Inference and Decision Making for 21st-Century Drug Development and Approval

ABSTRACT

The cost and time of pharmaceutical drug development continue to grow at rates that many say are unsustainable. These trends have enormous impact on what treatments get to patients, when they get them and how they are used. The statistical framework for supporting decisions in regulated clinical development of new medicines has followed a traditional path of frequentist methodology. Trials using hypothesis tests of “no treatment effect” are done routinely, and the p-value < 0.05 is often the determinant of what constitutes a “successful” trial. Many drugs fail in clinical development, adding to the cost of new medicines, and some evidence points blame at the deficiencies of the frequentist paradigm. An unknown number effective medicines may have been abandoned because trials were declared “unsuccessful” due to a p-value exceeding 0.05. Recently, the Bayesian paradigm has shown utility in the clinical drug development process for its probability-based inference. We argue for a Bayesian approach that employs data from other trials as a “prior” for Phase 3 trials so that synthesized evidence across trials can be utilized to compute probability statements that are valuable for understanding the magnitude of treatment effect. Such a Bayesian paradigm provides a promising framework for improving statistical inference and regulatory decision making.     

基于债务协商视角的债转股定量研究

针对我国政府、企业和银行等金融机构共同关注的债转股问题，基于债务协商谈判思想，建立部分债务股权互换模型，计算公司证券价格，探讨了债转股对公司价值、破产概率、破产损失成本和资本结构的影响，给出了银行等债权人愿意债转股的充分条件。结果表明：在事先破产清算协议贷款下，事后全部债转股总能提高公司股权价值，但并不一定能提高债券价值。只有其协商谈判能力满足一定条件，公司债权人才愿意事后选择债转股，实现帕累托改进、提高社会福利水平。其次，在公司股东协商谈判能力的一定范围内，部分债转股能提高公司价值，其最优转股债息比例随着公司资产风险的增大而增加。再次，债转股能降低公司破产风险和破产损失成本，但同时也提高了债券风险溢价。最后，随着股东谈判能力增强，最优协商转股债务比例、杠杆率都减少，而债券风险溢价增大。本文所得结果对我国政府、企业和银行如何实施债转股提供理论参考和实践指导。     

Confidence intervals,significance values,maximum likelihood estimates,etc. sharpened into Occam’s razors

Abstract

Confidence sets, p values, maximum likelihood estimates, and other results of non-Bayesian statistical methods may be adjusted to favor sampling distributions that are simple compared to others in the parametric family. The adjustments are derived from a prior likelihood function previously used to adjust posterior distributions.     

Hierarchical Bayesian Modeling of Post-Earthquake Ignition Probabilities Considering Inter-Earthquake Heterogeneity

Post-earthquake fires are high-consequence events with extensive damage potential. They are also low-frequency events, so their nature remains underinvestigated. One difficulty in modeling post-earthquake ignition probabilities is reducing the model uncertainty attributed to the scarce source data. The data scarcity problem has been resolved by pooling the data indiscriminately collected from multiple earthquakes. However, this approach neglects the inter-earthquake heterogeneity in the regional and seasonal characteristics, which is indispensable for risk assessment of future post-earthquake fires. Thus, the present study analyzes the post-earthquake ignition probabilities of five major earthquakes in Japan from 1995 to 2016 (1995 Kobe, 2003 Tokachi-oki, 2004 Niigata–Chuetsu, 2011 Tohoku, and 2016 Kumamoto earthquakes) by a hierarchical Bayesian approach. As the ignition causes of earthquakes share a certain commonality, common prior distributions were assigned to the parameters, and samples were drawn from the target posterior distribution of the parameters by a Markov chain Monte Carlo simulation. The results of the hierarchical model were comparatively analyzed with those of pooled and independent models. Although the pooled and hierarchical models were both robust in comparison with the independent model, the pooled model underestimated the ignition probabilities of earthquakes with few data samples. Among the tested models, the hierarchical model was least affected by the source-to-source variability in the data. The heterogeneity of post-earthquake ignitions with different regional and seasonal characteristics has long been desired in the modeling of post-earthquake ignition probabilities but has not been properly considered in the existing approaches. The presented hierarchical Bayesian approach provides a systematic and rational framework to effectively cope with this problem, which consequently enhances the statistical reliability and stability of estimating post-earthquake ignition probabilities.     

Empirical likelihood confidence intervals for the mean of a population containing many zero values

If a population contains many zero values and the sample size is not very large, the traditional normal approximation‐based confidence intervals for the population mean may have poor coverage probabilities. This problem is substantially reduced by constructing parametric likelihood ratio intervals when an appropriate mixture model can be found. In the context of survey sampling, however, there is a general preference for making minimal assumptions about the population under study. The authors have therefore investigated the coverage properties of nonparametric empirical likelihood confidence intervals for the population mean. They show that under a variety of hypothetical populations, these intervals often outperformed parametric likelihood intervals by having more balanced coverage rates and larger lower bounds. The authors illustrate their methodology using data from the Canadian Labour Force Survey for the year 2000.     

Non-ignorable missing covariate data in survival analysis: a case-study of an International Breast Cancer Study Group trial

Summary.  Non-ignorable missing data, a serious problem in both clinical trials and observational studies, can lead to biased inferences. Quality-of-life measures have become increasingly popular in clinical trials. However, these measures are often incompletely observed, and investigators may suspect that missing quality-of-life data are likely to be non-ignorable. Although several recent references have addressed missing covariates in survival analysis, they all required the assumption that missingness is at random or that all covariates are discrete. We present a method for estimating the parameters in the Cox proportional hazards model when missing covariates may be non-ignorable and continuous or discrete. Our method is useful in reducing the bias and improving efficiency in the presence of missing data. The methodology clearly specifies assumptions about the missing data mechanism and, through sensitivity analysis, helps investigators to understand the potential effect of missing data on study results.     

Merging information for semiparametric density estimation

Summary.  The density ratio model specifies that the likelihood ratio of m −1 probability density functions with respect to the m th is of known parametric form without reference to any parametric model. We study the semiparametric inference problem that is related to the density ratio model by appealing to the methodology of empirical likelihood. The combined data from all the samples leads to more efficient kernel density estimators for the unknown distributions. We adopt variants of well-established techniques to choose the smoothing parameter for the density estimators proposed.     

Assessing goodness-of-fit of categorical regression models based on case-control data

Demonstrated equivalence between a categorical regression model based on case‐control data and an I‐sample semiparametric selection bias model leads to a new goodness‐of‐fit test. The proposed test statistic is an extension of an existing Kolmogorov–Smirnov‐type statistic and is the weighted average of the absolute differences between two estimated distribution functions in each response category. The paper establishes an optimal property for the maximum semiparametric likelihood estimator of the parameters in the I‐sample semiparametric selection bias model. It also presents a bootstrap procedure, some simulation results and an analysis of two real datasets.     

Empirical Non-Parametric Control Charts: Estimation Effects and Corrections

Owing to the extreme quantiles involved, standard control charts are very sensitive to the effects of parameter estimation and non-normality. More general parametric charts have been devised to deal with the latter complication and corrections have been derived to compensate for the estimation step, both under normal and parametric models. The resulting procedures offer a satisfactory solution over a broad range of underlying distributions. However, situations do occur where even such a large model is inadequate and nothing remains but to consider non- parametric charts. In principle, these form ideal solutions, but the problem is that huge sample sizes are required for the estimation step. Otherwise the resulting stochastic error is so large that the chart is very unstable, a disadvantage that seems to outweigh the advantage of avoiding the model error from the parametric case. Here we analyse under what conditions non-parametric charts actually become feasible alternatives for their parametric counterparts. In particular, corrected versions are suggested for which a possible change point is reached at sample sizes that are markedly less huge (but still larger than the customary range). These corrections serve to control the behaviour during in-control (markedly wrong outcomes of the estimates only occur sufficiently rarely). The price for this protection will clearly be some loss of detection power during out-of-control. A change point comes in view as soon as this loss can be made sufficiently small.     

A Bayesian method for classification and discrimination

We discuss Bayesian analyses of traditional normal-mixture models for classification and discrimination. The development involves application of an iterative resampling approach to Monte Carlo inference, commonly called Gibbs sampling, and demonstrates routine application. We stress the benefits of exact analyses over traditional classification and discrimination techniques, including the ease with which such analyses may be performed in a quite general setting, with possibly several normal-mixture components having different covariance matrices, the computation of exact posterior classification probabilities for observed data and for future cases to be classified, and posterior distributions for these probabilities that allow for assessment of second-level uncertainties in classification.