131st Annual Meeting Joint Statistical Meetings of the American Statistical Association,The Blometrlc Society,Enar and Wnar,The Institute of Mathematical Statistics

(We are attempting to inaugurate a different type of questions and answers page in this issue of the American Statistician. Our purpose is to stimulate an interest in conceptual and measurement problems which arise in the course of statistical work and which require discussion apart from purely mathematical considerations. It is hoped that our readers will find this approach of interest and value. We are inviting questions of this type.)     

Expert knowledge elicitation using item response theory

In an expert knowledge elicitation exercise, experts face a carefully constructed list of questions that they answer according to their knowledge. The elicitation process concludes when a probability distribution is found that adequately captures the experts' beliefs in the light of those answers. In many situations, it is very difficult to create a set of questions that will efficiently capture the experts' knowledge, since experts might not be able to make precise probabilistic statements about the parameter of interest. We present an approach for capturing expert knowledge based on item response theory, in which a set of binary response questions is proposed to the expert, trying to capture responses directly related to the quantity of interest. As a result, the posterior distribution of the parameter of interest will represent the elicited prior distribution that does not assume any particular parametric form. The method is illustrated by a simulated example and by an application involving the elicitation of rain prophets' predictions for the rainy season in the north-east of Brazil.     

A Method for Analyzing Disease-Specific Mortality with Missing Cause of Death Information

In this paper, we examine a method for analyzing competing risks data where the failure type of interest is missing or incomplete, but where there is an intermediate event, and only patients who experience the intermediate event can die of the cause of interest. In some applications, a method called “log-rank subtraction” has been applied to these problems. There has been no systematic study of this methodology, though. We investigate the statistical properties of the method and further propose a modified method by including a weight function in the construction of the test statistic to correct for potential biases. A class of tests is then proposed for comparing the disease-specific mortality in the two groups. The tests are based on comparing the difference of weighted log-rank scores for the failure type of interest. We derive the asymptotic properties for the modified test procedure. Simulation studies indicate that the tests are unbiased and have reasonable power. The results are also illustrated with data from a breast cancer study.     

Response‐adaptive designs for binary responses: How to offer patient benefit while being robust to time trends?

Response‐adaptive randomisation (RAR) can considerably improve the chances of a successful treatment outcome for patients in a clinical trial by skewing the allocation probability towards better performing treatments as data accumulates. There is considerable interest in using RAR designs in drug development for rare diseases, where traditional designs are not either feasible or ethically questionable. In this paper, we discuss and address a major criticism levelled at RAR: namely, type I error inflation due to an unknown time trend over the course of the trial. The most common cause of this phenomenon is changes in the characteristics of recruited patients—referred to as patient drift. This is a realistic concern for clinical trials in rare diseases due to their lengthly accrual rate. We compute the type I error inflation as a function of the time trend magnitude to determine in which contexts the problem is most exacerbated. We then assess the ability of different correction methods to preserve type I error in these contexts and their performance in terms of other operating characteristics, including patient benefit and power. We make recommendations as to which correction methods are most suitable in the rare disease context for several RAR rules, differentiating between the 2‐armed and the multi‐armed case. We further propose a RAR design for multi‐armed clinical trials, which is computationally efficient and robust to several time trends considered.     

How many ways can you look at a proportion?: cross-community vote transfers in Northern Ireland after the Belfast Agreement

Summary.  The single transferable vote is a method of election that allows voters to mark candidates in order of preference. Votes that are not required to elect a candidate are passed to the next candidate in the voter's order of preference. Results of this kind of election give us data about the degree to which voters of a given persuasion are willing to pass their vote to a candidate of a different persuasion. Measures of voters' willingness to pass a vote to a candidate of a different persuasion are of particular interest in places such as Northern Ireland, where communities differ by religion and national aspiration, and agreed new political institutions are based on cross-community power-sharing. How we quantify this voting data may depend on the questions that we want to answer, of course. But, to understand changes in how the voter orders her or his preference, one may need to ask several questions, and to quantify the results of the election in more than one way.     

Data augmentation in multi-way contingency tables with fixed marginal totals

We describe and illustrate approaches to data augmentation in multi-way contingency tables for which partial information, in the form of subsets of marginal totals, is available. In such problems, interest lies in questions of inference about the parameters of models underlying the table together with imputation for the individual cell entries. We discuss questions of structure related to the implications for inference on cell counts arising from assumptions about log-linear model forms, and a class of simple and useful prior distributions on the parameters of log-linear models. We then discuss “local move” and “global move” Metropolis–Hastings simulation methods for exploring the posterior distributions for parameters and cell counts, focusing particularly on higher-dimensional problems. As a by-product, we note potential uses of the “global move” approach for inference about numbers of tables consistent with a prescribed subset of marginal counts. Illustration and comparison of MCMC approaches is given, and we conclude with discussion of areas for further developments and current open issues.     

Nonparametric approaches to testing and multiple comparisons in a one-way anova

Two questions of interest involving nonparametric multiple comparisons are considered. The first question concerns whether it is appropriate to use a multiple comparison procedure as a test of the equality of k treatments, and if it is, which procedure performs best as a test. Our results show that for smaller k values some multiple comparison procedures perform well as tests. The second question concerns whether a joint ranking or a separate ranking multiple comparison procedure performs better as a test and as a device for treatment separation. We find that the joint ranking procedure does slightly better as a test, but for treatment separation the answer depends on the situation.     

Refusal to Answer Specific Questions in a Survey: A Case Study

It is well known that non ignorable item non response may occur when the cause of the non response is the value of the latent variable of interest. In these cases, a refusal by a respondent to answer specific questions in a survey should be treated sometimes as a non ignorable item non response. The Rasch-Rasch model (RRM) is a new two-dimensional item response theory model for addressing non ignorable non response. This article demonstrates the use of the RRM on data from an Italian survey focused on assessment of healthcare workers’ knowledge about sudden infant death syndrome (that is, a context in which non response is presumed to be more likely among individuals with a low level of competence). We compare the performance of the RRM with other models within the Rasch model family that assume the unidimensionality of the latent trait. We conclude that this assumption should be considered unreliable for the data at hand, whereas the RRM provides a better fit of the data.     

Finding local departures from a parametric model using nonparametric regression

Goodness-of-fit evaluation of a parametric regression model is often done through hypothesis testing, where the fit of the model of interest is compared statistically to that obtained under a broader class of models. Nonparametric regression models are frequently used as the latter type of model, because of their flexibility and wide applicability. To date, this type of tests has generally been performed globally, by comparing the parametric and nonparametric fits over the whole range of the data. However, in some instances it might be of interest to test for deviations from the parametric model that are localized to a subset of the data. In this case, a global test will have low power and hence can miss important local deviations. Alternatively, a naive testing approach that discards all observations outside the local interval will suffer from reduced sample size and potential overfitting. We therefore propose a new local goodness-of-fit test for parametric regression models that can be applied to a subset of the data but relies on global model fits, and propose a bootstrap-based approach for obtaining the distribution of the test statistic. We compare the new approach with the global and the naive tests, both theoretically and through simulations, and illustrate its practical behavior in an application. We find that the local test has a better ability to detect local deviations than the other two tests.     

Should the two-trial paradigm still be the gold standard in drug assessment?

Two significant pivotal trials are usually required for a new drug approval by a regulatory agency. This standard requirement is known as the two-trial paradigm. However, several authors have questioned why we need exactly two pivotal trials, what statistical error the regulators are trying to protect against, and potential alternative approaches. Therefore, it is important to investigate these questions to better understand the regulatory decision-making in the assessment of drugs' effectiveness. It is common that two identically designed trials are run solely to adhere to the two-trial rule. Previous work showed that combining the data from the two trials into a single trial (one-trial paradigm) would increase the power while ensuring the same level of type I error protection as the two-trial paradigm. However, this is true only under a specific scenario and there is little investigation on the type I error protection over the whole null region. In this article, we compare the two paradigms by considering scenarios in which the two trials are conducted in identical or different populations as well as with equal or unequal size. With identical populations, the results show that a single trial provides better type I error protection and higher power. Conversely, with different populations, although the one-trial rule is more powerful in some cases, it does not always protect against the type I error. Hence, there is the need for appropriate flexibility around the two-trial paradigm and the appropriate approach should be chosen based on the questions we are interested in.     

基于RAM的我国财险公司效率与偿付能力关系研究

 保险公司有不同的利益主体,投资者和公司管理者关注的重点是公司效率,而投保人和监管机构关注的核心是保险公司的偿付能力,那么效率与偿付能力是否存在冲突,或者说,监管机构的偿付能力约束是否影响公司效率以及影响程度究竟如何,是业界和学术界关注的主要内容。本文从金融中介的视角,考虑不同利益主体,把偿付能力作为一产出指标,通过分析该指标的介入对效率的影响来研究偿付能力与效率之间的关系;在实证研究中,引入DEA的扩展模型—RAM,因为相对于DEA,RAM能更全面地反映保险公司的相对效率,所得到的效率值具有严格单调性,而且能处理指标出现负值的情况,这对于不多的样本特别具有吸引力;在检验不同类型保险公司的效率差异时,考虑到RAM方法得到的效率值是一个序数概念而不是绝对数量,本文采用Mann-Whitney秩和方法进行检验。     

Order statistics and the length of the best-n-of-(2n − 1) competition

The best-4-of-7 series is a popular playoff format to decide the champion in most North American professional sports. World Series (best-4-of-7) type competitions give rise to interesting probabilistic and statistical questions. We determine the expected length of this type of series by relating it to a problem involving order statistics. We also calculate the variance of the length and provide a simple formula for series of fair games. The method can be extended to derive higher order moments. This novel approach leads to new results that can be formulated in closed forms in terms of the distribution function of various binomial distributions. The emphasis is on establishing the connection to order statistics and obtaining closed forms. The relation to the negative binomial distribution as well as to the sooner waiting time problem in sequential testing is also discussed. We also consider the case when ties are allowed in the single games.     

Applying competing risks regression models: an overview

In many clinical research applications the time to occurrence of one event of interest, that may be obscured by another??so called competing??event, is investigated. Specific interventions can only have an effect on the endpoint they address or research questions might focus on risk factors for a certain outcome. Different approaches for the analysis of time-to-event data in the presence of competing risks were introduced in the last decades including some new methodologies, which are not yet frequently used in the analysis of competing risks data. Cause-specific hazard regression, subdistribution hazard regression, mixture models, vertical modelling and the analysis of time-to-event data based on pseudo-observations are described in this article and are applied to a dataset of a cohort study intended to establish risk stratification for cardiac death after myocardial infarction. Data analysts are encouraged to use the appropriate methods for their specific research questions by comparing different regression approaches in the competing risks setting regarding assumptions, methodology and interpretation of the results. Notes on application of the mentioned methods using the statistical software R are presented and extensions to the presented standard methods proposed in statistical literature are mentioned.     

Cox regression with missing covariate data using a modified partial likelihood method

Missing covariate values is a common problem in survival analysis. In this paper we propose a novel method for the Cox regression model that is close to maximum likelihood but avoids the use of the EM-algorithm. It exploits that the observed hazard function is multiplicative in the baseline hazard function with the idea being to profile out this function before carrying out the estimation of the parameter of interest. In this step one uses a Breslow type estimator to estimate the cumulative baseline hazard function. We focus on the situation where the observed covariates are categorical which allows us to calculate estimators without having to assume anything about the distribution of the covariates. We show that the proposed estimator is consistent and asymptotically normal, and derive a consistent estimator of the variance–covariance matrix that does not involve any choice of a perturbation parameter. Moderate sample size performance of the estimators is investigated via simulation and by application to a real data example.     

Estimand framework: Are we asking the right questions? A case study in the solid tumor setting

The estimand framework requires a precise definition of the clinical question of interest (the estimand) as different ways of accounting for “intercurrent” events post randomization may result in different scientific questions. The initiation of subsequent therapy is common in oncology clinical trials and is considered an intercurrent event if the start of such therapy occurs prior to a recurrence or progression event. Three possible ways to account for this intercurrent event in the analysis are to censor at initiation, consider recurrence or progression events (including death) that occur before and after the initiation of subsequent therapy, or consider the start of subsequent therapy as an event in and of itself. The new estimand framework clarifies that these analyses address different questions (“does the drug delay recurrence if no patient had received subsequent therapy?” vs “does the drug delay recurrence with or without subsequent therapy?” vs “does the drug delay recurrence or start of subsequent therapy?”). The framework facilitates discussions during clinical trial planning and design to ensure alignment between the key question of interest, the analysis, and interpretation. This article is a result of a cross-industry collaboration to connect the International Council for Harmonisation E9 addendum concepts to applications. Data from previously reported randomized phase 3 studies in the renal cell carcinoma setting are used to consider common intercurrent events in solid tumor studies, and to illustrate different scientific questions and the consequences of the estimand choice for study design, data collection, analysis, and interpretation.     

Marginal Means/Rates Models for Multiple Type Recurrent Event Data

Recurrent events are frequently observed in biomedical studies, and often more than one type of event is of interest. Follow-up time may be censored due to loss to follow-up or administrative censoring. We propose a class of semi-parametric marginal means/rates models, with a general relative risk form, for assessing the effect of covariates on the censored event processes of interest. We formulate estimating equations for the model parameters, and examine asymptotic properties of the parameter estimators. Finite sample properties of the regression coefficients are examined through simulations. The proposed methods are applied to a retrospective cohort study of risk factors for preschool asthma.     

Fitting Cox Models with Doubly Censored Data Using Spline‐Based Sieve Marginal Likelihood

In some applications, the failure time of interest is the time from an originating event to a failure event while both event times are interval censored. We propose fitting Cox proportional hazards models to this type of data using a spline‐based sieve maximum marginal likelihood, where the time to the originating event is integrated out in the empirical likelihood function of the failure time of interest. This greatly reduces the complexity of the objective function compared with the fully semiparametric likelihood. The dependence of the time of interest on time to the originating event is induced by including the latter as a covariate in the proportional hazards model for the failure time of interest. The use of splines results in a higher rate of convergence of the estimator of the baseline hazard function compared with the usual non‐parametric estimator. The computation of the estimator is facilitated by a multiple imputation approach. Asymptotic theory is established and a simulation study is conducted to assess its finite sample performance. It is also applied to analyzing a real data set on AIDS incubation time.     

Simplified Estimating Functions for Diffusion Models with a High-dimensional Parameter

We consider estimating functions for discretely observed diffusion processes of the following type: for one part of the parameter of interest we propose to use a simple and explicit estimating function of the type studied by Kessler (2000); for the remaining part of the parameter we use a martingale estimating function. Such an approach is particularly useful in practical applications when the parameter is high-dimensional. It is also often necessary to supplement a simple estimating function by another type of estimating function because only the part of the parameter on which the invariant measure depends can be estimated by a simple estimating function. Under regularity conditions the resulting estimators are consistent and asymptotically normal. Several examples are considered in order to demonstrate the idea of the estimating procedure. The method is applied to two data sets comprising wind velocities and stock prices. In one example we also propose a general method for constructing diffusion models with a prescribed marginal distribution which have a flexible dependence structure.     

Uncertainty in functional principal component analysis

Principal component analysis (PCA) and functional principal analysis are key tools in multivariate analysis, in particular modelling yield curves, but little attention is given to questions of uncertainty, neither in the components themselves nor in any derived quantities such as scores. Actuaries using PCA to model yield curves to assess interest rate risk for insurance companies are required to show any uncertainty in their calculations. Asymptotic results based on assumptions of multivariate normality are unsatisfactory for modest samples, and application of bootstrap methods is not straightforward, with the novel pitfalls of possible inversions in order of sample components and reversals of signs. We present methods for overcoming these difficulties and discuss arising of other potential hazards.     

CONFIDENTIALITY, PRIVACY AND SENSITIVITY IN HOUSEHOLD SURVEYS

Editorial Note: The personal nature of questions included in some surveys is a matter of interest and possibly concern to statisticians. At the Editor's request Dr. Ware and Professor Caldwell take up this issue, their comments being largely based on experience gained from a project carried out in 1971.