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.     

英汉互译中的音义对应及其可译性限度

声音、节奏等具有伴随意义,有时是对语言本身意义的补充.在翻译时力求音义对应是实现等效翻译的一种重要手段.当然,英汉语音在结构、功能和表达方式上的差异也使音义对应有一定的限度.     

Holistic trajectories: a study of combined employment, housing and family careers by using multiple-sequence analysis

Summary.  Social science applications of sequence analysis have thus far involved the development of a typology on the basis of an analysis of one or two variables which have had a relatively low number of different states. There is a yet unexplored potential for sequence analysis to be applied to a greater number of variables and thereby a much larger state space. The development of a typology of employment experiences, for example, without reference to data on changes in housing, marital and family status is arguably inadequate. The paper demonstrates the use of sequence analysis in the examination of multivariable combinations of status as they change over time and shows that this method can provide insights that are difficult to achieve through other analytic methods. The data that are examined here provide support to intuitive understandings of clusters of common experiences which are both life course specific and related to socio-economic factors. Housing tenure is found to be of key importance in understanding the holistic trajectories that are examined. This suggests that life course trajectories are sharply differentiated by experience of social housing.     

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.     

BAYESIAN SUBSET SELECTION AND MODEL AVERAGING USING A CENTRED AND DISPERSED PRIOR FOR THE ERROR VARIANCE

This article proposes a new data‐based prior distribution for the error variance in a Gaussian linear regression model, when the model is used for Bayesian variable selection and model averaging. For a given subset of variables in the model, this prior has a mode that is an unbiased estimator of the error variance but is suitably dispersed to make it uninformative relative to the marginal likelihood. The advantage of this empirical Bayes prior for the error variance is that it is centred and dispersed sensibly and avoids the arbitrary specification of hyperparameters. The performance of the new prior is compared to that of a prior proposed previously in the literature using several simulated examples and two loss functions. For each example our paper also reports results for the model that orthogonalizes the predictor variables before performing subset selection. A real example is also investigated. The empirical results suggest that for both the simulated and real data, the performance of the estimators based on the prior proposed in our article compares favourably with that of a prior used previously in the literature.     

Weak disintegrability as a form of preservation of coherence

Summary Weak disintegrations are investigated from various points of view. Kolmogorov's definition of conditional probability is critically analysed, and it is noted how the notion of disintegrability plays some role in connecting Kolmogorov's definition with the one given in line with de Finetti's coherence principle. Conditions are given, on the domain of a prevision, implying the equivalence between weak disintegrability and conglomerability. Moreover, weak sintegrations are characterized in terms of coherence, in de Finetti's sense, of, a suitable function. This fact enables us to give, an interpretation of weak disintegrability as a form of “preservation of coherence”. The previous results are also applied to a hypothetical inferential problem. In particular, an inference is shown to be coherent, in the sense of Heath and Sudderth, if and only if a suitable function is coherent, in de Finetti's sense. Research partially supported by: M.U.R.S.T. 40% “Problemi di inferenza pura”.     

Assessing accuracy of a continuous screening test in the presence of verification bias

Summary.  In studies to assess the accuracy of a screening test, often definitive disease assessment is too invasive or expensive to be ascertained on all the study subjects. Although it may be more ethical or cost effective to ascertain the true disease status with a higher rate in study subjects where the screening test or additional information is suggestive of disease, estimates of accuracy can be biased in a study with such a design. This bias is known as verification bias. Verification bias correction methods that accommodate screening tests with binary or ordinal responses have been developed; however, no verification bias correction methods exist for tests with continuous results. We propose and compare imputation and reweighting bias-corrected estimators of true and false positive rates, receiver operating characteristic curves and area under the receiver operating characteristic curve for continuous tests. Distribution theory and simulation studies are used to compare the proposed estimators with respect to bias, relative efficiency and robustness to model misspecification. The bias correction estimators proposed are applied to data from a study of screening tests for neonatal hearing loss.