Consultants' forum: should post hoc sample size calculations be done?

Pre‐study sample size calculations for clinical trial research protocols are now mandatory. When an investigator is designing a study to compare the outcomes of an intervention, an essential step is the calculation of sample sizes that will allow a reasonable chance (power) of detecting a pre‐determined difference (effect size) in the outcome variable, at a given level of statistical significance. Frequently studies will recruit fewer patients than the initial pre‐study sample size calculation suggested. Investigators are faced with the fact that their study may be inadequately powered to detect the pre‐specified treatment effect and the statistical analysis of the collected outcome data may or may not report a statistically significant result. If the data produces a “non‐statistically significant result” then investigators are frequently tempted to ask the question “Given the actual final study size, what is the power of the study, now, to detect a treatment effect or difference?” The aim of this article is to debate whether or not it is desirable to answer this question and to undertake a power calculation, after the data have been collected and analysed. Copyright © 2008 John Wiley & Sons, Ltd.     

A copula-based Markov chain model for the analysis of binary longitudinal data

A fully parametric first-order autoregressive (AR(1)) model is proposed to analyse binary longitudinal data. By using a discretized version of a copula, the modelling approach allows one to construct separate models for the marginal response and for the dependence between adjacent responses. In particular, the transition model that is focused on discretizes the Gaussian copula in such a way that the marginal is a Bernoulli distribution. A probit link is used to take into account concomitant information in the behaviour of the underlying marginal distribution. Fixed and time-varying covariates can be included in the model. The method is simple and is a natural extension of the AR(1) model for Gaussian series. Since the approach put forward is likelihood-based, it allows interpretations and inferences to be made that are not possible with semi-parametric approaches such as those based on generalized estimating equations. Data from a study designed to reduce the exposure of children to the sun are used to illustrate the methods.     

Forecast mean squared error reductionin the VAR(1) process

When VAR models are used to predict future outcomes, the forecast error can be substantial. Through imposition of restrictions on the off-diagonal elements of the parameter matrix, however, the information in the process may be condensed to the marginal processes. In particular, if the cross-autocorrelations in the system are small and only a small sample is available, then such a restriction may reduce the forecast mean squared error considerably.

In this paper, we propose three different techniques to decide whether to use the restricted or unrestricted model, i.e. the full VAR(1) model or only marginal AR(1) models. In a Monte Carlo simulation study, all three proposed tests have been found to behave quite differently depending on the parameter setting. One of the proposed tests stands out, however, as the preferred one and is shown to outperform other estimators for a wide range of parameter settings.     

On estimating the distribution of data envelopment analysis efficiency scores: an application to nursing homes’ care planning process

Data envelopment analysis (DEA) is a deterministic econometric model for calculating efficiency by using data from an observed set of decision-making units (DMUs). We propose a method for calculating the distribution of efficiency scores. Our framework relies on estimating data from an unobserved set of DMUs. The model provides posterior predictive data for the unobserved DMUs to augment the frontier in the DEA that provides a posterior predictive distribution for the efficiency scores. We explore the method on a multiple-input and multiple-output DEA model. The data for the example are from a comprehensive examination of how nursing homes complete a standardized mandatory assessment of residents.     

A new estimation method for Weibull-type tails based on the mean excess function

Studying the right tail of a distribution, one can classify the distributions into three classes based on the extreme value index γ$\gamma$. The class γ>0$\gamma >0$ corresponds to Pareto-type or heavy tailed distributions, while γ<0$\gamma <0$ indicates that the underlying distribution has a finite endpoint. The Weibull-type distributions form an important subgroup within the Gumbel class with γ=0$\gamma =0$. The tail behaviour can then be specified using the Weibull tail index. Classical estimators of this index show severe bias. In this paper we present a new estimation approach based on the mean excess function, which exhibits improved bias and mean squared error. The asserted properties are supported by simulation experiments and asymptotic results. Illustrations with real life data sets are provided.     

Bayesian credible intervals for response surface optima

In response surface methodology, one is usually interested in estimating the optimal conditions based on a small number of experimental runs which are designed to optimally sample the experimental space. Typically, regression models are constructed from the experimental data and interrogated in order to provide a point estimate of the independent variable settings predicted to optimize the response. Unfortunately, these point estimates are rarely accompanied with uncertainty intervals. Though classical frequentist confidence intervals can be constructed for unconstrained quadratic models, higher order, constrained or nonlinear models are often encountered in practice. Existing techniques for constructing uncertainty estimates in such situations have not been implemented widely, due in part to the need to set adjustable parameters or because of limited or difficult applicability to constrained or nonlinear problems. To address these limitations a Bayesian method of determining credible intervals for response surface optima was developed. The approach shows good coverage probabilities on two test problems, is straightforward to implement and is readily applicable to the kind of constrained and/or nonlinear problems that frequently appear in practice.     

A re-evaluation of random-effects meta-analysis

Summary.  Meta-analysis in the presence of unexplained heterogeneity is frequently undertaken by using a random-effects model, in which the effects underlying different studies are assumed to be drawn from a normal distribution. Here we discuss the justification and interpretation of such models, by addressing in turn the aims of estimation, prediction and hypothesis testing. A particular issue that we consider is the distinction between inference on the mean of the random-effects distribution and inference on the whole distribution. We suggest that random-effects meta-analyses as currently conducted often fail to provide the key results, and we investigate the extent to which distribution-free, classical and Bayesian approaches can provide satisfactory methods. We conclude that the Bayesian approach has the advantage of naturally allowing for full uncertainty, especially for prediction. However, it is not without problems, including computational intensity and sensitivity to a priori judgements. We propose a simple prediction interval for classical meta-analysis and offer extensions to standard practice of Bayesian meta-analysis, making use of an example of studies of 'set shifting' ability in people with eating disorders.     

Active‐controlled,non‐inferiority trials in oncology: arbitrary limits,infeasible sample sizes and uninformative data analysis. Is there another way?

In oncology, it may not always be possible to evaluate the efficacy of new medicines in placebo-controlled trials. Furthermore, while some newer, biologically targeted anti-cancer treatments may be expected to deliver therapeutic benefit in terms of better tolerability or improved symptom control, they may not always be expected to provide increased efficacy relative to existing therapies. This naturally leads to the use of active-control, non-inferiority trials to evaluate such treatments. In recent evaluations of anti-cancer treatments, the non-inferiority margin has often been defined in terms of demonstrating that at least 50% of the active control effect has been retained by the new drug using methods such as those described by Rothmann et al., Statistics in Medicine 2003; 22:239-264 and Wang and Hung Controlled Clinical Trials 2003; 24:147-155. However, this approach can lead to prohibitively large clinical trials and results in a tendency to dichotomize trial outcome as either 'success' or 'failure' and thus oversimplifies interpretation. With relatively modest modification, these methods can be used to define a stepwise approach to design and analysis. In the first design step, the trial is sized to show indirectly that the new drug would have beaten placebo; in the second analysis step, the probability that the new drug is superior to placebo is assessed and, if sufficiently high in the third and final step, the relative efficacy of the new drug to control is assessed on a continuum of effect retention via an 'effect retention likelihood plot'. This stepwise approach is likely to provide a more complete assessment of relative efficacy so that the value of new treatments can be better judged.     

Women–Family in Quality Perspective

Bringing together women and family in quality perspective bring about interesting discussions in this paper. By integrating previous studies and considering expert opinions, we determinate the variables and dimensions with respect to women’s existence regarding their roles both in the family and at work. Many activities carried out by women represent the consumer aspects of their role. Women undertake these activities to fulfill their needs, which can be classified in the order of preference using Maslow’s Hierarchy of Need. Women success can be measured based on their ability to perform their roles successfully. We identify women’s performance by using quality approach of Personal Quality Maintenance (PQM), which is widely applied in many organizations in order to maintain the service delivery, which meets the customer satisfaction. The effort to enhance women’s satisfaction for their success in playing the multirole in the family and at work is our main consideration. This study may contribute a new point of view regarding for the women’s welfare and existence.