Predictively consistent prior effective sample sizes.

Determining the sample size of an experiment can be challenging, even more so when incorporating external information via a prior distribution. Such information is increasingly used to reduce the size of the control group in randomized clinical trials. Knowing the amount of prior information, expressed as an equivalent prior effective sample size (ESS), clearly facilitates trial designs. Various methods to obtain a prior's ESS have been proposed recently. They have been justified by the fact that they give the standard ESS for one-parameter exponential families. However, despite being based on similar information-based metrics, they may lead to surprisingly different ESS for nonconjugate settings, which complicates many designs with prior information. We show that current methods fail a basic predictive consistency criterion, which requires the expected posterior-predictive ESS for a sample of size N to be the sum of the prior ESS and N. The expected local-information-ratio ESS is introduced and shown to be predictively consistent. It corrects the ESS of current methods, as shown for normally distributed data with a heavy-tailed Student-t prior and exponential data with a generalized Gamma prior. Finally, two applications are discussed: the prior ESS for the control group derived from historical data and the posterior ESS for hierarchical subgroup analyses.

Bayesian leveraging of historical control data for a clinical trial with time-to-event endpoint.

The recent 21st Century Cures Act propagates innovations to accelerate the discovery, development, and delivery of 21st century cures. It includes the broader application of Bayesian statistics and the use of evidence from clinical expertise. An example of the latter is the use of trial-external (or historical) data, which promises more efficient or ethical trial designs. We propose a Bayesian meta-analytic approach to leverage historical data for time-to-event endpoints, which are common in oncology and cardiovascular diseases. The approach is based on a robust hierarchical model for piecewise exponential data. It allows for various degrees of between trial-heterogeneity and for leveraging individual as well as aggregate data. An ovarian carcinoma trial and a non-small cell cancer trial illustrate methodological and practical aspects of leveraging historical data for the analysis and design of time-to-event trials.

Beyond p-values: A phase II dual-criterion design with statistical significance and clinical relevance.

Background Well-designed phase II trials must have acceptable error rates relative to a pre-specified success criterion, usually a statistically significant p-value. Such standard designs may not always suffice from a clinical perspective because clinical relevance may call for more. For example, proof-of-concept in phase II often requires not only statistical significance but also a sufficiently large effect estimate. Purpose We propose dual-criterion designs to complement statistical significance with clinical relevance, discuss their methodology, and illustrate their implementation in phase II. Methods Clinical relevance requires the effect estimate to pass a clinically motivated threshold (the decision value (DV)). In contrast to standard designs, the required effect estimate is an explicit design input, whereas study power is implicit. The sample size for a dual-criterion design needs careful considerations of the study's operating characteristics (type I error, power). Results Dual-criterion designs are discussed for a randomized controlled and a single-arm phase II trial, including decision criteria, sample size calculations, decisions under various data scenarios, and operating characteristics. The designs facilitate GO/NO-GO decisions due to their complementary statistical-clinical criterion. Limitations While conceptually simple, implementing a dual-criterion design needs care. The clinical DV must be elicited carefully in collaboration with clinicians, and understanding similarities and differences to a standard design is crucial. Conclusion To improve evidence-based decision-making, a formal yet transparent quantitative framework is important. Dual-criterion designs offer an appealing statistical-clinical compromise, which may be preferable to standard designs if evidence against the null hypothesis alone does not suffice for an efficacy claim.

Using phase II data for the analysis of phase III studies: An application in rare diseases.

BACKGROUND: Clinical research and drug development in orphan diseases are challenging, since large-scale randomized studies are difficult to conduct. Formally synthesizing the evidence is therefore of great value, yet this is rarely done in the drug-approval process. Phase III designs that make better use of phase II data can facilitate drug development in orphan diseases. METHODS: A Bayesian meta-analytic approach is used to inform the phase III study with phase II data. It is particularly attractive, since uncertainty of between-trial heterogeneity can be dealt with probabilistically, which is critical if the number of studies is small. Furthermore, it allows quantifying and discounting the phase II data through the predictive distribution relevant for phase III. A phase III design is proposed which uses the phase II data and considers approval based on a phase III interim analysis. The design is illustrated with a non-inferiority case study from a Food and Drug Administration approval in herpetic keratitis (an orphan disease). Design operating characteristics are compared to those of a traditional design, which ignores the phase II data. RESULTS: An analysis of the phase II data reveals good but insufficient evidence for non-inferiority, highlighting the need for a phase III study. For the phase III study supported by phase II data, the interim analysis is based on half of the patients. For this design, the meta-analytic interim results are conclusive and would justify approval. In contrast, based on the phase III data only, interim results are inconclusive and require further evidence. CONCLUSION: To accelerate drug development for orphan diseases, innovative study designs and appropriate methodology are needed. Taking advantage of randomized phase II data when analyzing phase III studies looks promising because the evidence from phase II supports informed decision-making. The implementation of the Bayesian design is straightforward with public software such as R.

Meta-analysis of two studies in the presence of heterogeneity with applications in rare diseases.

Random-effects meta-analyses are used to combine evidence of treatment effects from multiple studies. Since treatment effects may vary across trials due to differences in study characteristics, heterogeneity in treatment effects between studies must be accounted for to achieve valid inference. The standard model for random-effects meta-analysis assumes approximately normal effect estimates and a normal random-effects model. However, standard methods based on this model ignore the uncertainty in estimating the between-trial heterogeneity. In the special setting of only two studies and in the presence of heterogeneity, we investigate here alternatives such as the Hartung-Knapp-Sidik-Jonkman method (HKSJ), the modified Knapp-Hartung method (mKH, a variation of the HKSJ method) and Bayesian random-effects meta-analyses with priors covering plausible heterogeneity values; R code to reproduce the examples is presented in an appendix. The properties of these methods are assessed by applying them to five examples from various rare diseases and by a simulation study. Whereas the standard method based on normal quantiles has poor coverage, the HKSJ and mKH generally lead to very long, and therefore inconclusive, confidence intervals. The Bayesian intervals on the whole show satisfying properties and offer a reasonable compromise between these two extremes.

Robust exchangeability designs for early phase clinical trials with multiple strata.

Clinical trials with multiple strata are increasingly used in drug development. They may sometimes be the only option to study a new treatment, for example in small populations and rare diseases. In early phase trials, where data are often sparse, good statistical inference and subsequent decision-making can be challenging. Inferences from simple pooling or stratification are known to be inferior to hierarchical modeling methods, which build on exchangeable strata parameters and allow borrowing information across strata. However, the standard exchangeability (EX) assumption bears the risk of too much shrinkage and excessive borrowing for extreme strata. We propose the exchangeability-nonexchangeability (EXNEX) approach as a robust mixture extension of the standard EX approach. It allows each stratum-specific parameter to be exchangeable with other similar strata parameters or nonexchangeable with any of them. While EXNEX computations can be performed easily with standard Bayesian software, model specifications and prior distributions are more demanding and require a good understanding of the context. Two case studies from phases I and II (with three and four strata) show promising results for EXNEX. Data scenarios reveal tempered degrees of borrowing for extreme strata, and frequentist operating characteristics perform well for estimation (bias, mean-squared error) and testing (less type-I error inflation).

Robust meta-analytic-predictive priors in clinical trials with historical control information.

Historical information is always relevant for clinical trial design. Additionally, if incorporated in the analysis of a new trial, historical data allow to reduce the number of subjects. This decreases costs and trial duration, facilitates recruitment, and may be more ethical. Yet, under prior-data conflict, a too optimistic use of historical data may be inappropriate. We address this challenge by deriving a Bayesian meta-analytic-predictive prior from historical data, which is then combined with the new data. This prospective approach is equivalent to a meta-analytic-combined analysis of historical and new data if parameters are exchangeable across trials. The prospective Bayesian version requires a good approximation of the meta-analytic-predictive prior, which is not available analytically. We propose two- or three-component mixtures of standard priors, which allow for good approximations and, for the one-parameter exponential family, straightforward posterior calculations. Moreover, since one of the mixture components is usually vague, mixture priors will often be heavy-tailed and therefore robust. Further robustness and a more rapid reaction to prior-data conflicts can be achieved by adding an extra weakly-informative mixture component. Use of historical prior information is particularly attractive for adaptive trials, as the randomization ratio can then be changed in case of prior-data conflict. Both frequentist operating characteristics and posterior summaries for various data scenarios show that these designs have desirable properties. We illustrate the methodology for a phase II proof-of-concept trial with historical controls from four studies. Robust meta-analytic-predictive priors alleviate prior-data conflicts ' they should encourage better and more frequent use of historical data in clinical trials.

The current state of Bayesian methods in medical product development: survey results and recommendations from the DIA Bayesian Scientific Working Group.

Bayesian applications in medical product development have recently gained popularity. Despite many advances in Bayesian methodology and computations, increase in application across the various areas of medical product development has been modest. The DIA Bayesian Scientific Working Group (BSWG), which includes representatives from industry, regulatory agencies, and academia, has adopted the vision to ensure Bayesian methods are well understood, accepted more broadly, and appropriately utilized to improve decision making and enhance patient outcomes. As Bayesian applications in medical product development are wide ranging, several sub-teams were formed to focus on various topics such as patient safety, non-inferiority, prior specification, comparative effectiveness, joint modeling, program-wide decision making, analytical tools, and education. The focus of this paper is on the recent effort of the BSWG Education sub-team to administer a Bayesian survey to statisticians across 17 organizations involved in medical product development. We summarize results of this survey, from which we provide recommendations on how to accelerate progress in Bayesian applications throughout medical product development. The survey results support findings from the literature and provide additional insight on regulatory acceptance of Bayesian methods and information on the need for a Bayesian infrastructure within an organization. The survey findings support the claim that only modest progress in areas of education and implementation has been made recently, despite substantial progress in Bayesian statistical research and software availability.

Use of historical control data for assessing treatment effects in clinical trials.

Clinical trials rarely, if ever, occur in a vacuum. Generally, large amounts of clinical data are available prior to the start of a study, particularly on the current study's control arm. There is obvious appeal in using (i.e., 'borrowing') this information. With historical data providing information on the control arm, more trial resources can be devoted to the novel treatment while retaining accurate estimates of the current control arm parameters. This can result in more accurate point estimates, increased power, and reduced type I error in clinical trials, provided the historical information is sufficiently similar to the current control data. If this assumption of similarity is not satisfied, however, one can acquire increased mean square error of point estimates due to bias and either reduced power or increased type I error depending on the direction of the bias. In this manuscript, we review several methods for historical borrowing, illustrating how key parameters in each method affect borrowing behavior, and then, we compare these methods on the basis of mean square error, power and type I error. We emphasize two main themes. First, we discuss the idea of 'dynamic' (versus 'static') borrowing. Second, we emphasize the decision process involved in determining whether or not to include historical borrowing in terms of the perceived likelihood that the current control arm is sufficiently similar to the historical data. Our goal is to provide a clear review of the key issues involved in historical borrowing and provide a comparison of several methods useful for practitioners.

Using historical control information for the design and analysis of clinical trials with overdispersed count data.

Results from clinical trials are never interpreted in isolation. Previous studies in a similar setting provide valuable information for designing a new trial. For the analysis, however, the use of trial-external information is challenging and therefore controversial, although it seems attractive from an ethical or efficiency perspective. Here, we consider the formal use of historical control data on lesion counts in a multiple sclerosis trial. The approach to incorporating historical data is Bayesian, in that historical information is captured in a prior that accounts for between-trial variability and hence leads to discounting of historical data. We extend the meta-analytic-predictive approach, a random-effects meta-analysis of historical data combined with the prediction of the parameter in the new trial, from normal to overdispersed count data of individual-patient or aggregate-trial format. We discuss the prior derivation for the lesion mean count in the control group of the new trial for two populations. For the general population (without baseline enrichment), with 1936 control patients from nine historical trials, between-trial variability was moderate to substantial, leading to a prior effective sample size of about 45 control patients. For the more homogenous population (with enrichment), with 412 control patients from five historical trials, the prior effective sample size was approximately 63 patients. Although these numbers are small relative to the historical data, they are fairly typical in settings where between-trial heterogeneity is moderate. For phase II, reducing the number of control patients by 45 or by 63 may be an attractive option in many multiple sclerosis trials.

Femtosecond Laser-Induced Periodic Surface Structures in Titanium-Doped Diamond-like Nanocomposite Films: Effects of the Beam Polarization Rotation.

We study the properties of laser-induced periodic surface structures (LIPSS) formed on titanium-doped diamond-like nanocomposite (DLN) a-C:H:Si:O films during ablation processing with linearly-polarized beams of a visible femtosecond laser (wavelength 515 nm, pulse duration 320 fs, pulse repetition rates 100 kHz-2 MHz, scanning beam velocity 0.05-1 m/s). The studies are focused on (i) laser ablation characteristics of Ti-DLN films at different pulse frequencies and constant fluence close to the ablation threshold, (ii) effects of the polarization angle rotation on the properties of low spatial frequency LIPSS (LSFL), and (iii) nanofriction properties of the 'rotating' LIPSS using atomic force microscopy (AFM) in a lateral force mode. It is found that (i) all LSFL are oriented perpendicular to the beam polarization direction, so being rotated with the beam polarization, and (ii) LSFL periods are gradually changed from 360 ± 5 nm for ripples parallel to the beam scanning direction to 420 ± 10 nm for ripples formed perpendicular to the beam scanning. The obtained results are discussed in the frame of the surface plasmon polaritons model of the LIPSS formation. Also, the findings of the nanoscale friction behavior, dependent on the LIPSS orientation relative to the AFM tip scanning direction, are presented and discussed.

Composition and micromechanical properties of the femoral neck compact bone in relation to patient age, sex and hip fracture occurrence.

Current clinical methods of bone health assessment depend to a great extent on bone mineral density (BMD) measurements. However, these methods only act as a proxy for bone strength and are often only carried out after the fracture occurs. Besides BMD, composition and tissue-level mechanical properties are expected to affect the whole bone's strength and toughness. While the elastic properties of the bone extracellular matrix (ECM) have been extensively investigated over the past two decades, there is still limited knowledge of the yield properties and their relationship to composition and architecture. In the present study, morphological, compositional and micropillar compression bone data was collected from patients who underwent hip arthroplasty. Femoral neck samples from 42 patients were collected together with anonymous clinical information about age, sex and primary diagnosis (coxarthrosis or hip fracture). The femoral neck cortex from the inferomedial region was analyzed in a site-matched manner using a combination of micromechanical testing (nanoindentation, micropillar compression) together with micro-CT and quantitative polarized Raman spectroscopy for both morphological and compositional characterization. Mechanical properties, as well as the sample-level mineral density, were constant over age. Only compositional properties demonstrate weak dependence on patient age: decreasing mineral to matrix ratio (p = 0.02, R2 = 0.13, 2.6 % per decade) and increasing amide I sub-peak ratio I∼1660/I∼1683 (p = 0.04, R2 = 0.11, 1.5 % per decade). The patient's sex and diagnosis did not seem to influence investigated bone properties. A clear zonal dependence between interstitial and osteonal cortical zones was observed for compositional and elastic bone properties (p < 0.0001). Site-matched microscale analysis confirmed that all investigated mechanical properties except yield strain demonstrate a positive correlation with the mineral fraction of bone. The output database is the first to integrate the experimentally assessed microscale yield properties, local tissue composition and morphology with the available patient clinical information. The final dataset was used for bone fracture risk prediction in-silico through the principal component analysis and the Naïve Bayes classification algorithm. The analysis showed that the mineral to matrix ratio, indentation hardness and micropillar yield stress are the most relevant parameters for bone fracture risk prediction at 70 % model accuracy (0.71 AUC). Due to the low number of samples, further studies to build a universal fracture prediction algorithm are anticipated with the higher number of patients (N > 200). The proposed classification algorithm together with the output dataset of bone tissue properties can be used for the future comparison of existing methods to evaluate bone quality as well as to form a better understanding of the mechanisms through which bone tissue is affected by aging or disease.

Discussion of the article by Trippa, Rosner, and Müller on Bayesian enrichment strategies for randomized discontinuation trials.

We congratulate Trippa, Rosner, and Müller (2011, Biometrics, in press) on an intriguing and timely article. The randomized discontinuation design (RDD) has only recently been used in cancer clinical trials, and methodological understanding on how to best design such studies is limited. The authors' approach to optimize RDD designs based on prior information and utility considerations is an important step forward. A noteworthy element is their use of a semimechanistic model to describe tumor growth. Mathematical models have provided considerable insight on the complex process of tumor evolution (Preziosi, 2003, Cancer Modelling and Simulation). Utilizing this knowledge should lead to better design, analysis, and decisions.

The Predictive Individual Effect for Survival Data.

BACKGROUND: The call for patient-focused drug development is loud and clear, as expressed in the twenty-first Century Cures Act and in recent guidelines and initiatives of regulatory agencies. Among the factors contributing to modernized drug development and improved health-care activities are easily interpretable measures of clinical benefit. In addition, special care is needed for cancer trials with time-to-event endpoints if the treatment effect is not constant over time. OBJECTIVE: To quantify the potential clinical survival benefit for a new patient, would he/she be treated with the test or control treatment. METHODS: We propose the predictive individual effect which is a patient-centric and tangible measure of clinical benefit under a wide variety of scenarios. It can be obtained by standard predictive calculations under a rank preservation assumption that has been used previously in trials with treatment switching. RESULTS: We discuss four recent Oncology trials that cover situations with proportional as well as non-proportional hazards (delayed treatment effect or crossing of survival curves). It is shown that the predictive individual effect offers valuable insights beyond p-values, estimates of hazard ratios or differences in median survival. CONCLUSION: Compared to standard statistical measures, the predictive individual effect is a direct, easily interpretable measure of clinical benefit. It facilitates communication among clinicians, patients, and other parties and should therefore be considered in addition to standard statistical results.

Sub-Threshold Fabrication of Laser-Induced Periodic Surface Structures on Diamond-like Nanocomposite Films with IR Femtosecond Pulses.

In the paper, we study the formation of laser-induced periodic surface structures (LIPSS) on diamond-like nanocomposite (DLN) a-C:H:Si:O films during nanoscale ablation processing at low fluences-below the single-pulse graphitization and spallation thresholds-using an IR fs-laser (wavelength 1030 nm, pulse duration 320 fs, pulse repetition rate 100 kHz, scanning beam velocity 0.04-0.08 m/s). The studies are focused on microscopic analysis of the nanostructured DLN film surface at different stages of LIPSS formation and numerical modeling of surface plasmon polaritons in a thin graphitized surface layer. Important findings are concerned with (i) sub-threshold fabrication of high spatial frequency LIPSS (HSFL) and low spatial frequency LIPSS (LSFL) under negligible surface graphitization of hard DLN films, (ii) transition from the HSFL (periods of 140 ± 30 and 230 ± 40 nm) to LSFL (period of 830-900 nm) within a narrow fluence range of 0.21-0.32 J/cm2, (iii) visualization of equi-field lines by ablated nanoparticles at an initial stage of the LIPSS formation, providing proof of larger electric fields in the valleys and weaker fields at the ridges of a growing surface grating, (iv) influence of the thickness of a laser-excited glassy carbon (GC) layer on the period of surface plasmon polaritons excited in a three-layer system "air/GC layer/DLN film".

Assessing minipig compact jawbone quality at the microscale.

Preclinical studies often require animal models for in vivo experiments. Particularly in dental research, pig species are extensively used due to their anatomical similarity to humans. However, there is a considerable knowledge gap on the multiscale morphological and mechanical properties of the miniature pigs' jawbones, which is crucial for implant studies and a direct comparison to human tissue. In the present work, we demonstrate a multimodal framework to assess the jawbone quantity and quality for a minipig animal model that could be further extended to humans. Three minipig genotypes, commonly used in dental research, were examined: Yucatan, Göttingen, and Sinclair. Three animals per genotype were tested. Cortical bone samples were extracted from the premolar region of the mandible, opposite to the teeth growth. Global morphological, compositional, and mechanical properties were assessed using micro-computed tomography (micro-CT) together with Raman spectroscopy and nanoindentation measurements, averaged over the sample area. Local mineral-mechanical relationships were investigated with the site-matched Raman spectroscopy and micropillar compression tests. For this, a novel femtosecond laser ablation protocol was developed, allowing high-throughput micropillar fabrication and testing without exposure to high vacuum. At the global averaged sample level, bone relative mineralization demonstrated a significant difference between the genotypes, which was not observed from the complementary micro-CT measurements. Moreover, bone hardness measured by nanoindentation showed a positive trend with the relative mineralization. For all genotypes, significant differences between the relative mineralization and elastic properties were more pronounced within the osteonal regions of cortical bone. Site-matched micropillar compression and Raman spectroscopy highlighted the differences between the genotypes' yield stress and mineral to matrix ratios. The methods used at the global level (averaged over sample area) could be potentially correlated to the medical tools used to assess jawbone toughness and morphology in clinics. On the other hand, the local analysis methods can be applied to quantify compressive bone mechanical properties and their relationship to bone mineralization.

A proof of concept phase II non-inferiority criterion.

Traditional phase III non-inferiority trials require compelling evidence that the treatment vs control effect bfθ is better than a pre-specified non-inferiority margin θ(NI) . The standard approach compares this margin to the 95 per cent confidence interval of the effect parameter. In the phase II setting, in order to declare Proof of Concept (PoC) for non-inferiority and proceed in the development of the drug, different criteria that are specifically tailored toward company internal decision making may be more appropriate. For example, less evidence may be needed as long as the effect estimate is reasonably convincing. We propose a non-inferiority design that addresses the specifics of the phase II setting. The requirements are that (1) the effect estimate be better than a critical threshold θ(C), and (2) the type I error with regard to θ(NI) is controlled at a pre-specified level. This design is compared with the traditional design from a frequentist as well as a Bayesian perspective, where the latter relies on the Level of Proof (LoP) metric, i.e. the probability that the true effect is better than effect values of interest. Clinical input is required to establish the value θ(C), which makes the design transparent and improves interactions within clinical teams. The proposed design is illustrated for a non-inferiority trial for a time-to-event endpoint in oncology.

Bayesian models for subgroup analysis in clinical trials.

BACKGROUND: In a pharmaceutical drug development setting, possible interactions between the treatment and particular baseline clinical or demographic factors are often of interest. However, the subgroup analysis required to investigate such associations remains controversial. Concerns with classical hypothesis testing approaches to the problem include low power, multiple testing, and the possibility of data dredging. PURPOSE: As an alternative to hypothesis testing, the use of shrinkage estimation techniques is investigated in the context of an exploratory post hoc subgroup analysis. A range of models that have been suggested in the literature are reviewed. Building on this, we explore a general modeling strategy, considering various options for shrinkage of effect estimates. This is applied to a case-study, in which evidence was available from seven-phase II-III clinical trials examining a novel therapy, and also to two artificial datasets with the same structure. METHODS: Emphasis is placed on hierarchical modeling techniques, adopted within a Bayesian framework using freely available software. A range of possible subgroup model structures are applied, each incorporating shrinkage estimation techniques. RESULTS: The investigation of the case-study showed little evidence of subgroup effects. Because inferences appeared to be consistent across a range of well-supported models, and model diagnostic checks showed no obvious problems, it seemed this conclusion was robust. It is reassuring that the structured shrinkage techniques appeared to work well in a situation where deeper inspection of the data suggested little evidence of subgroup effects. LIMITATIONS: The post hoc examination of subgroups should be seen as an exploratory analysis, used to help make better informed decisions regarding potential future studies examining specific subgroups. To a certain extent, the degree of understanding provided by such assessments will be limited by the quality and quantity of available data. CONCLUSIONS: In light of recent interest by health authorities into the use of subgroup analysis in the context of drug development, it appears that Bayesian approaches involving shrinkage techniques could play an important role in this area. Hopefully, the developments outlined here provide useful methodology for tackling such a problem, in-turn leading to better informed decisions regarding subgroups.

Review on Experimental and Theoretical Investigations of Ultra-Short Pulsed Laser Ablation of Metals with Burst Pulses.

Laser processing with ultra-short double pulses has gained attraction since the beginning of the 2000s. In the last decade, pulse bursts consisting of multiple pulses with a delay of several 10 ns and less found their way into the area of micromachining of metals, opening up completely new process regimes and allowing an increase in the structuring rates and surface quality of machined samples. Several physical effects such as shielding or re-deposition of material have led to a new understanding of the related machining strategies and processing regimes. Results of both experimental and numerical investigations are placed into context for different time scales during laser processing. This review is dedicated to the fundamental physical phenomena taking place during burst processing and their respective effects on machining results of metals in the ultra-short pulse regime for delays ranging from several 100 fs to several microseconds. Furthermore, technical applications based on these effects are reviewed.