Traditional Frequentist Approach Research Articles

Bayesian survival analysis in clinical trials: What methods are used in practice?

Background Bayesian statistics are an appealing alternative to the traditional frequentist approach to designing, analysing, and reporting of clinical trials, especially in rare diseases. Time-to-event endpoints are widely used in many medical fields. There are additional complexities to designing Bayesian survival trials which arise from the need to specify a model for the survival distribution. The objective of this article was to critically review the use and reporting of Bayesian methods in survival trials. Methods A systematic review of clinical trials using Bayesian survival analyses was performed through PubMed and Web of Science databases. This was complemented by a full text search of the online repositories of pre-selected journals. Cost-effectiveness, dose-finding studies, meta-analyses, and methodological papers using clinical trials were excluded. Results In total, 28 articles met the inclusion criteria, 25 were original reports of clinical trials and 3 were re-analyses of a clinical trial. Most trials were in oncology (n = 25), were randomised controlled (n = 21) phase III trials (n = 13), and half considered a rare disease (n = 13). Bayesian approaches were used for monitoring in 14 trials and for the final analysis only in 14 trials. In the latter case, Bayesian survival analyses were used for the primary analysis in four cases, for the secondary analysis in seven cases, and for the trial re-analysis in three cases. Overall, 12 articles reported fitting Bayesian regression models (semi-parametric, n = 3; parametric, n = 9). Prior distributions were often incompletely reported: 20 articles did not define the prior distribution used for the parameter of interest. Over half of the trials used only non-informative priors for monitoring and the final analysis (n = 12) when it was specified. Indeed, no articles fitting Bayesian regression models placed informative priors on the parameter of interest. The prior for the treatment effect was based on historical data in only four trials. Decision rules were pre-defined in eight cases when trials used Bayesian monitoring, and in only one case when trials adopted a Bayesian approach to the final analysis. Conclusion Few trials implemented a Bayesian survival analysis and few incorporated external data into priors. There is scope to improve the quality of reporting of Bayesian methods in survival trials. Extension of the Consolidated Standards of Reporting Trials statement for reporting Bayesian clinical trials is recommended.

Fisher, Neyman, and Bayes at FDA

ABSTRACTThe wise use of statistical ideas in practice essentially requires some Bayesian thinking, in contrast to the classical rigid frequentist dogma. This dogma too often has seemed to influence the applications of statistics, even at agencies like the FDA. Greg Campbell was one of the most important advocates there for more nuanced modes of thought, especially Bayesian statistics. Because two brilliant statisticians, Ronald Fisher and Jerzy Neyman, are often credited with instilling the traditional frequentist approach in current practice, I argue that both men were actually seeking very Bayesian answers, and neither would have endorsed the rigid application of their ideas.

Dynamic approach to linear statistical calibration with an application in microwave radiometry

ABSTRACTThe problem of statistical calibration of a measuring instrument can be framed both in a statistical context as well as in an engineering context. In the first, the problem is dealt with by distinguishing between the ‘classical’ approach and the ‘inverse’ regression approach. Both of these models are static models and are used to estimate exact measurements from measurements that are affected by error. In the engineering context, the variables of interest are considered to be taken at the time at which you observe it. The Bayesian time series analysis method of Dynamic Linear Models can be used to monitor the evolution of the measures, thus introducing a dynamic approach to statistical calibration. The research presented employs a new approach to performing statistical calibration. A simulation study in the context of microwave radiometry is conducted that compares the dynamic model to traditional static frequentist and Bayesian approaches. The focus of the study is to understand how well the dynamic statistical calibration method performs under various signal-to-noise ratios, r.

Vulnerability to pine sawfly damage decreases with site fertility but the opposite is true with Scleroderris canker damage; results from Finnish ICP Forests and NFI data

The probability of pine sawfly damage was highest in drier sites, while Gremmeniella abietina damage showed an opposite pattern. ICP Forests and rolling National Forest Inventory (NFI) data have good potential for quantifying patterns in damage occurrence, but region-wise NFIs may produce biased results. Factors affecting the occurrence of important biotic damage on Pinus sylvestris were studied with data from large-scale forest monitoring networks. We tested how much the probability of damage caused by pine sawflies (Neodiprion sertifer Geoffr. and Diprion pini L.) and G. abietina (Lagerb. (Morelet)) differed between different forest site types and the effects of relevant climatic factors on damage probabilities. Long-term damage observations from ICP Forests Level 1 monitoring and National Forest Inventory (NFI) data were used. In addition to the traditional frequentist approach, we used a hierarchical Bayesian (HB) framework with the ICP Forests data to model the probabilities of pine sawfly outbreaks starting and continuing. The probability of pine sawfly damage was highest in drier sites while the probabilities for G. abietina damage showed an opposite pattern. The HB analysis revealed clear differences between forest site types in the probability of outbreak starting, but the differences in the probabilities of outbreaks continuing were not clear. ICP Forests and rolling NFI data have good potential for quantifying patterns in damage occurrence, but annually region-wise NFIs may produce biased results.

Comparative Efficacy of Radiofrequency and Laser Ablation for the Treatment of Benign Thyroid Nodules: Systematic Review Including Traditional Pooling and Bayesian Network Meta-analysis

To compare the efficacy of radiofrequency ablation (RFA) and laser ablation (LA) for treatment of benign solid thyroid nodules, using a systematic review including traditional pooling and Bayesian network meta-analysis. A comprehensive literature search in PubMed-MEDLINE, EMBASE, and the Cochrane Library databases identified prospective studies evaluating the percentage mean change [absolute mean change (mL)] in nodule volume after RFA or LA. Studies from January 1, 2000, to November 1, 2013, were included. Review of 128 potential papers, including a full-text review of 33, identified 10 eligible papers covering a total of 184 patients for meta-analysis. The percentage mean change [absolute mean change] in nodule volume over a 6-month follow-up was compared between RFA and LA. Based on the traditional frequentist approach, the pooled percentage mean changes (95% confidence interval) of RFA and LA were 76.1% (70.1-82.1) and 49.9% (41.4-58.5), respectively, and the pooled absolute mean changes (95% confidence interval) of RFA and LA were 8.9 mL (6.6-11.2) and 5.2 mL (4.3-6.1), respectively. Based on the Bayesian network meta-analysis, RFA achieved a larger pooled percentage mean change (95% credible interval) and absolute mean change (95% credible interval) compared to LA [77.8% (67.7-88.0) vs 49.5% (26.7-72.4), and 9.2 mL (5.8-11.9) vs 5.3 mL (2.1-8.5), respectively]. The RFA group has the highest probability of having the most efficacious treatment (98.7%). There were no major complications after either RFA or LA. RFA appears to be superior to LA in reducing benign solid thyroid nodule volume, despite the smaller number of treatment sessions without major side effects.

Métodos de máxima verosimilitud en ecología y su aplicación en modelos de vecindad

Gomez-Aparicio, L., Avila, J.M, Cayuela, L. 2013. Maximum likelihood methods and their application in neighbourhood models. Ecosistemas 22(3):12-20. Doi.: 10.7818/ECOS.2013.22-3.03 Maximum likelihood methods and their application in neighborhood models. Maximum likelihood methods (MLM) offer an alternative framework to the traditional frequentist approach of data analysis, where the use of p-values to reject a single null (usually trivial) hypothesis is replaced by the use of likelihoods to evaluate the support in the data for a set of alternative working hypotheses of scientific relevance. These methods have been widely applied in the ecological framework of the neighborhood models. These models use a spatially-explicit approach to describe demographic or ecosystem processes as a function of the attributes of neighboring plants. They are therefore phenomenological models that serve as a tool of synthesis of the multiple mechanisms by which species can interact and modify its immediate environment, offering an estimate of the per-capita influence of individuals of different characteristics (e.g. size, species, functional traits) on the processes of study. A fundamental advantage of applying MMV in the framework of the neighborhood models is that it allows fitting and comparing multiple models that use contrasting neighbor attributes and/or functional forms to select the one with the largest empirical support. In this way, each model works as a “virtual experiment” to answer questions related with the magnitude and spatial extent of the effects of different coexisting species and their potential implications for the function of communities and ecosystems. This paper reviews the use of MMV and neighborhood models in terrestrial ecology, synthesizing the state of the art and emphasizing new avenues of application.

ARE VALUE OF INFORMATION METHODS READY FOR PRIME TIME? AN APPLICATION TO ALTERNATIVE TREATMENT STRATEGIES FOR NSTEMI PATIENTS

The use of value of information methods to inform trial design has been widely advocated but there have been few empirical applications of these methods and there is little evidence they are widely used in decision making. This study considers the usefulness of value of information models in the context of a real clinical decision problem relating to alternative diagnostic strategies for patients with a recent non-ST elevated myocardial infarction. A pretrial economic model is constructed to consider the cost-effectiveness of two competing strategies: coronary angiography alone or in conjunction with fractional flow reserve measurement. A closed-form solution to the expected benefits of information is used with optimal sample size estimated for a range of models reflecting increasingly realistic assumptions and alternative decision contexts. Fractional flow reserve measurement is expected to be cost-effective with an incremental cost-effectiveness ratio of GBP 1,621, however, there is considerable uncertainty in this estimate and consequently a large expected value to reducing this uncertainty via a trial. The recommended sample size is strongly affected by the reality of the assumptions of the expected value of information (EVI) model and the decision context. Value of information models can provide a simple and flexible approach to clinical trial design and are more consistent with the constraints and objectives of the healthcare system than traditional frequentist approaches. However, the variation in sample size estimates demonstrates that it is essential that appropriate model parameters and decision contexts are used in their application.

How Many Batches Are Needed for Process Validation under the New FDA Guidance?

The newly updated FDA Guidance for Industry on Process Validation: General Principles and Practices ushers in a life cycle approach to process validation. While the guidance no longer considers the use of traditional three-batch validation appropriate, it does not prescribe the number of validation batches for a prospective validation protocol, nor does it provide specific methods to determine it. This potentially could leave manufacturers in a quandary. In this paper, I develop a Bayesian method to address the issue. By combining process knowledge gained from Stage 1 Process Design (PD) with expected outcomes of Stage 2 Process Performance Qualification (PPQ), the number of validation batches for PPQ is determined to provide a high level of assurance that the process will consistently produce future batches meeting quality standards. Several examples based on simulated data are presented to illustrate the use of the Bayesian method in helping manufacturers make risk-based decisions for Stage 2 PPQ, and they highlight the advantages of the method over traditional Frequentist approaches. The discussions in the paper lend support for a life cycle and risk-based approach to process validation recommended in the new FDA guidance. The newly updated FDA Guidance for Industry on Process Validation: General Principles and Practices ushers in a life cycle approach to process validation. While the guidance no longer considers the use of traditional three-batch validation appropriate, it does not prescribe the number of validation batches for a prospective validation protocol, nor does it provide specific methods to determine it. This potentially could leave manufacturers in a quandary. In this paper, I develop a Bayesian method to address the issue. By combining process knowledge gained from Stage 1 Process Design (PD) with expected outcomes of Stage 2 Process Performance Qualification (PPQ), the number of validation batches for PPQ is determined to provide a high level of assurance that the process will consistently produce future batches meeting quality standards. Several examples based on simulated data are presented to illustrate the use of the Bayesian method in helping manufacturers make risk-based decisions for Stage 2 PPQ, and THEY highlight the advantages of the method over traditional Frequentist approaches. The discussions in the paper lend support for a life cycle and risk-based approach to process validation recommended in the new FDA guidance.

Final report on CCQM-K80: Comparison of value-assigned CRMs and PT materials: Creatinine in human serum

The 2009 CCQM-K80 'Comparison of value-assigned CRMs and PT materials: creatinine in human serum' is the first in a series of key comparisons directly testing the chemical measurement services provided to customers by National Metrology Institutes (NMIs) and Designated Institutes. CCQM-K80 compared the assigned serum creatinine values of certified reference materials (CRMs) using measurements made on these materials under repeatability conditions. Six NMIs submitted 17 CRM materials for evaluation, all intended for sale to customers. These materials represent nearly all of the higher-order CRMs then available for this clinically important measurand.The certified creatinine mass fraction in the materials ranged from 3 mg/kg to 57 mg/kg. All materials were stored and prepared according the specifications provided by each NMI. Samples were processed and analyzed under repeatability conditions by one analyst using isotope dilution liquid chromatography–mass spectrometry. The instrumental repeatability imprecision, expressed as a percent relative standard deviation, was 1.2%.Given the number of materials and the time required for each analysis, the measurements were made in two measurement campaigns ('runs'). In both campaigns, replicate analyses (two injections of one preparation separated in time) were made on each of two or three independently prepared aliquots from one randomly selected unit of each of the 17 materials. The mean value, between-campaign, between-aliquot and between-replicate variance components, standard uncertainty of the mean value, and the number of degrees of freedom associated with the standard uncertainty were estimated using a linear mixed model. Since several of the uncertainties estimated using this traditional frequentist approach were associated with a single degree of freedom, Markov Chain Monte Carlo Bayesian analysis was used to estimate 95% level-of-confidence coverage intervals, U95. Uncertainty-weighted generalized distance regression was used to establish the key comparison reference function (KCRF) relating the assigned values to the repeatability measurements. Parametric bootstrap Monte Carlo was used to estimate 95% level-of-confidence coverage intervals for the degrees of equivalence of materials, d ± U95(d), and of the participating NMIs, D ± U95(D). Because of the wide range of creatinine mass fraction in the materials, these degrees of equivalence are expressed in percent relative form: %d ± U95(%d) and %D ± U95(%D).On the basis of leave-one-out cross-validation, the assigned values for 16 of the 17 materials were deemed equivalent at the 95% level of confidence. These materials were used to define the KCRF. The excluded material was identified as having a marginally underestimated assigned uncertainty, giving it large and potentially anomalous influence on the KCRF. However, this material's %d of 1.4 ± 1.5 indicates that it is equivalent with the other materials at the 95% level of confidence. The median |%d| for all 17 of the materials is 0.3 with a median U95(%d) of 1.9. All of these higher-order CRMs for creatinine in human serum are equivalent within their assigned uncertainties.The median |%D| for the participating NMIs is 0.3 with a median U95(%D) of 2.1. These results demonstrate that all participating NMIs have the ability to correctly value-assign CRMs and proficiency test materials for creatinine in human serum and similar measurands.Main text.To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/.The final report has been peer-reviewed and approved for publication by the CCQM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).

Bayesian Probability and Statistics in Management Research

Special Issue Purpose This special issue is focused on how a Bayesian approach to estimation, inference, and reasoning in organizational research might supplement—and in some cases supplant—traditional frequentist approaches. Bayesian methods are well suited to address the increasingly complex phenomena and problems faced by 21st-century researchers and organizations, where very complex data abound and the validity of knowledge and methods are often seen as contextually driven and constructed. Traditional modeling techniques and a frequentist view of probability and method are challenged by this new reality.

Finding Design Space and a Reliable Operating Region Using a Multivariate Bayesian Approach with Experimental Design

The posterior predictive approach for multiple response surface optimization presented by Peterson [7] is used to identify a region of process operating conditions where all quality attributes of the product are highly likely to meet specifications. The approach consists of calculating the probability that future responses will meet specification over a multidimensional grid of operating conditions. Examples from the pharmaceutical industry are used to show how the method is applied to statistically designed experiments and the results are used to generate reliability surface plots. The approach supplements traditional analysis and optimization techniques with calculated values that capture the maturity of the process under development, and provide a useful figure of merit in the definition of Design Space [5]. Also considered is the distinction between determining a Design Space to meet the specifications of critical quality attributes (CQA’s) [2] for the active pharmaceutical ingredient (API), and a reliable operating region (ROR) that also satisfies desirable manufacturing attributes, such as cost, yield, or throughput. A Bayesian posterior predictive approach offers benefits over traditional frequentist approaches to optimization. The traditional approaches, such as desirability functions or overlapping contours, do not account for model parameter uncertainty and the correlation of the responses at fixed operating conditions.

A Bayesian Procedure for Assessing Process Performance Based on Expected Relative Loss with Asymmetric Tolerances

Taguchi has introduced the loss function approach to quality improvement by focusing on the reduction of variation around the target value. This concept pays attention to the product designer’s original intent; that is, values of a critical characteristic at a target lead to maximum product performance. To address this concept, Johnson (1992) proposed the concept of expected relative squared error loss L e for symmetric cases, by approaching capability in terms of loss functions. Unfortunately, the index L e inconsistently measures process capability for processes with asymmetric tolerances, and thus reflects process potential and performance inaccurately. To remedy this, Pearn et al. (2006) proposed a modification of expected loss index, which is referred to as , to handle processes with both symmetric and asymmetric tolerances. The majority of the researches for assessing process performance based on the process loss indices are investigated using the traditional frequentist approach. However, the sampling distribution of the estimated is intractable, this makes establishing the exact confidence interval and testing process performance difficult. In the paper, we consider an alternative Bayesian approach to assess process performance based on the loss index for processes with asymmetric tolerances. Based on the derived posterior probability, a simple but practical procedure is proposed for practitioners to assess process performance on their shop floor, whether the manufacturing tolerance is symmetric or asymmetric.

A Bayesian Independence Test for Small Datasets

We propose a Bayesian test for independence among signals where only a small dataset is available. Traditional frequentist approaches often fail in this case due to inaccurate estimation of either the source statistical models or the threshold used by the test statistics. In addition, these frequentist methods cannot incorporate prior information into the computation of the test statistics. Our procedure renders parametric the nonparametric problem of testing for independence by quantizing the observed data samples into a table of cell counts. The test statistic is based on the likelihood of the observed cell counts under the independence hypothesis where the marginal cell probabilities are modeled by independent symmetric Dirichlet priors. We apply our Bayesian test to validate the solutions to the problem of blind source separation with small datasets using both synthetic and real-life benchmark data. The experimental results indicate that our approach can overcome the scarcity of data samples and significantly outperform the standard frequentist parametric methods with a proper selection of the prior parameters

A Hierarchical Bayesian Approach to Seasonal Hurricane Modeling

A hierarchical Bayesian strategy for modeling annual U.S. hurricane counts from the period 1851-2000 is illustrated. The approach is based on a separation of the reliable twentieth-century records from the less precise nineteenth-century records and makes use of Poisson regression. The work extends a recent climatological analysis of U.S. hurricanes by including predictors (covariates) in the form of indices for the El Nino-Southern Oscillation (ENSO) and the North Atlantic Oscillation (NAO). Model integration is achieved through a Markov chain Monte Carlo algorithm. A Bayesian strategy that uses only hurricane counts from the twentieth century together with noninformative priors compares favorably to a traditional (frequentist) approach and confirms a statistical relationship between climate patterns and coastal hurricane activity. Coinciding La Nina and negative NAO conditions significantly increase the probability of a U.S. hurricane. Hurricane counts from the nineteenth century are bootstrapped to obtain informative priors on the model parameters. The earlier records, though less reliable, allow for a more precise description of U.S. hurricane activity. This translates to a greater certainty in the authors' belief about the effects of ENSO and NAO on coastal hurricane activity. Similar conclusions are drawn when annual U.S. hurricane counts are disaggregated into regional counts. Contingent on the availability of values for the covariates, the models can be used to make predictive inferences about the hurricane season.

Bayesian deconvolution analysis of pulsatile hormone concentration profiles.

Many hormones are secreted into the circulatory system in a pulsatile manner and are cleared exponentially. The most common method of analyzing these systems is to deconvolve the hormone concentration into a secretion function and a clearance function. Accurate estimation of the model parameters depends on the number and location of the secretion pulses. To date, deconvolution analysis assumes the number and approximate location of these pulses are known a priori. In this article, we present a novel Bayesian approach to deconvolution that jointly models the number of pulses along with all other model parameters. Our method stochastically searches for the secretion pulses. This is accomplished by viewing the set of parameters that define the pulses as a point process. Pulses are determined by a birth-death process which is embedded in Markov chain Monte Carlo algorithm. This idea originated with Stephens (2000, Annals of Statistics 28, 40-74) in the context of finite mixture model density estimation, where the number of mixture components is unknown. There are several advantages that our model enjoys over the traditional frequentist approaches. These advantages are highlighted with four datasets consisting of serum concentration levels of luteinizing hormone obtained from ovariectomized ewes.

A Bayesian approach to stochastic cost-effectiveness analysis. An illustration and application to blood pressure control in type 2 diabetes.

The aim of this paper is to discuss the use of Bayesian methods in cost-effectiveness analysis (CEA) and the common ground between Bayesian and traditional frequentist approaches. A further aim is to explore the use of the net benefit statistic and its advantages over the incremental cost-effectiveness ratio (ICER) statistic. In particular, the use of cost-effectiveness acceptability curves is examined as a device for presenting the implications of uncertainty in a CEA to decision makers. Although it is argued that the interpretation of such curves as the probability that an intervention is cost-effective given the data requires a Bayesian approach, this should generate no misgivings for the frequentist. Furthermore, cost-effectiveness acceptability curves estimated using the net benefit statistic are exactly equivalent to those estimated from an appropriate analysis of ICERs on the cost-effectiveness plane. The principles examined in this paper are illustrated by application to the cost-effectiveness of blood pressure control in the U.K. Prospective Diabetes Study (UKPDS 40). Due to a lack of good-quality prior information on the cost and effectiveness of blood pressure control in diabetes, a Bayesian analysis assuming an uninformative prior is argued to be most appropriate. This generates exactly the same cost-effectiveness results as a standard frequentist analysis.

A Bayesian approach to stochastic cost-effectiveness analysis.

The aim of this paper is to briefly outline a Bayesian approach to cost-effectiveness analysis (CEA). Historically, frequentists have been cautious of Bayesian methodology, which is often held as synonymous with a subjective approach to statistical analysis. In this paper, the potential overlap between Bayesian and frequentist approaches to CEA is explored--the focus being on the empirical and uninformative prior-based approaches to Bayesian methods rather than the use of subjective beliefs. This approach emphasizes the advantage of a Bayesian interpretation for decision-making while retaining the robustness of the frequentist approach. In particular the use of cost-effectiveness acceptability curves is examined. A traditional frequentist approach is equivalent to a Bayesian approach assuming no prior information, while where there is pre-existing information available from which to construct a prior distribution, an empirical Bayes approach is equivalent to a frequentist approach based on pooling the available data. Cost-effectiveness acceptability curves directly address the decision-making problem in CEA. Although it is argued that their interpretation as the probability that an intervention is cost-effective given the data requires a Bayesian interpretation, this should generate no misgivings for the frequentist.