Informative noncompliance in endpoint trials

Noncompliance with study medications is an important issue in the design of endpoint clinical trials. Including noncompliant patient data in an intention-to-treat analysis could seriously decrease study power. Standard methods for calculating sample size account for noncompliance, but all assume that noncompliance is noninformative, i.e., that the risk of discontinuation is independent of the risk of experiencing a study endpoint. Using data from several published clinical trials (OPTIMAAL, LIFE, RENAAL, SOLVD-Prevention and SOLVD-Treatment), we demonstrate that this assumption is often untrue, and we discuss the effect of informative noncompliance on power and sample size.     

Test equality and sample size calculation based on risk difference in a randomized clinical trial with noncompliance and missing outcomes

In a randomized clinical trial (RCT), noncompliance with an assigned treatment can occur due to serious side effects, while missing outcomes on patients may happen due to patients' withdrawal or loss to follow up. To avoid the possible loss of power to detect a given risk difference (RD) of interest between two treatments, it is essentially important to incorporate the information on noncompliance and missing outcomes into sample size calculation. Under the compound exclusion restriction model proposed elsewhere, we first derive the maximum likelihood estimator (MLE) of the RD among compliers between two treatments for a RCT with noncompliance and missing outcomes and its asymptotic variance in closed form. Based on the MLE with tanh(-1)(x) transformation, we develop an asymptotic test procedure for testing equality of two treatment effects among compliers. We further derive a sample size calculation formula accounting for both noncompliance and missing outcomes for a desired power 1 - beta at a nominal alpha-level. To evaluate the performance of the test procedure and the accuracy of the sample size calculation formula, we employ Monte Carlo simulation to calculate the estimated Type I error and power of the proposed test procedure corresponding to the resulting sample size in a variety of situations. We find that both the test procedure and the sample size formula developed here can perform well. Finally, we include a discussion on the effects of various parameters, including the proportion of compliers, the probability of non-missing outcomes, and the ratio of sample size allocation, on the minimum required sample size.     

Sotorasib in KRASG12C mutated lung cancer: Can we rule out cracking KRAS led to worse overall survival?

The KRAS oncogene is present in up to 25% of solid tumors and for decades had been undruggable. Sotorasib was the first-in-class KRAS inhibitor to reach the US and European market, and its pharmacological inhibition is restricted to the KRAS p.G12C mutation. Sotorasib showed activity (tumor shrinkage) in patients with non-small cell lung cancer harboring this specific mutation, and efficacy was tested in the CodeBreaK 200, open-label, phase 3 trial (NCT04303780). The results were presented in the ESMO 2022 meeting. CodeBreaK 200 found an improvement in the primary endpoint of progression-free survival (PFS), but overall survival, a key secondary endpoint, was not improved. However, critical questions about the trial's design may limit inferences regarding the reported results. The control arm treatment was inferior to the best standard of care. A late protocol modification (which lowered the sample size and allowed a problematic crossover) prohibited the trial from making a determination regarding overall survival. Imbalance in censoring rates, with potential informative censoring, makes PFS estimates unreliable. Quality-of-life data were also limited. Ultimately, CodeBreaK 200 does not clarify how this therapy should be used in practice, and while we maintain cautious enthusiasm for this and other Ras inhibitors, we await more informative trials     

The joint modeling of a longitudinal disease progression marker and the failure time process in the presence of cure

In this paper we present an extension of cure models: to incorporate a longitudinal disease progression marker. The model is motivated by studies of patients with prostate cancer undergoing radiation therapy. The patients are followed until recurrence of the prostate cancer or censoring, with the PSA marker measured intermittently. Some patients are cured by the treatment and are immune from recurrence. A joint-cure model is developed for this type of data, in which the longitudinal marker and the failure time process are modeled jointly, with a fraction of patients assumed to be immune from the endpoint. A hierarchical nonlinear mixed-effects model is assumed for the marker and a time-dependent Cox proportional hazards model is used to model the time to endpoint. The probability of cure is modeled by a logistic link. The parameters are estimated using a Monte Carlo EM algorithm. Importance sampling with an adaptively chosen t-distribution and variable Monte Carlo sample size is used. We apply the method to data from prostate cancer and perform a simulation study. We show that by incorporating the longitudinal disease progression marker into the cure model, we obtain parameter estimates with better statistical properties. The classification of the censored patients into the cure group and the susceptible group based on the estimated conditional recurrence probability from the joint-cure model has a higher sensitivity and specificity, and a lower misclassification probability compared with the standard cure model. The addition of the longitudinal data has the effect of reducing the impact of the identifiability problems in a standard cure model and can help overcome biases due to informative censoring.     

Sample sizes based on the log-rank statistic in complex clinical trials

The log-rank test is frequently used to compare survival curves. While sample size estimation for comparison of binomial proportions has been adapted to typical clinical trial conditions such as noncompliance, lag time, and staggered entry, the estimation of sample size when the log-rank statistic is to be used has not been generalized to these types of clinical trial conditions. This paper presents a method of estimating sample sizes for the comparison of survival curves by the log-rank statistic in the presence of unrestricted rates of noncompliance, lag time, and so forth. The method applies to stratified trials in which the above conditions may vary across the different strata, and does not assume proportional hazards. Power and duration, as well as sample sizes, can be estimated. The method also produces estimates for binomial proportions and the Tarone-Ware class of statistics.     

Accounting for variability in sample size estimation with applications to nonadherence and estimation of variance and effect size

We consider sample size calculations for testing differences in means between two samples and allowing for different variances in the two groups. Typically, the power functions depend on the sample size and a set of parameters assumed known, and the sample size needed to obtain a prespecified power is calculated. Here, we account for two sources of variability: we allow the sample size in the power function to be a stochastic variable, and we consider estimating the parameters from preliminary data. An example of the first source of variability is nonadherence (noncompliance). We assume that the proportion of subjects who will adhere to their treatment regimen is not known before the study, but that the proportion is a stochastic variable with a known distribution. Under this assumption, we develop simple closed form sample size calculations based on asymptotic normality. The second source of variability is in parameter estimates that are estimated from prior data. For example, we account for variability in estimating the variance of the normal response from existing data which are assumed to have the same variance as the study for which we are calculating the sample size. We show that we can account for the variability of the variance estimate by simply using a slightly larger nominal power in the usual sample size calculation, which we call the calibrated power. We show that the calculation of the calibrated power depends only on the sample size of the existing data, and we give a table of calibrated power by sample size. Further, we consider the calculation of the sample size in the rarer situation where we account for the variability in estimating the standardized effect size from some existing data. This latter situation, as well as several of the previous ones, is motivated by sample size calculations for a Phase II trial of a malaria vaccine candidate.     

Blinded Sample Size Recalculation for Normally Distributed Outcomes Using Long‐ and Short‐term Data

Clinical trials are often planned with high uncertainty about the variance of the primary outcome variable. A poor estimate of the variance, however, may lead to an over‐ or underpowered study. In the internal pilot study design, the sample variance is calculated at an interim step and the sample size can be adjusted if necessary. The available recalculation procedures use the data of those patients for sample size recalculation that have already completed the study. In this article, we consider a variance estimator that takes into account both the data at the endpoint and at an intermediate point of the treatment phase. We derive asymptotic properties of this estimator and the relating sample size recalculation procedure. In a simulation study, the performance of the proposed approach is evaluated and compared with the procedure that uses only long‐term data. Simulation results demonstrate that the sample size resulting from the proposed procedure shows in general a smaller variability. At the same time, the Type I error rate is not inflated and the achieved power is close to the desired value.     

Properties of a nonparametric test for early comparison of treatments in clinical trials in the presence of surrogate endpoints

A nonparametric test is derived for comparing treatments with respect to the final endpoint in clinical trials in which the final endpoint has been observed for a random subset of patients, but results are available for a surrogate endpoint for a larger sample of patients. The test is an adaptation of the Wilcoxon-Mann-Whitney two-sample test, with an adjustment that involves a comparison of the ranks of the surrogate endpoints between patients with and without final endpoints. The validity of the test depends on the assumption that the patients with final endpoints represent a random sample of the patients registered in the study. This assumption is viable in trials in which the final endpoint is evaluated at a "landmark" timepoint in the patients' natural history. A small sample simulation study demonstrates that the test has a size that is close to the nominal value for all configurations evaluated. When compared with the conventional test based only on the final endpoints, the new test delivers substantial increases in power only when the surrogate endpoint is highly correlated with the true endpoint. Our research indicates that, in the absence of modeling assumptions, auxiliary information derived from surrogate endpoints can provide significant additional information only under special circumstances.     

Two-stage designs for dose-finding trials with a biologic endpoint using stepwise tests

Summary.   We deal with the design problem of early phase dose-finding clinical trials with monotone biologic endpoints, such as biological measurements, laboratory values of serum level, and gene expression. A specific objective of this type of trial is to identify the minimum dose that exhibits adequate drug activity and shifts the mean of the endpoint from a zero dose to the so-called minimum effective dose. Stepwise test procedures for dose finding have been well studied in the context of nonhuman studies where the sampling plan is done in one stage. In this article, we extend the notion of stepwise testing to a two-stage enrollment plan in an attempt to reduce the potential sample size requirement by shutting down unpromising doses in a futility interim. In particular, we examine four two-stage designs and apply them to design a statin trial with four doses and a placebo in patients with Hodgkin's disease. We discuss the calibration of the design parameters and the implementation of these proposed methods. In the context of the statin trial, a calibrated two-stage design can reduce the average total sample size up to 38% (from 125 to 78) from a one-stage step-down test, while maintaining comparable error rates and probability of correct selection. The price for the reduction in the average sample size is the slight increase in the maximum total sample size from 125 to 130.     

Interim analysis incorporating short‐ and long‐term binary endpoints

Designs incorporating more than one endpoint have become popular in drug development. One of such designs allows for incorporation of short‐term information in an interim analysis if the long‐term primary endpoint has not been yet observed for some of the patients. At first we consider a two‐stage design with binary endpoints allowing for futility stopping only based on conditional power under both fixed and observed effects. Design characteristics of three estimators: using primary long‐term endpoint only, short‐term endpoint only, and combining data from both are compared. For each approach, equivalent cut‐off point values for fixed and observed effect conditional power calculations can be derived resulting in the same overall power. While in trials stopping for futility the type I error rate cannot get inflated (it usually decreases), there is loss of power. In this study, we consider different scenarios, including different thresholds for conditional power, different amount of information available at the interim, different correlations and probabilities of success. We further extend the methods to adaptive designs with unblinded sample size reassessments based on conditional power with inverse normal method as the combination function. Two different futility stopping rules are considered: one based on the conditional power, and one from P‐values based on Z‐statistics of the estimators. Average sample size, probability to stop for futility and overall power of the trial are compared and the influence of the choice of weights is investigated.     

Profiting from pilot studies: Analysing mortality using Bayesian models with informative priors

Pilot studies are often used to help design ecological studies. Ideally the pilot data are incorporated into the full-scale study data, but if the pilot study's results indicate a need for major changes to experimental design, then pooling pilot and full-scale study data is difficult. The default position is to disregard the preliminary data. But ignoring pilot study data after a more comprehensive study has been completed forgoes statistical power or costs more by sampling additional data equivalent to the pilot study's sample size. With Bayesian methods, pilot study data can be used as an informative prior for a model built from the full-scale study dataset. We demonstrate a Bayesian method for recovering information from otherwise unusable pilot study data with a case study on eucalypt seedling mortality. A pilot study of eucalypt tree seedling mortality was conducted in southeastern Australia in 2005. A larger study with a modified design was conducted the following year. The two datasets differed substantially, so they could not easily be combined. Posterior estimates from pilot dataset model parameters were used to inform a model for the second larger dataset. Model checking indicated that incorporating prior information maintained the predictive capacity of the model with respect to the training data. Importantly, adding prior information improved model accuracy in predicting a validation dataset. Adding prior information increased the precision and the effective sample size for estimating the average mortality rate. We recommend that practitioners move away from the default position of discarding pilot study data when they are incompatible with the form of their full-scale studies. More generally, we recommend that ecologists should use informative priors more frequently to reap the benefits of the additional data.     

Linkage analysis of a complex disease through use of admixed populations

Linkage disequilibrium arising from the recent admixture of genetically distinct populations can be potentially useful in mapping genes for complex diseases. McKeigue has proposed a method that conditions on parental admixture to detect linkage. We show that this method tests for linkage only under specific assumptions, such as equal admixture in the parental generation and admixture that occurs in a single generation. In practice, these assumptions are unlikely to hold for natural populations, resulting in an inflation of the type I error rate when testing for linkage by this method. In this article, we generalize McKeigue's approach of testing for linkage to allow two different admixture models: (1) intermixture admixture and (2) continuous gene flow. We calculate the sample size required for a genomewide search by this method under different disease models: multiplicative, additive, recessive, and dominant. Our results show that the sample size required to obtain 90% power to detect a putative mutant allele at a genomewide significance level of 5% can usually be achieved in practice if informative markers are available at a density of 2 cM.     

Optimal adaptive two‐stage designs for phase II cancer clinical trials

In oncology, single‐arm two‐stage designs with binary endpoint are widely applied in phase II for the development of cytotoxic cancer therapies. Simon's optimal design with prefixed sample sizes in both stages minimizes the expected sample size under the null hypothesis and is one of the most popular designs. The search algorithms that are currently used to identify phase II designs showing prespecified characteristics are computationally intensive. For this reason, most authors impose restrictions on their search procedure. However, it remains unclear to what extent this approach influences the optimality of the resulting designs. This article describes an extension to fixed sample size phase II designs by allowing the sample size of stage two to depend on the number of responses observed in the first stage. Furthermore, we present a more efficient numerical algorithm that allows for an exhaustive search of designs. Comparisons between designs presented in the literature and the proposed optimal adaptive designs show that while the improvements are generally moderate, notable reductions in the average sample size can be achieved for specific parameter constellations when applying the new method and search strategy.     

Scombroid Fishes Provide Novel Insights into the Trait/Rate Associations of Molecular Evolution

The study of which life history traits primarily affect molecular evolutionary rates is often confounded by the covariance of these traits. Scombroid fishes (billfishes, tunas, barracudas, and their relatives) are unusual in that their mass-specific metabolic rate is positively associated with body size. This study exploits this atypical pattern of trait variation, which allows for direct tests of whether mass-specific metabolic rate or body size is the more important factor of molecular evolutionary rates. We inferred a phylogeny for scombroids from a supermatrix of molecular and morphological characters and used new phylogenetic comparative approaches to assess the associations of body size and mass-specific metabolic rate with substitution rate. As predicted by the body size hypothesis, there is a negative correlation between body size and substitution rate. However, unexpectedly, we also find a negative association between mass-specific metabolic and substitution rates. These relationships are supported by analyses of the total molecular data, separate mitochondrial and nuclear genes, and individual loci, and they are robust to phylogenetic uncertainty. The molecular evolutionary rates of scombroids are primarily tied to body size. This study demonstrates that groups with novel patterns of trait variation can be particularly informative for identifying which life history traits are the primary factors of molecular evolutionary rates.     

Strategies for selecting subsets of single-nucleotide polymorphisms to genotype in association studies

In genetic association studies, linkage disequilibrium (LD) within a region can be exploited to select a subset of single-nucleotide polymorphisms (SNPs) to genotype with minimal loss of information. A novel entropy-based method for selecting SNPs is proposed and compared to an existing method based on the coefficient of determination (R2) using simulated data from Genetic Analysis Workshop 14. The effect of the size of the sample used to investigate LD (by estimating haplotype frequencies) and hence select the SNPs is also investigated for both measures. It is found that the novel method and the established method select SNP subsets that do not differ greatly. The entropy-based measure may thus have value because it is easier to compute than R2. Increasing the sample size used to estimate haplotype frequencies improves the predictive power of the subset of SNPs selected. A smaller subset of SNPs chosen using a large initial sample to estimate LD can in some instances be more informative than a larger subset chosen based on poor estimates of LD (using a small initial sample). An initial sample size of 50 individuals is sufficient in most situations investigated, which involved selection from a set of 7 SNPs, although to select a larger number of SNPs, a larger initial sample size may be required.     

Comparisons of case-selection approaches based on allele sharing and/or disease severity index: application to the GAW14 simulated data

For mapping complex disease traits, linkage studies are often followed by a case-control association strategy in order to identify disease-associated genes/single-nucleotide polymorphisms (SNPs). Substantial efforts are required in selecting the most informative cases from a large collection of affected individuals in order to maximize the power of the study, while taking into consideration study cost. In this article, we applied and extended three case-selection strategies that use allele-sharing information method for families with multiple affected offspring to select most informative cases using additional information on disease severity. Our results revealed that most significant associations, as measured by the lowest p-values, were obtained from a strategy that selected a case with the most allele sharing with other affected sibs from linked families ("linked-best"), despite reduction in sample size resulting from discarding unlinked families. Moreover, information on disease severity appears to be useful to improve the ability to detect associations between markers and disease loci.     

A robust identity-by-descent procedure using affected sib pairs: multipoint mapping for complex diseases

Multipoint linkage analysis is a powerful tool to localize susceptibility genes for complex diseases. However, the conventional lod score method relies critically on the correct specification of mode of inheritance for accurate estimation of gene position. On the other hand, allele-sharing methods, as currently practiced, are designed to test the null hypothesis of no linkage rather than estimate the location of the susceptibility gene(s). In this paper, we propose an identity-by-descent (IBD)-based procedure to estimate the location of an unobserved susceptibility gene within a chromosomal region framed by multiple markers. Here we deal with the practical situation where some of the markers might not be fully informative. Rather the IBD statistic at an arbitrary within the region is imputed using the multipoint marker information. The method is robust in that no assumption about the genetic mechanism is required other than that the region contains no more than one susceptibility gene. In particular, this approach builds upon a simple representation for the expected IBD at any arbitrary locus within the region using data from affected sib pairs. With this representation, one can carry out a parametric inference procedure to locate an unobserved susceptibility gene. In addition, here we derive a sample size formula for the number of affected sib pairs needed to detect linkage with multiple markers. Throughout, the proposed method is illustrated through simulated data. We have implemented this method including exploratory and formal model-fitting procedures to locate susceptibility genes, plus sample size and power calculations in a program, GENEFINDER, which will be made available shortly.     

Exact sample size needed to detect dependence in 2 x 2 x 2 tables

In the Georgia Centenarian Study (Poon et al., Exceptional Longevity, 2006), centenarian cases and young controls are classified according to three categories (age, ethnic origin, and single nucleotide polymorphisms [SNPs] of candidate longevity genes), where each factor has two possible levels. Here we provide methodologies to determine the minimum sample size needed to detect dependence in 2 x 2 x 2 tables based on Fisher's exact test evaluated exactly or by Markov chain Monte Carlo (MCMC), assuming only the case total L and the control total N are known. While our MCMC method uses serial computing, parallel computing techniques are employed to solve the exact sample size problem. These tools will allow researchers to design efficient sampling strategies and to select informative SNPs. We apply our tools to 2 x 2 x 2 tables obtained from a pilot study of the Georgia Centenarians Study, and the sample size results provided important information for the subsequent major study. A comparison between the results of an exact method and those of a MCMC method showed that the MCMC method studied needed much less computation time on average (10.16 times faster on average for situations examined with S.E. = 2.60), but its sample size results were only valid as a rule for larger sample sizes (in the hundreds).     

A top-r feature selection algorithm for microarray gene expression data

Most of the conventional feature selection algorithms have a drawback whereby a weakly ranked gene that could perform well in terms of classification accuracy with an appropriate subset of genes will be left out of the selection. Considering this shortcoming, we propose a feature selection algorithm in gene expression data analysis of sample classifications. The proposed algorithm first divides genes into subsets, the sizes of which are relatively small (roughly of size h), then selects informative smaller subsets of genes (of size r < h) from a subset and merges the chosen genes with another gene subset (of size r) to update the gene subset. We repeat this process until all subsets are merged into one informative subset. We illustrate the effectiveness of the proposed algorithm by analyzing three distinct gene expression data sets. Our method shows promising classification accuracy for all the test data sets. We also show the relevance of the selected genes in terms of their biological functions.     

Feasibility and Recommendations for Swift Fox Fecal DNA Profiling

Abstract: Genetic profiling using fecal samples collected noninvasively in the wild can provide managers with an alternative to live-trapping. However, before embarking on a large-scale survey, feasibility of this methodology should be assessed for the focal species. Costs associated with fecal genotyping can be high because of the need for multiple amplifications to prevent and detect errors. Assessing the relative amount of target DNA before genotyping means samples can be eliminated where error rates will be high or amplification success will be low, thereby reducing costs. We collected fecal samples from an endangered population of swift fox (Vulpes velox) and employed target-DNA quantification and a screening protocol to assess sample quality before genetic profiling. Quantification was critical in identifying samples of low quality (68%, <0.2 ng/μL). Comparison of the amplification, from a subset of loci in 25 samples that did not meet the screening criteria, confirmed the effectiveness of this method. The protocol, however, used a considerable amount of DNA, and an assessment of the locus and sample variability allowed us to refine it for future population surveys. Although we did not use <50% of the samples we collected, the remaining samples provided 36 unique genotypes, which corresponded to approximately 70% of animals estimated to be present in the study area. Although obtaining fecal DNA from small carnivores is challenging, our protocol, including the quantification and qualification of DNA, the selection of markers, and the use of postgenotyping analyses, such as DROPOUT, CAPWIRE, and geographic information, provides a more cost-effective way to produce reliable results. The method we have developed is an informative approach that wildlife managers can use to conduct population surveys where the collection of feces is possible without the need for live-trapping.