Incorporating individual historical controls and aggregate treatment effect estimates into a Bayesian survival trial: a simulation study.
ABSTRACT: BACKGROUND:Performing well-powered randomised controlled trials (RCTs) of new treatments for rare diseases is often infeasible. However, with the increasing availability of historical data, incorporating existing information into trials with small sample sizes is appealing in order to increase the power. Bayesian approaches enable one to incorporate historical data into a trial's analysis through a prior distribution. METHODS:Motivated by a RCT intended to evaluate the impact on event-free survival of mifamurtide in patients with osteosarcoma, we performed a simulation study to evaluate the impact on trial operating characteristics of incorporating historical individual control data and aggregate treatment effect estimates. We used power priors derived from historical individual control data for baseline parameters of Weibull and piecewise exponential models, while we used a mixture prior to summarise aggregate information obtained on the relative treatment effect. The impact of prior-data conflicts, both with respect to the parameters and survival models, was evaluated for a set of pre-specified weights assigned to the historical information in the prior distributions. RESULTS:The operating characteristics varied according to the weights assigned to each source of historical information, the variance of the informative and vague component of the mixture prior and the level of commensurability between the historical and new data. When historical and new controls follow different survival distributions, we did not observe any advantage of choosing a piecewise exponential model compared to a Weibull model for the new trial analysis. However, we think that it remains appealing given the uncertainty that will often surround the shape of the survival distribution of the new data. CONCLUSION:In the setting of Sarcome-13 trial, and other similar studies in rare diseases, the gains in power and accuracy made possible by incorporating different types of historical information commensurate with the new trial data have to be balanced against the risk of biased estimates and a possible loss in power if data are not commensurate. The weights allocated to the historical data have to be carefully chosen based on this trade-off. Further simulation studies investigating methods for incorporating historical data are required to generalise the findings.
Project description:Bayesian clinical trial designs offer the possibility of a substantially reduced sample size, increased statistical power, and reductions in cost and ethical hazard. However when prior and current information conflict, Bayesian methods can lead to higher than expected type I error, as well as the possibility of a costlier and lengthier trial. This motivates an investigation of the feasibility of hierarchical Bayesian methods for incorporating historical data that are adaptively robust to prior information that reveals itself to be inconsistent with the accumulating experimental data. In this article, we present several models that allow for the commensurability of the information in the historical and current data to determine how much historical information is used. A primary tool is elaborating the traditional power prior approach based upon a measure of commensurability for Gaussian data. We compare the frequentist performance of several methods using simulations, and close with an example of a colon cancer trial that illustrates a linear models extension of our adaptive borrowing approach. Our proposed methods produce more precise estimates of the model parameters, in particular, conferring statistical significance to the observed reduction in tumor size for the experimental regimen as compared to the control regimen.
Project description:In this paper, we develop the fixed-borrowing adaptive design, a Bayesian adaptive design which facilitates information borrowing from a historical trial using subject-level control data while assuring a reasonable upper bound on the maximum type I error rate and lower bound on the minimum power. First, one constructs an informative power prior from the historical data to be used for design and analysis of the new trial. At an interim analysis opportunity, one evaluates the degree of prior-data conflict. If there is too much conflict between the new trial data and the historical control data, the prior information is discarded and the study proceeds to the final analysis opportunity at which time a noninformative prior is used for analysis. Otherwise, the trial is stopped early and the informative power prior is used for analysis. Simulation studies are used to calibrate the early stopping rule. The proposed design methodology seamlessly accommodates covariates in the statistical model, which the authors argue is necessary to justify borrowing information from historical controls. Implementation of the proposed methodology is straightforward for many common data models, including linear regression models, generalized linear regression models, and proportional hazards models. We demonstrate the methodology to design a cardiovascular outcomes trial for a hypothetical new therapy for treatment of type 2 diabetes mellitus and borrow information from the SAVOR trial, one of the earliest cardiovascular outcomes trials designed to assess cardiovascular risk in antidiabetic therapies.
Project description:High-density genetic marker data, especially sequence data, imply an immense multiple testing burden. This can be ameliorated by filtering genetic variants, exploiting or accounting for correlations between variants, jointly testing variants, and by incorporating informative priors. Priors can be based on biological knowledge or predicted variant function, or even be used to integrate gene expression or other omics data. Based on Genetic Analysis Workshop (GAW) 19 data, this article discusses diversity and usefulness of functional variant scores provided, for example, by PolyPhen2, SIFT, or RegulomeDB annotations. Incorporating functional scores into variant filters or weights and adjusting the significance level for correlations between variants yielded significant associations with blood pressure traits in a large family study of Mexican Americans (GAW19 data set). Marker rs218966 in gene PHF14 and rs9836027 in MAP4 significantly associated with hypertension; additionally, rare variants in SNUPN significantly associated with systolic blood pressure. Variant weights strongly influenced the power of kernel methods and burden tests. Apart from variant weights in test statistics, prior weights may also be used when combining test statistics or to informatively weight p values while controlling false discovery rate (FDR). Indeed, power improved when gene expression data for FDR-controlled informative weighting of association test p values of genes was used. Finally, approaches exploiting variant correlations included identity-by-descent mapping and the optimal strategy for joint testing rare and common variants, which was observed to depend on linkage disequilibrium structure.
Project description:Data of previous trials with a similar setting are often available in the analysis of clinical trials. Several Bayesian methods have been proposed for including historical data as prior information in the analysis of the current trial, such as the (modified) power prior, the (robust) meta-analytic-predictive prior, the commensurate prior and methods proposed by Pocock and Murray et al. We compared these methods and illustrated their use in a practical setting, including an assessment of the comparability of the current and the historical data. The motivating data set consists of randomised controlled trials for acute myeloid leukaemia. A simulation study was used to compare the methods in terms of bias, precision, power and type I error rate. Methods that estimate parameters for the between-trial heterogeneity generally offer the best trade-off of power, precision and type I error, with the meta-analytic-predictive prior being the most promising method. The results show that it can be feasible to include historical data in the analysis of clinical trials, if an appropriate method is used to estimate the heterogeneity between trials, and the historical data satisfy criteria for comparability.
Project description:Increasing evidence suggests that single nucleotide polymorphisms (SNPs) associated with complex traits are more likely to be expression quantitative trait loci (eQTLs). Incorporating eQTL information hence has potential to increase power of genome-wide association studies (GWAS). In this paper, we propose using eQTL weights as prior information in SNP based association tests to improve test power while maintaining control of the family-wise error rate (FWER) or the false discovery rate (FDR). We apply the proposed methods to the analysis of a GWAS for childhood asthma consisting of 1296 unrelated individuals with German ancestry. The results confirm that eQTLs are enriched for previously reported asthma SNPs. We also find that some SNPs are insignificant using procedures without eQTL weighting, but become significant using eQTL-weighted Bonferroni or Benjamini-Hochberg procedures, while controlling the same FWER or FDR level. Some of these SNPs have been reported by independent studies in recent literature. The results suggest that the eQTL-weighted procedures provide a promising approach for improving power of GWAS. We also report the results of our methods applied to the large-scale European GABRIEL consortium data.
Project description:We consider the problem of Bayesian sample size determination for a clinical trial in the presence of historical data that inform the treatment effect. Our broadly applicable, simulation-based methodology provides a framework for calibrating the informativeness of a prior while simultaneously identifying the minimum sample size required for a new trial such that the overall design has appropriate power to detect a non-null treatment effect and reasonable type I error control. We develop a comprehensive strategy for eliciting null and alternative sampling prior distributions which are used to define Bayesian generalizations of the traditional notions of type I error control and power. Bayesian type I error control requires that a weighted-average type I error rate not exceed a prespecified threshold. We develop a procedure for generating an appropriately sized Bayesian hypothesis test using a simple partial-borrowing power prior which summarizes the fraction of information borrowed from the historical trial. We present results from simulation studies that demonstrate that a hypothesis test procedure based on this simple power prior is as efficient as those based on more complicated meta-analytic priors, such as normalized power priors or robust mixture priors, when all are held to precise type I error control requirements. We demonstrate our methodology using a real data set to design a follow-up clinical trial with time-to-event endpoint for an investigational treatment in high-risk melanoma.
Project description:During drug evaluation trials, information from clinical trials previously conducted on another population, indications or schedules may be available. In these cases, it might be desirable to share information by efficiently using the available resources. In this work, we developed an adaptive power prior with a commensurability parameter for using historical or external information. It allows, at each stage, full borrowing when the data are not in conflict, no borrowing when the data are in conflict or "tuned" borrowing when the data are in between. We propose to apply our adaptive power prior method to bridging studies between Caucasians and Asians, and we focus on the sequential adaptive allocation design, although other design settings can be used. We weight the prior information in two steps: the effective sample size approach is used to set the maximum desirable amount of information to be shared from historical data at each step of the trial; then, in a sort of Empirical Bayes approach, a commensurability parameter is chosen using a measure of distribution distance. This approach avoids elicitation and computational issues regarding the usual Empirical Bayes approach. We propose several versions of our method, and we conducted an extensive simulation study evaluating the robustness and sensitivity to prior choices.
Project description:We study the temporal variation in the empirical relationships among body size (S), species richness (R), and abundance (A) in a shallow marine epibenthic faunal community in Coliumo Bay, Chile. We also extend previous analyses by calculating individual energy use (E) and test whether its bivariate and trivariate relationships with S and R are in agreement with expectations derived from the energetic equivalence rule. Carnivorous and scavenger species representing over 95% of sample abundance and biomass were studied. For each individual, body size (g) was measured and E was estimated following published allometric relationships. Data for each sample were tabulated into exponential body size bins, comparing species-averaged values with individual-based estimates which allow species to potentially occupy multiple size classes. For individual-based data, both the number of individuals and species across body size classes are fit by a Weibull function rather than by a power law scaling. Species richness is also a power law of the number of individuals. Energy use shows a piecewise scaling relationship with body size, with energetic equivalence holding true only for size classes above the modal abundance class. Species-based data showed either weak linear or no significant patterns, likely due to the decrease in the number of data points across body size classes. Hence, for individual-based size spectra, the SRA relationship seems to be general despite seasonal forcing and strong disturbances in Coliumo Bay. The unimodal abundance distribution results in a piecewise energy scaling relationship, with small individuals showing a positive scaling and large individuals showing energetic equivalence. Hence, strict energetic equivalence should not be expected for unimodal abundance distributions. On the other hand, while species-based data do not show unimodal SRA relationships, energy use across body size classes did not show significant trends, supporting energetic equivalence.
Project description:Bayesian Network (BN) is a powerful approach to reconstructing genetic regulatory networks from gene expression data. However, expression data by itself suffers from high noise and lack of power. Incorporating prior biological knowledge can improve the performance. As each type of prior knowledge on its own may be incomplete or limited by quality issues, integrating multiple sources of prior knowledge to utilize their consensus is desirable.We introduce a new method to incorporate the quantitative information from multiple sources of prior knowledge. It first uses the Naïve Bayesian classifier to assess the likelihood of functional linkage between gene pairs based on prior knowledge. In this study we included cocitation in PubMed and schematic similarity in Gene Ontology annotation. A candidate network edge reservoir is then created in which the copy number of each edge is proportional to the estimated likelihood of linkage between the two corresponding genes. In network simulation the Markov Chain Monte Carlo sampling algorithm is adopted, and samples from this reservoir at each iteration to generate new candidate networks. We evaluated the new algorithm using both simulated and real gene expression data including that from a yeast cell cycle and a mouse pancreas development/growth study. Incorporating prior knowledge led to a ~2 fold increase in the number of known transcription regulations recovered, without significant change in false positive rate. In contrast, without the prior knowledge BN modeling is not always better than a random selection, demonstrating the necessity in network modeling to supplement the gene expression data with additional information.our new development provides a statistical means to utilize the quantitative information in prior biological knowledge in the BN modeling of gene expression data, which significantly improves the performance.
Project description:In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies…). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.