Inaccuracy of the log-rank approximation in cancer data analysis.
Ontology highlight
ABSTRACT:
SUBMITTER: Rappoport N
PROVIDER: S-EPMC6690426 | biostudies-literature | 2019 Aug
REPOSITORIES: biostudies-literature
Publications
Inaccuracy of the log-rank approximation in cancer data analysis.
Rappoport Nimrod N Shamir Ron R
Molecular systems biology 20190801 8
The log-rank test statistic is very broadly used in biology. Unfortunately, P-values based on the popular chi-square approximation are often inaccurate and can be misleading. ...[more]
Similar Datasets
Project description:Recurrent events data are frequently encountered in clinical trials. This article develops robust covariate-adjusted log-rank statistics applied to recurrent events data with arbitrary numbers of events under independent censoring and the corresponding sample size formula. The proposed log-rank tests are robust with respect to different data-generating processes and are adjusted for predictive covariates. It reduces to the Kong and Slud (1997, Biometrika 84, 847-862) setting in the case of a single event. The sample size formula is derived based on the asymptotic normality of the covariate-adjusted log-rank statistics under certain local alternatives and a working model for baseline covariates in the recurrent event data context. When the effect size is small and the baseline covariates do not contain significant information about event times, it reduces to the same form as that of Schoenfeld (1983, Biometrics 39, 499-503) for cases of a single event or independent event times within a subject. We carry out simulations to study the control of type I error and the comparison of powers between several methods in finite samples. The proposed sample size formula is illustrated using data from an rhDNase study.
| S-EPMC2795392 | biostudies-literature
Project description:Gene set analysis is widely used to facilitate biological interpretations in the analyses of differential expression from high throughput profiling data. Wilcoxon Rank-Sum (WRS) test is one of the commonly used methods in gene set enrichment analysis. It compares the ranks of genes in a gene set against those of genes outside the gene set. This method is easy to implement and it eliminates the dichotomization of genes into significant and non-significant in a competitive hypothesis testing. Due to the large number of genes being examined, it is impractical to calculate the exact null distribution for the WRS test. Therefore, the normal distribution is commonly used as an approximation. However, as we demonstrate in this paper, the normal approximation is problematic when a gene set with relative small number of genes is tested against the large number of genes in the complementary set. In this situation, a uniform approximation is substantially more powerful, more accurate, and less intensive in computation. We demonstrate the advantage of the uniform approximations in Gene Ontology (GO) term analysis using simulations and real data sets.
| S-EPMC3274536 | biostudies-literature
Project description:In the era of open data, Poisson and other count regression models are increasingly important. Still, conventional Poisson regression has remaining issues in terms of identifiability and computational efficiency. Especially, due to an identification problem, Poisson regression can be unstable for small samples with many zeros. Provided this, we develop a closed-form inference for an over-dispersed Poisson regression including Poisson additive mixed models. The approach is derived via mode-based log-Gaussian approximation. The resulting method is fast, practical, and free from the identification problem. Monte Carlo experiments demonstrate that the estimation error of the proposed method is a considerably smaller estimation error than the closed-form alternatives and as small as the usual Poisson regressions. For counts with many zeros, our approximation has better estimation accuracy than conventional Poisson regression. We obtained similar results in the case of Poisson additive mixed modeling considering spatial or group effects. The developed method was applied for analyzing COVID-19 data in Japan. This result suggests that influences of pedestrian density, age, and other factors on the number of cases change over periods.
| S-EPMC8741021 | biostudies-literature
Project description:MotivationLog rank test is a widely used test that serves to assess the statistical significance of observed differences in survival, when comparing two or more groups. The log rank test is based on several assumptions that support the validity of the calculations. It is naturally assumed, implicitly, that no errors occur in the labeling of the samples. That is - that the mapping between samples and groups is perfectly correct. In this work we investigate how test results may be affected when considering some errors in the original labeling.ResultsWe introduce and define the uncertainty that arises from labeling errors in log rank test. In order to deal with this uncertainty, we develop a novel algorithm for efficiently calculating a stability interval around the original log rank p-value and prove its correctness. We demonstrate our algorithm on several datasets.AvailabilityWe provide a Python implementation, called LoRSI, for calculating the stability interval using our algorithm. https://github.com/YakhiniGroup/LoRSI.Supplementary informationSupplementary data are available at Bioinformatics online.
| S-EPMC8652036 | biostudies-literature
Project description:Pharmacometric models using lognormal distributions have become commonplace in pharmacokinetic-pharmacodynamic investigations. The extent to which it can be interpreted by traditional description of variability through the normal distribution remains elusive. In this tutorial, the comparison is made using formal approximation methods. The quality of the resulting approximation was assessed by the similarity of prediction intervals (PIs) to true values, illustrated using 80% PIs. Approximated PIs were close to true values when lognormal standard deviation (omega) was smaller than about 0.25, depending mostly on the desired precision. With increasing omega values, the precision of approximation worsens and starts to deteriorate at omega values of about 1. With such high omega values, there is no resemblance between the lognormal and normal distribution anymore. To support dissemination and interpretation of these nonlinear properties, some additional statistics are discussed in the context of the three regions of behavior of the lognormal distribution.
| S-EPMC7239339 | biostudies-literature
Project description:Whereas the theory of confirmatory adaptive designs is well understood for uncensored data, implementation of adaptive designs in the context of survival trials remains challenging. Commonly used adaptive survival tests are based on the independent increments structure of the log-rank statistic. This implies some relevant limitations: On the one hand, essentially only the interim log-rank statistic may be used for design modifications (such as data-dependent sample size recalculation). Furthermore, the treatment arm allocation ratio in these classical methods is assumed to be constant throughout the trial period. Here, we propose an extension of the independent increments approach to adaptive survival tests that addresses some of these limitations. We present a confirmatory adaptive two-sample log-rank test that allows rejection regions and sample size recalculation rules to be based not only on the interim log-rank statistic, but also on point-wise survival rate estimates, simultaneously. In addition, the possibility is opened to adapt the treatment arm allocation ratio after each interim analysis in a data-dependent way. The ability to include point-wise survival rate estimators in the rejection region of a test for comparing survival curves might be attractive, e.g., for seamless phase II/III designs. Data-dependent adaptation of the allocation ratio could be helpful in multi-arm trials in order to successively steer recruitment into the study arms with the greatest chances of success. The methodology is motivated by the LOGGIC Europe Trial from pediatric oncology. Distributional properties are derived using martingale techniques in the large sample limit. Small sample properties are studied by simulation.
| S-EPMC8649467 | biostudies-literature
Project description:BackgroundCopy number variation (CNV) analysis has become one of the most important research areas for understanding complex disease. With increasing resolution of array-based comparative genomic hybridization (aCGH) arrays, more and more raw copy number data are collected for multiple arrays. It is natural to realize the co-existence of both recurrent and individual-specific CNVs, together with the possible data contamination during the data generation process. Therefore, there is a great need for an efficient and robust statistical model for simultaneous recovery of both recurrent and individual-specific CNVs.ResultWe develop a penalized weighted low-rank approximation method (WPLA) for robust recovery of recurrent CNVs. In particular, we formulate multiple aCGH arrays into a realization of a hidden low-rank matrix with some random noises and let an additional weight matrix account for those individual-specific effects. Thus, we do not restrict the random noise to be normally distributed, or even homogeneous. We show its performance through three real datasets and twelve synthetic datasets from different types of recurrent CNV regions associated with either normal random errors or heavily contaminated errors.ConclusionOur numerical experiments have demonstrated that the WPLA can successfully recover the recurrent CNV patterns from raw data under different scenarios. Compared with two other recent methods, it performs the best regarding its ability to simultaneously detect both recurrent and individual-specific CNVs under normal random errors. More importantly, the WPLA is the only method which can effectively recover the recurrent CNVs region when the data is heavily contaminated.
| S-EPMC4676147 | biostudies-literature
Project description:BackgroundLocal similarity analysis (LSA) of time series data has been extensively used to investigate the dynamics of biological systems in a wide range of environments. Recently, a theoretical method was proposed to approximately calculate the statistical significance of local similarity (LS) scores. However, the method assumes that the time series data are independent identically distributed, which can be violated in many problems.ResultsIn this paper, we develop a novel approach to accurately approximate statistical significance of LSA for dependent time series data using nonparametric kernel estimated long-run variance. We also investigate an alternative method for LSA statistical significance approximation by computing the local similarity score of the residuals based on a predefined statistical model. We show by simulations that both methods have controllable type I errors for dependent time series, while other approaches for statistical significance can be grossly oversized. We apply both methods to human and marine microbial datasets, where most of possible significant associations are captured and false positives are efficiently controlled.ConclusionsOur methods provide fast and effective approaches for evaluating statistical significance of dependent time series data with controllable type I error. They can be applied to a variety of time series data to reveal inherent relationships among the different factors.
| S-EPMC6348690 | biostudies-literature
Project description:In confirmatory cancer clinical trials, overall survival (OS) is normally a primary endpoint in the intention-to-treat (ITT) analysis under regulatory standards. After the tumor progresses, it is common that patients allocated to the control group switch to the experimental treatment, or another drug in the same class. Such treatment switching may dilute the relative efficacy of the new drug compared to the control group, leading to lower statistical power. It would be possible to decrease the estimation bias by shortening the follow-up period but this may lead to a loss of information and power. Instead we propose a modified weighted log-rank test (mWLR) that aims at balancing these factors by down-weighting events occurring when many patients have switched treatment. As the weighting should be pre-specified and the impact of treatment switching is unknown, we predict the hazard ratio function and use it to compute the weights of the mWLR. The method may incorporate information from previous trials regarding the potential hazard ratio function over time. We are motivated by the RECORD-1 trial of everolimus against placebo in patients with metastatic renal-cell carcinoma where almost 80% of the patients in the placebo group received everolimus after disease progression. Extensive simulations show that the new test gives considerably higher efficiency than the standard log-rank test in realistic scenarios.
| S-EPMC8592474 | biostudies-literature
Project description:Microbiome composition data collected through amplicon sequencing are count data on taxa in which the total count per sample (the library size) is an artefact of the sequencing platform, and as a result, such data are compositional. To avoid library size dependency, one common way of analysing multivariate compositional data is to perform a principal component analysis (PCA) on data transformed with the centred log-ratio, hereafter called a log-ratio PCA. Two aspects typical of amplicon sequencing data are the large differences in library size and the large number of zeroes. In this study, we show on real data and by simulation that, applied to data that combine these two aspects, log-ratio PCA is nevertheless heavily dependent on the library size. This leads to a reduction in power when testing against any explanatory variable in log-ratio redundancy analysis. If there is additionally a correlation between the library size and the explanatory variable, then the type 1 error becomes inflated. We explore putative solutions to this problem.
| S-EPMC8360050 | biostudies-literature