Competing risks simulation with the survsim R package

Simulating time-to-event data subject to competing risks and clustering: A review and synthesis

Simulation studies play an important role in evaluating the performance of statistical models developed for analyzing complex survival data such as those with competing risks and clustering. This article aims to provide researchers with a basic understanding of competing risks data generation, techniques for inducing cluster-level correlation, and ways to combine them together in simulation studies, in the context of randomized clinical trials with a binary exposure or treatment. We review data generation with competing and semi-competing risks and three approaches of inducing cluster-level correlation for time-to-event data: the frailty model framework, the probability transform, and Moran's algorithm. Using exponentially distributed event times as an example, we discuss how to introduce cluster-level correlation into generating complex survival outcomes, and illustrate multiple ways of combining these methods to simulate clustered, competing and semi-competing risks data with pre-specified correlation values or degree of clustering.

A robust biostatistical method leverages informative but uncertainly determined qPCR data for biomarker detection, early diagnosis, and treatment

As a common medium-throughput technique, qPCR (quantitative real-time polymerase chain reaction) is widely used to measure levels of nucleic acids. In addition to accurate and complete data, experimenters have unavoidably observed some incomplete and uncertainly determined qPCR data because of intrinsically low overall amounts of biological materials, such as nucleic acids present in biofluids. When there are samples with uncertainly determined qPCR data, some investigators apply the statistical complete-case method by excluding the subset of samples with uncertainly determined data from analysis (CO), while others simply choose not to analyze (CNA) these datasets altogether. To include as many observations as possible in analysis for interesting differential changes between groups, some investigators set incomplete observations equal to the maximum quality qPCR cycle (MC), such as 32 and 40. Although straightforward, these methods may decrease the sample size, skew the data distribution, and compromise statistical power and research reproducibility across replicate qPCR studies. To overcome the shortcomings of the existing, commonly-used qPCR data analysis methods and to join the efforts in advancing statistical analysis in rigorous preclinical research, we propose a robust nonparametric statistical cycle-to-threshold method (CTOT) to analyze incomplete qPCR data for two-group comparisons. CTOT incorporates important characteristics of qPCR data and time-to-event statistical methodology, resulting in a novel analytical method for qPCR data that is built around good quality data from all subjects, certainly determined or not. Considering the benchmark full data (BFD), we compared the abilities of CTOT, CO, MC, and CNA statistical methods to detect interesting differential changes between groups with informative but uncertainly determined qPCR data. Our simulations and applications show that CTOT improves the power of detecting and confirming differential changes in many situations over the three commonly used methods without excess type I errors. The robust nonparametric statistical method of CTOT helps leverage qPCR technology and increase the power to detect differential changes that may assist decision making with respect to biomarker detection and early diagnosis, with the goal of improving the management of patient healthcare.

We need stronger evidence for (or against) hepatocellular carcinoma surveillance

Current guidelines from EASL recommend that most patients with cirrhosis are offered surveillance for hepatocellular carcinoma (HCC), but fewer patients than expected actually receive it. The recommendation is based on observational studies and simulations, not randomised trials. In this opinion piece we argue that a randomised trial of HCC surveillance vs. no surveillance is necessary and feasible, and we believe that clinician and patient participation in HCC surveillance would be better if it were based on trial results demonstrating its value.

Quantitative assessment of adverse events in clinical trials: Comparison of methods at an interim and the final analysis

In clinical study reports (CSRs), adverse events (AEs) are commonly summarized using the incidence proportion (IP). IPs can be calculated for all types of AEs and are often interpreted as the probability that a treated patient experiences specific AEs. Exposure time can be taken into account with time-to-event methods. Using one minus Kaplan-Meier (1-KM) is known to overestimate the AE probability in the presence of competing events (CEs). The use of a nonparametric estimator of the cumulative incidence function (CIF) has therefore been advocated as more appropriate. In this paper, we compare different methods to estimate the probability of one selected AE. In particular, we investigate whether the proposed methods provide a reasonable estimate of the AE probability at an interim analysis (IA). The characteristics of the methods in the presence of a CE are illustrated using data from a breast cancer study and we quantify the potential bias in a simulation study. At the final analysis performed for the CSR, 1-KM systematically overestimates and in most cases IP slightly underestimates the given AE probability. CIF has the lowest bias in most simulation scenarios. All methods might lead to biased estimates at the IA except for AEs with early onset. The magnitude of the bias varies with the time-to-AE and/or CE occurrence, the selection of event-specific hazards and the amount of censoring. In general, reporting AE probabilities for prespecified fixed time points is recommended.

Competing-risks model for predicting the prognosis of penile cancer based on the SEER database

Objectives

This study performed a competing‐risks analysis using data from the SEER database on penile cancer patients with the aim of identifying more accurate prognostic factors.

Methods

Data on patients with penile cancer were extracted from the SEER database. A univariate analysis used the cumulative incidence function and Gray's test, while multivariate analysis was performed using the Fine‐Gray model. Cumulative hazards were compared with a competing‐risks model constructed using Kaplan‐Meier estimation.

Results

The multivariate Fine‐Gray analysis indicated that being black (HR = 1.51, 95%CI: 1.10‐2.07, P = .01), AJCC stage II (HR = 1.94, 95%CI: 1.36‐2.77, P < .001), AJCC stage III (HR = 1.98, 95%CI: 1.34‐2.91, P < .001), tumor size > 5 cm (HR = 2.23, 95%CI: 1.33‐3.72, P < .05), and TNM stages N1 (HR = 2.49, 95%CI: 1.71‐3.61, P < .001), N2 (HR = 3.25, 95%CI: 2.18‐4.84, P < .001), N3 (HR = 5.05, 95%CI: 2.69‐9.50, P < .001), and M1 (HR = 2.21, 95%CI: 1.28‐3.84, P < .05) were statistically significant. The results obtained using multivariate Cox regression were different, while Kaplan‐Meier curve analysis led to an overestimation of the cumulative risk of the patient.

Conclusions

This study established a competing‐risks analysis model for the first time based on the SEER database for the risk assessment of penile cancer patients. The results may help clinicians to better understand penile cancer and provide these patients with more appropriate support.

Tree-based models for survival data with competing risks

OBJECTIVE

Tree-based models belong to common, assumption-free methods of data analysis. Their application in survival data is narrowed to univariate models, which partition the feature space with axis-parallel hyperplanes, meaning that each internal node involves a single feature. In this paper, I extend the idea of oblique survival tree induction for competing risks by modifying a piecewise-linear criterion function. Additionally, the use of tree-based ensembles to analyze the competing events is proposed.

METHOD AND MATERIALS

Two types of competing risks trees are proposed: a single event tree designed for analysis of the event of interest and a composite event tree, in which all the competing events are taken into account. The induction process is similar, except that the calculation of the criterion function is minimized for the individual tree nodes generation. These two tree types were also used for building the ensembles with aggregated cumulative incidence functions as an outcome. Nine real data sets, as well as a simulated data set, were taken to assess performance of the models, while detailed analysis was conducted on the basis of follicular cell lymphoma data.

RESULTS

The evaluation was focused on two measures: the prediction error expressed by an integrated Brier score (IBS), and the ranked measure of predictive ability calculated as a time-truncated concordance index (C-index). The proposed techniques were compared with the existing approaches of the Fine-Gray subdistribution hazard model, Fine-Gray regression model with backward elimination, and random survival forest for competing risks. The results for both the IBS and the C-index indicated statistically significant differences between these methods (p < .0001).

CONCLUSIONS

The prediction error of the individual trees was similar to the other methods, but the results of the C-index differ in comparison to the Fine-Gray subdistribution hazard model and the Fine-Gray regression with backward elimination. The ensembles prediction ability was comparable to existing algorithms, but their IBS values were better than either random survival forest or Fine-Gray regression with backward elimination.