level. In the survival data setting, a two-step model based on copulas is commonly used. We present a new approach which employs a bivariate survival model with an individual random effect shared between the two endpoints and correlated treatment-by-trial interactions. We fit this model using auxiliary mixed Poisson models. We study via simulations the operating characteristics of this mixed Poisson approach as compared to the two-step copula approach. We illustrate the application of the methods on two individual patient data meta-analyses in gastric cancer, in the advanced setting (4069 patients from 20 randomized trials) and in the adjuvant setting (3288 patients from 14 randomized trials).

Incorporation of nested frailties into semiparametric multi-state models.

Proportional hazards models are among the most popular regression models in survival analysis. Multi-state models generalize them by jointly considering different types of events and their interrelations, whereas frailty models incorporate random effects to account for unobserved risk factors, possibly shared by clusters of subjects. The integration of multi-state and frailty methodology is an interesting way to control for unobserved heterogeneity in the presence of complex event history structures and is particularly appealing for multicenter clinical trials. We propose the incorporation of correlated frailties in the transition-specific hazard function, thanks to a nested hierarchy. We studied a semiparametric estimation approach based on maximum integrated partial likelihood. We show in a simulation study that the nested frailty multi-state model improves the estimation of the effect of covariates, as well as the coverage probability of their confidence intervals. We present a case study concerning a prostate cancer multicenter clinical trial. The multi-state nature of the model allows us to evidence the effect of treatment on death taking into account intermediate events.

Testing the treatment effect on competing causes of death in oncology clinical trials

BackgroundChemotherapy is expected to reduce cancer deaths (CD), while possibly being harmful in terms of non-cancer deaths (NCD) because of toxicity. Peto’s log-rank test is popular in the medical literature, but its operating characteristics are barely known. We compared this test to the most common ones in the statistical literature: the cause-specific hazard test and Gray’s test on the hazard of the subdistribution. We investigated for the first time the impact of reclassifications of causes of death (CoD) after recurrences, and of misclassification of CoD.MethodsWe present a simulation study in which we varied the censoring rate and the correlation between CD and NCD times, we generated recurrence times to study the role of the reclassification of CoD, and we added 20% misclassified CoD. We considered four scenarios for the treatment effect: none; none for CD and negative for NCD; positive for CD and none for NCD; positive for CD and negative for NCD. We applied the three tests to a randomized clinical trial evaluating adjuvant chemotherapy in 1,867 patients with non-small-cell lung cancer.ResultsMost often the three tests well preserved their nominal size, Gray’s test did not when the treatment had an effect on the competing CoD. With a high rate of misclassified CoD, Gray’s and the cause-specific tests lost much of their power, whereas the Peto’s test had the highest power. The cause-specific test had inflated size for NCD when the treatment was beneficial for CD with many misclassified CoD, but had the highest power for NCD when the treatment had no effect on CD, and had similar power to Peto’s test for CD when the treatment had no effect on NCD. Gray’s test performed best when the effect on the two CoD was opposite. The higher the censoring, the lower the rejection probabilities of all the tests and the smaller their differences.ConclusionsIn this first head-to-head comparison of the three tests, the cause-specific test often proved to be the most reliable. Comparing results with and without misclassification of the CoD, Peto’s test was the least influenced by the presence of such misclassification.