Sample size calculations for single-arm survival studies using transformations of the Kaplan-Meier estimator.

PRO13 Nice Assessment of Orphan Treatments Supported By Single-Arm Trials

6576 Background: The aim of phase II trials is to determine if a new treatment is promising for further testing in confirmatory clinical trials. Most phase II clinical trials are designed as single-arm trials using a binary outcome with or without interim monitoring for early stopping. In this context, we propose a Bayesian adaptive design denoted as PSSD, predictive sample size selection design (Statistics in Medicine 2012;31:4243-4254). Methods: The design allows for sample size selection followed by any planned interim analyses for early stopping of a trial, together with sample size determination before starting the trial. In the PSSD, we determined the sample size using the predictive probability criterion with two kinds of prior distributions, that is, an ‘analysis prior’ used to compute posterior probabilities and a ‘design prior’ used to obtain prior predictive distributions. In the sample size determination, we provide two sample sizes, that is, N and Nmax, using two types of design priors. At each interim analysis, we calculate the predictive probability of achieving a successful result at the end of the trial using analysis prior in order to stop the trial in case of low or high efficacy, and we select an optimal sample size, that is, either N or Nmax as needed, on the basis of the predictive probabilities. Results: We investigated the operating characteristics through simulation studies, and the PSSD retrospectively applies to a lung cancer clinical trial. As the number of interim looks increases, the probability of type I errors slightly decreases, and that of type II errors increases. The type I error probabilities of the probabilities of the proposed PSSD are almost similar to those of the non-adaptive design. The type II error probabilities in the PSSD are between those of the two fixed sample size (N or Nmax) designs. Conclusions: From a practical standpoint, the proposed design could be useful in phase II single-arm clinical trials with a binary endpoint. In the near future, this approach will be implemented in actual clinical trials to assess its usefulness and to extend it to more complicated clinical trials.

This manuscript consists of two topics. Firstly, we explore the utility of internal pilot study (IPS) approach for reestimating sample size at an interim stage when a reliable estimate of the nuisance shape parameter of the Weibull distribution for modeling survival data is unavailable during the planning phase of a study. Although IPS approach can help rescue the study power, it is noted that the adjusted sample size can be as much as twice the initially planned sample size, which may put substantial practical constraints to continue the study. Secondly, we discuss Bayesian predictive probability for conducting interim analyses to obtain preliminary evidence of efficacy or futility of an experimental treatment warranting early termination of a clinical trial. In the context of single-arm clinical trials with time-to-event endpoints following Weibull distribution, we present the calculation of the Bayesian predictive probability when the shape parameter of the Weibull distribution is unknown. Based on the data accumulated at the interim, we propose two approaches which rely on the posterior mode or the entire posterior distribution of the shape parameter. To account for uncertainty in the shape parameter, it is recommended to incorporate its entire posterior distribution in our calculation.

Considerations of sample size in medical research

294 Background: Economic evaluations in oncology aim to assess the value of new therapies in the long term based on clinical trial data that often have restricted follow-up times (< 5 years) and small sample sizes (< 500 patients). This requires the use of extrapolation assumptions on long-term survival that go beyond the observed data. In this analysis, differences in survival extrapolation methods are tested in samples of sizes and follow-up reflecting typical clinical trials against a background of known survival in prostate cancer from a US based cancer registry. Methods: Data from the National Cancer Institute's Surveillance Epidemiology and End Results (SEER) registry on long-term survival in patients with stage IV prostate cancer were employed. The data set comprised those patients diagnosed between 1988 and 2003, with follow-up data available until 2012. Additional survival for those who received surgery (compared to those who did not), was estimated based on extrapolations using standard parametric statistical models (exponential, Weibull, log-logistic, log-normal, Gamma) fitted to the observed data. Survival analyses were run for 5 sample size scenarios (n = 27,670, 1000, 500, 200, 50) and 6 follow-up scenarios (follow-up years = 25, 20, 10, 5, 2, 1) yielding 30 combination scenarios. Performance of the methods was tested relative to the maximum follow-up, maximum sample size scenario (i.e. reference case) from the SEER registry. Results: Log-logistic and log-normal models were associated with flat tails which led to inflated survival estimations. For scenarios with smaller sizes, gamma models often did not converge. Exponential models were the most frequently reported as best model fit (in approximately 50% of scenarios). Also, gains in OS were consistent when exponential models were selected, and closely matched gain in OS from the reference case. Conclusions: Since clinical trials in oncology are often associated with small patient sample sizes and restricted follow-up, selecting an exponential model may lead to the most consistent and stable results based on the experiment constructed here. Further research should confirm these results for other types of cancer.

Optimal continuous-monitoring design of single-arm phase II trial based on the simulated annealing method

Describe and compare the clinical evidence, post-marketing requirements, and regulatory outcomes of all anticancer drugs that have obtained conditional or accelerated approval based on single-arm trial data in China and the United States. This paper took all the anticancer drugs that had received accelerated or conditional approval based on single-arm trials in the United States and China as of August 31, 2025, as a research sample, and conducted a comparative analysis of the approval status based on single-arm trials in the United States and China from three aspects: the clinical evidence for the accelerated or conditional approval, the conditions attached to the marketing, and the regulatory outcomes. Regarding clinical evidence, the phase and number of pivotal clinical trials and sample size in China and the United States were similar, with significant differences in geographic distribution and supporting evidence. In terms of the conditions attached to marketing, there were significant differences between the United States and China in the purpose and confirmatory trial design requirements. In terms of regulatory outcomes, significant differences existed in the time taken to convert to regular approval (RA) and the response rate (RR) of anticancer drugs converted to regular approval in China and the United States. Among these drugs, those simultaneously granted accelerated or conditional approval in both countries based on single-arm trials experienced a significant approval lag in China. Only two conditional approvals were withdrawn in China. At the same time, there was a statistically significant difference between the RR values of anticancer drugs withdrawn in the United States due to unproven clinical benefits and those withdrawn for other reasons. There are substantial differences between the United States and China across multiple aspects. Compared with the experience of the United States for more than 30years, China is still in the initial stage, and it is advisable for China to thoroughly learn from the experiences and lessons of the United States to optimize its conditional approval pathway for anticancer drugs supported by single-arm trials.

In contrast to isocitrate dehydrogenase (IDH) mutation analysis, which is homogenous within a given tumor, diagnostic errors in histological analysis following the 2016 World Health Organization (WHO) classification could be due to small samples because of histological heterogeneity. To assess whether the sample size sent to histopathology influences the tumor grading in IDH wild-type gliomas. Histologically diagnosed WHO grade, sample volume, and preoperative tumor volume data of 111 patients aged who received resection of IDHwt gliomas between January 2007 and December 2015 at our hospital were evaluated. The differences between absolute and relative pathological sample sizes stratified by WHO grade were conducted using One-Way-Permutation-Test. With a mean sample size of 10.9 cc, 83.8% of patients were histologically diagnosed as WHO grade IV, while 16.2% of patients with a mean sample size of 2.62 cc were diagnosed as WHO grade II/III. One-Way-Permutation-Test showed a significant difference between absolute tissue samples stratified by WHO grade (P=.0374). The distribution of preoperative tumor volumes with WHO grade IV vs WHO grade II/III showed no significant difference (P=.8587). Of all tumors with a sample size>10 cc 100% were pathologically diagnosed as WHO grade IV and those with sample size>5 cc 93.5% were diagnosed as WHO grade IV. Small sample sizes are associated with a higher risk of under-estimating malignancy in histological grading in IDHwt gliomas. This study suggests a standard minimum sample size (>5cc) in every resection. Modalities of adjuvant treatment for IDHwt, WHO grade II/III gliomas need to reflect a prognosis that is only marginally better than of a glioblastoma.

We discuss different methods of sample size calculation for two independent means, aiming to provide insight into the calculation of sample size at the design stage of a parallel two-arm randomised controlled trial (RCT). We compare different methods for sample size calculation, using published results from a previous RCT. We use variances and correlation coefficients to compare sample sizes using different methods, including1. The choice of the primary outcome measure: post-intervention score vs. change from baseline score.2. The choice of statistical methods: t-test without using correlation coefficients vs. analysis of covariance (ANCOVA).We show that the required sample size will depend on whether the outcome measure is the post-intervention score, or the change from baseline score, with or without baseline score included as a covariate. We show that certain assumptions have to be met when using simplified sample size equations, and discuss their implications in sample size calculation when planning an RCT. We strongly recommend publishing the crucial result “mean change (SE, standard error)” in a study paper, because it allows (i) the calculation of the variance of the change score in each arm, and (ii) to pool the variances from both arms. It also enables us to calculate the correlation coefficient in each arm. This subsequently allows us to calculate sample size using change score as the outcome measure. We use simulation to demonstrate how sample sizes by different methods are influenced by the strength of the correlation.

We propose a non-parametric approach to reduce the overestimation of the Kaplan-Meier (KM) estimator when the event and censoring times are independent. We adjust the KM estimator based on the interval-specific censoring set, a collection of intervals where censored data are observed between two adjacent event times. The proposed interval-specific censoring set adjusted KM estimator reduces to the KM estimator if there are no censored observations or the sample size tends to infinity and the proposed estimator is consistent, as is the case for the KM estimator. We prove theoretically that the proposed estimator reduces the overestimation compared to the KM estimator and provide a mathematical formula to estimate the variance of the proposed estimator based on Greenwood's approach. We also provide a modified log-rank test based on the proposed estimator. We perform four simulation studies to compare the proposed estimator with the KM estimator when the failure rate is constant, decreasing, increasing, and based on the flexible hazard method. The bias reduction in median survival time and survival rate using the proposed estimator is considerably large, especially when the censoring rate is high. The standard deviations are comparable between the two estimators. We implement the proposed and KM estimator for the Nonalcoholic Fatty Liver Disease patients from a population study. The results show the proposed estimator substantially reduce the overestimation in the presence of high observed censoring rate.

With recent success in supervised learning, artificial intelligence (AI) and machine learning (ML) can play a vital role in precision medicine. Deep learning neural networks have been used in drug discovery when larger data is available. However, applications of machine learning in clinical trials with small sample size (around a few hundreds) are limited. We propose a Similarity-Principle-Based Machine Learning (SBML) method, which is applicable for small and large sample size problems. In SBML, the attribute-scaling factors are introduced to objectively determine the relative importance of each attribute (predictor). The gradient method is used in learning (training), that is, updating the attribute-scaling factors. We evaluate SBML when the sample size is small and investigate the effects of tuning parameters. Simulations show that SBML achieves better predictions in terms of mean squared errors for various complicated nonlinear situations than full linear models, optimal and ridge regressions, mixed effect models, support vector machine and decision tree methods.

Reasonable prediction makes significant practical sense to stochastic and unstable time series analysis with small or limited sample size. Motivated by the rolling idea in grey theory and the practical relevance of very short‐term forecasting or 1‐step‐ahead prediction, a novel autoregressive (AR) prediction approach with rolling mechanism is proposed. In the modeling procedure, a new developed AR equation, which can be used to model nonstationary time series, is constructed in each prediction step. Meanwhile, the data window, for the next step ahead forecasting, rolls on by adding the most recent derived prediction result while deleting the first value of the former used sample data set. This rolling mechanism is an efficient technique for its advantages of improved forecasting accuracy, applicability in the case of limited and unstable data situations, and requirement of little computational effort. The general performance, influence of sample size, nonlinearity dynamic mechanism, and significance of the observed trends, as well as innovation variance, are illustrated and verified with Monte Carlo simulations. The proposed methodology is then applied to several practical data sets, including multiple building settlement sequences and two economic series.

Sample size, namely the number of subjects that should be included in a study to reach the desired endpoint and statistical power, is a fundamental concept of scientific research. Indeed, sample size must be planned a priori, and tailored to the main endpoint of the study, to avoid including too many subjects, thus possibly exposing them to additional risks while also wasting time and resources, or too few subjects, failing to reach the desired purpose. We offer a simple, go-to review of methods for sample size calculation for studies concerning data reliability (repeatability/reproducibility) and diagnostic performance. For studies concerning data reliability, we considered Cohen’s κ or intraclass correlation coefficient (ICC) for hypothesis testing, estimation of Cohen’s κ or ICC, and Bland-Altman analyses. With regards to diagnostic performance, we considered accuracy or sensitivity/specificity versus reference standards, the comparison of diagnostic performances, and the comparisons of areas under the receiver operating characteristics curve. Finally, we considered the special cases of dropouts or retrospective case exclusions, multiple endpoints, lack of prior data estimates, and the selection of unusual thresholds for α and β errors. For the most frequent cases, we provide example of software freely available on the Internet.Relevance statement Sample size calculation is a fundamental factor influencing the quality of studies on repeatability/reproducibility and diagnostic performance in radiology.Key points• Sample size is a concept related to precision and statistical power.• It has ethical implications, especially when patients are exposed to risks.• Sample size should always be calculated before starting a study.• This review offers simple, go-to methods for sample size calculations.Graphical

The high throughput RNA sequencing (RNA-seq) technology has become the popular method of choice for transcriptomics and the detection of differentially expressed genes. Sample size calculations for RNA-seq experimental design are an important consideration in biological research and clinical trials. Currently, the sample size formulas derived from the Wald and the likelihood ratio statistical tests with a Poisson distribution to model RNA-seq data have been developed. However, since the mean read counts in the real RNA-seq data are not equal to the variance, an extended method to calculate sample sizes based on a negative binomial distribution using an exact test statistic was proposed by Li et al. in 2013. In this study, we alternatively derive five sample size calculation methods based on the negative binomial distribution using the Wald test, the log-transformed Wald test and the log-likelihood ratio test statistics. A comparison of our five methods and an existing method was performed by calculating the sample sizes and the simulated power in different scenarios. We first calculated the sample sizes for testing a single gene using the six methods given a nominal significance level α at 0.05 and 80% power. Then, we calculated the sample sizes for testing multiple genes given a false discovery rate (FDR) at 0.05 and 0.10. The empirical power and true prognostic genes for differential gene expression analysis corresponding to the estimated sample sizes from the six methods are also estimated via the simulation studies. Using the sample size formulas derived from log-transformed and Wald-based tests, we observed smaller sample properties while maintaining the nominal power close to or higher than 80% in all the settings compared to other methods. Moreover, the Wald test based sample size calculation method is easier to compute and faster in an RNA-seq experimental design.

Effect of high-flow oxygen therapy on regional oxygen saturation during vaso-occlusive pain crisis: An observational study.