Diagnostic tests for bias of estimating equations in weighted regression with missing covariates

The authors propose two tests, one parametric and the other semiparametric, for testing bias of estimating equations in weighted regression with partially missing covariates when the primary regression model is correctly specified. More generally, the proposed tests may be thought of as a diagnostic tool for the combined package of the primary regression model and the missingness assumptions. The asymptotic null distributions of the two test statistics are derived under the assumption of missingness at random for the partially missing covariates. A small scale simulation study completes the work.     

Misspecification of at‐risk periods and distributional assumptions in estimating COPD exacerbation rates: The resultant bias in treatment effect estimation

In trials comparing the rate of chronic obstructive pulmonary disease exacerbation between treatment arms, the rate is typically calculated on the basis of the whole of each patient's follow‐up period. However, the true time a patient is at risk should exclude periods in which an exacerbation episode is occurring, because a patient cannot be at risk of another exacerbation episode until recovered. We used data from two chronic obstructive pulmonary disease randomized controlled trials and compared treatment effect estimates and confidence intervals when using two different definitions of the at‐risk period. Using a simulation study we examined the bias in the estimated treatment effect and the coverage of the confidence interval, using these two definitions of the at‐risk period. We investigated how the sample size required for a given power changes on the basis of the definition of at‐risk period used. Our results showed that treatment efficacy is underestimated when the at‐risk period does not take account of exacerbation duration, and the power to detect a statistically significant result is slightly diminished. Correspondingly, using the correct at‐risk period, some modest savings in required sample size can be achieved. Using the proposed at‐risk period that excludes recovery times requires formal definitions of the beginning and end of an exacerbation episode, and we recommend these be always predefined in a trial protocol.     

The potential for bias in reporting of industry-sponsored clinical trials

Concerns about potentially misleading reporting of pharmaceutical industry research have surfaced many times. The potential for duality (and thereby conflict) of interest is only too clear when you consider the sums of money required for the discovery, development and commercialization of new medicines. As the ability of major, mid-size and small pharmaceutical companies to innovate has waned, as evidenced by the seemingly relentless decline in the numbers of new medicines approved by Food and Drug Administration and European Medicines Agency year-on-year, not only has the cost per new approved medicine risen: so too has the public and media concern about the extent to which the pharmaceutical industry is open and honest about the efficacy, safety and quality of the drugs we manufacture and sell. In 2005 an Editorial in Journal of the American Medical Association made clear that, so great was their concern about misleading reporting of industry-sponsored studies, henceforth no article would be published that was not also guaranteed by independent statistical analysis. We examine the precursors to this Editorial, as well as its immediate and lasting effects for statisticians, for the manner in which statistical analysis is carried out, and for the industry more generally.     

The estimating function bootstrap

The authors propose a bootstrap procedure which estimates the distribution of an estimating function by resampling its terms using bootstrap techniques. Studentized versions of this so‐called estimating function (EF) bootstrap yield methods which are invariant under reparametrizations. This approach often has substantial advantage, both in computation and accuracy, over more traditional bootstrap methods and it applies to a wide class of practical problems where the data are independent but not necessarily identically distributed. The methods allow for simultaneous estimation of vector parameters and their components. The authors use simulations to compare the EF bootstrap with competing methods in several examples including the common means problem and nonlinear regression. They also prove symptotic results showing that the studentized EF bootstrap yields higher order approximations for the whole vector parameter in a wide class of problems.     

The need for new statistical legislation for the UK

Summary. The paper is written to inform public discussion on whether or not statistical legislation for the UK is needed and, if so, on its nature and content. A brief account of the background to the current position is given. The Government's stated intention is to create an 'independent statistical service' and a discussion of the meaning of independence in the context of official stat- istics and governance arrangements is provided. Recent international experience is described and the Statistics Acts of some other countries are used to distil the key features of Statistics Acts in other countries. The arguments for and against possible legislation are described. Whether or not a Statistics Act is desirable for the UK depends strongly on the legislation being well framed. There are several key issues on which Parliament would need to develop an informed view and these are set out towards the end of the paper.     

The need for a federal lotteries review board

Three areas in the running of a lottery may be distinguished: the design of the prize structure, the marketing of the product, and the selection of the winners. The rules and regulations in each of these areas governing the large-scale Canadian lotteries are not clear. Some examples show the need for an independent body which would clarify these regulations and provide control over the large lottery operations in Canada.     

The quincunx: history and mathematics

Received: December 30, 1999; revised version: July 19, 2000     

The convolution theorem for estimating linear functionals in indirect nonparametric regression models

Nonparametric regression—directly or indirectly observed—is one of the important statistical models. On one hand it contains two infinite dimensional parameters (the regression function and the error density), and on the other it is of rather simple structure. Therefore, it may serve as an interesting paradigm for illustrating or developing abstract statistical theory for non-Euclidean parameters. In this paper estimation of a linear functional of the indirectly observed regression function is considered, when a deterministic design is used. It should be noted that any Fourier coefficient of an expansion of the regression function in an orthonormal basis is such a functional. Because the design is deterministic the observables are independent but not identically distributed. Local asymptotic normality is established and applied to prove Hájek's convolution theorem for this functional. Pertinent references are Beran [1977. Robust location estimates. Ann. Statist. 5, 431–444] and McNeney and Wellner [2000. Application of convolution theorems in semiparametric models with non-i.i.d. data. J. Statist. Plann. Inference 91, 441–480]. For purposes explained above, however, the paper is kept self-contained and full proofs are provided.     

The use of a mixture model for estimating vaccine efficacy

In this note a mixture model is applied to examine the effects of vaccination. It can directly estimate the efficacy parameters and their standard errors for the two models suggested in Smith et al. (1994) and Haber et al.(1991a). Furthermore, it can be shown that the action of the vaccine for the two models are equivalent. We illustrate the procedure to an outbreak of mumps in a middle school in Ashtabula County, Ohio.     

Combining estimating functions for volatility

Accurate estimates of volatility are needed in risk management. Generalized autoregressive conditional heteroscedastic (GARCH) models and random coefficient autoregressive (RCA) models have been used for volatility modelling. Following Heyde [1997. Quasi-likelihood and its Applications. Springer, New York], volatility estimates are obtained by combining two different estimating functions. It turns out that the combined estimating function for the parameter in autoregressive processes with GARCH errors and RCA models contains maximum information. The combination of the least squares (LS) estimating function and the least absolute deviation (LAD) estimating function with application to GARCH model error identification is discussed as an application.     

Testing for not-at-home bias in social surveys

When subjects are not found at home in a social survey, the question arises whether the subsample encountered at home, on the first or subsequent visits, is random or biased. A procedure is presented by which this question can be statistically tested, by comparing the decline rate in unfound subjects, over repeated visits, with those expected if the subsample were random or strongly biased. The randomness of the subsamples can be compared between the first and subsequent visits. The procedure can be carried out during a programme of revisits, to check quickly whether a satisfactory sample is being obtained.     

Numerical techniques for estimating probabilities

In this article we consider the pioblem of finding the maximum likelihood estimate for a certain class of discrete sampling models. Methods are adapted from parts of convex optimization theory, includiug aspects of equivalence theory, duality theorv and iterative procedures Their application is illustrated through example.     

Adjusting for bias in randomized cluster trials

The randomized cluster design is typical in studies where the unit of randomization is a cluster of individuals rather than the individual. Evaluating various intervention strategies across medical care providers at either an institutional level or at a physician group practice level fits the randomized cluster model. Clearly, the analytical approach to such studies must take the unit of randomization and accompanying intraclass correlation into consideration. We review alternative methods to the typical Pearson's chi-square analysis and illustrate these alternatives. We have written and tested a Fortran program that produces the statistics outlined in this paper. The program, in an executable format is available from the author on request.     

The 'heuristics and biases' bias in expert elicitation

Summary.  In the early 1970s Tversky and Kahneman published a series of papers on 'heuristics and biases' describing human inadequacies in assessing probabilities, culminating in a highly popular article in Science . This seminal research has been heavily cited in many fields, including statistics, as the definitive research on probability assessment. Curiously, although this work was debated at the time and more recent work has largely refuted many of the claims, this apparent heuristics and biases bias in elicitation research has gone unremarked. Over a decade of research into the frequency effect, the importance of framing, and cognitive models more generally, has been almost completely ignored by the statistical literature on expert elicitation. To remedy this situation, this review offers a guide to the psychological research on assessing probabilities, both old and new, and gives concrete guidelines for eliciting expert knowledge.     

The cornish-fisher expansion for estimating percentage points: a numerical perspective

The expansion, in standard form, consists of some 66 terms involving polyno - mials in a normal deviate, and cumulants and cumulant products to order ten. An assumed order of magnitude reduces these terms to eight groups. Sign patterns in the terms are not obvious. We take a number of Pearson densities and assess from the expansions a set of standard percentiles (1%, 5%, 95%, 99%). Validity of the as-sessments is pivoted on two alternative models:(i) the Bowman-Shenton algorithm for percentage points of Pearson densities, (ii) the 4-moment Johnson translation model. This approach has wide application since the models have proved to be remarkably reliable when compared, and also when compared with simulation as-sessments. A brief account is given of acceleration of convergence for the series, but there seems to be no analogue of the Padè or Levin algorithms.

The Cornish-Fisher application to the Fisher z-statistic is studied and the cumu- lants defined in general. Irwin's expression for the density of means from Pearson Type II is recalled. There is an error in the Cornish-Fisher treatment of the z-statistic but this is one which has its source in the write-up. Again the Irwin density in the general case has a factor missing.