An extension of an over-dispersion test for count data

While over-dispersion in capture–recapture studies is well known to lead to poor estimation of population size, current diagnostic tools to detect the presence of heterogeneity have not been specifically developed for capture–recapture studies. To address this, a simple and efficient method of testing for over-dispersion in zero-truncated count data is developed and evaluated. The proposed method generalizes an over-dispersion test previously suggested for un-truncated count data and may also be used for testing residual over-dispersion in zero-inflation data. Simulations suggest that the asymptotic distribution of the test statistic is standard normal and that this approximation is also reasonable for small sample sizes. The method is also shown to be more efficient than an existing test for over-dispersion adapted for the capture–recapture setting. Studies with zero-truncated and zero-inflated count data are used to illustrate the test procedures.

The double triangular test in practice

The double triangular test was introduced twenty years ago, and the purpose of this paper is to review applications that have been made since then. In fact, take-up of the method was rather slow until the late 1990s, but in recent years several clinical trial reports have been published describing its use in a wide range of therapeutic areas. The core of this paper is a detailed account of five trials that have been published since 2000 in which the method was applied to studies of pancreatic cancer, breast cancer, myocardial infarction, epilepsy and bedsores. Before those accounts are given, the method is described and the history behind its evolution is presented. The future potential of the method for sequential case-control and equivalence trials is also discussed. Copyright © 2004 John Wiley & Sons, Ltd.

The sequential analysis of repeated binary responses: a score test for the case of three time points

In this paper a robust method is developed for the analysis of data consisting of repeated binary observations taken at up to three fixed time points on each subject. The primary objective is to compare outcomes at the last time point, using earlier observations to predict this for subjects with incomplete records. A score test is derived. The method is developed for application to sequential clinical trials, as at interim analyses there will be many incomplete records occurring in non-informative patterns. Motivation for the methodology comes from experience with clinical trials in stroke and head injury, and data from one such trial is used to illustrate the approach. Extensions to more than three time points and to allow for stratification are discussed. Copyright © 2005 John Wiley & Sons, Ltd.

The F test for comparing two normal variances: correct and incorrect calculation of the two-sided p-value?

This article illustrates that not all statistical software packages are correctly calculating a p-value for the classical F test comparison of two independent Normal variances. This is illustrated with a simple example, and the reasons why are discussed. Eight different software packages are considered.

Evaluation of a sequential global test of improved recovery following stroke as applied to the ICTUS trial of citicoline

The International Citicoline Trial in acUte Stroke is a sequential phase III study of the use of the drug citicoline in the treatment of acute ischaemic stroke, which was initiated in 2006 in 56 treatment centres. The primary objective of the trial is to demonstrate improved recovery of patients randomized to citicoline relative to those randomized to placebo after 12 weeks of follow-up. The primary analysis will take the form of a global test combining the dichotomized results of assessments on three well-established scales: the Barthel Index, the modified Rankin scale and the National Institutes of Health Stroke Scale. This approach was previously used in the analysis of the influential National Institute of Neurological Disorders and Stroke trial of recombinant tissue plasminogen activator in stroke. The purpose of this paper is to describe how this trial was designed, and in particular how the simultaneous objectives of taking into account three assessment scales, performing a series of interim analyses and conducting treatment allocation and adjusting the analyses to account for prognostic factors, including more than 50 treatment centres, were addressed. Copyright (C) 2008 John Wiley & Sons, Ltd.

A combined score test for binary and ordinal endpoints from clinical trials

There is growing interest, especially for trials in stroke, in combining multiple endpoints in a single clinical evaluation of an experimental treatment. The endpoints might be repeated evaluations of the same characteristic or alternative measures of progress on different scales. Often they will be binary or ordinal, and those are the cases studied here. In this paper we take a direct approach to combining the univariate score statistics for comparing treatments with respect to each endpoint. The correlations between the score statistics are derived and used to allow a valid combined score test to be applied. A sample size formula is deduced and application in sequential designs is discussed. The method is compared with an alternative approach based on generalized estimating equations in an illustrative analysis and replicated simulations, and the advantages and disadvantages of the two approaches are discussed.

Can portmanteau nonlinearity tests serve as general mis-specification tests?

A number of recent papers have employed the BDS test as a general test for mis-specification for linear and nonlinear models. We show that for a particular class of conditionally heteroscedastic models, the BDS test is unable to detect a common mis-specification. Our results also demonstrate that specific rather than portmanteau diagnostics are required to detect neglected asymmetry in volatility. However for both classes of tests reasonable power is only obtained using very large sample sizes.

Portmanteau model diagnostics and tests for nonlinearity: a comparative Monte Carlo study of two alternative methods

This paper employs an extensive Monte Carlo study to test the size and power of the BDS and close return methods of testing for departures from independent and identical distribution. It is found that the finite sample properties of the BDS test are far superior and that the close return method cannot be recommended as a model diagnostic. Neither test can be reliably used for very small samples, while the close return test has low power even at large sample sizes

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

A modified signed likelihood ratio test in elliptical structural models

In this paper we deal with the issue of performing accurate testing inference on a scalar parameter of interest in structural errors-in-variables models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, which has the multivariate normal distribution as special case. We derive a modified signed likelihood ratio statistic that follows a standard normal distribution with a high degree of accuracy. Our Monte Carlo results show that the modified test is much less size distorted than its unmodified counterpart. An application is presented.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

We propose a likelihood ratio test ( LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrapbased approach. LRT is shown to be significantly faster and statistically powerful even within non- Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided.

A home environment test battery for status assessment in patients with motor fluctuations

Background and aims Evaluating status in patients with motor fluctuations is complex and occasional observations/measurements do not give an adequate picture as to the time spent in different states. We developed a test battery to assess advanced Parkinson patients' status consisting of diary assessments and motor tests. This battery was constructed and implemented on a handheld computer with built-in mobile communication. In fluctuating patients, it should typically be used several times daily in the home environment, over periods of about one week. The aim of this battery is to provide status information in order to evaluate treatment effects in clinical practice and research, follow up treatments and disease progression and predict outcome to optimize treatment strategy. Methods Selection of diary questions was based on a previous study with Duodopa® (DIREQT). Tapping tests (with and without visual cueing) and a spiral drawing test were added. Rapid prototyping was used in development of the user interface. An evaluation with two pilot patients was performed before and after receiving new treatments for advanced disease (one received Duodopa® and one received DBS). Speed and proportion missed taps were calculated for the tapping tests and entropy of the radial drawing velocity was calculated for the spiral tests. Test variables were evaluated using non-parametric statistics. Results Post-treatment improvement was detected in both patients in many of the test variables. Conclusions Although validation work remains, preliminary results are promising and the test battery is currently being evaluated in a long-term health economics study with Duodopa® (DAPHNE).

Analysis of tapping test results in a test battery for advanced PD patients

Objective: To compare results from various tapping tests with diary responses in advanced PD. Background: A home environment test battery for assessing patient state in advanced PD, consisting of diary assessments and motor tests was constructed for a hand computer with touch screen and mobile communication. The diary questions: 1. walking, 2. time in off , on and dyskinetic states, 3. off at worst, 4. dyskinetic at worst, 5. cramps, and 6. satisfied with function, relate to the recent past. Question 7, self-assessment, allows seven steps from -3 ( very off ) to +3 ( very dyskinetic ) and relate to right now. Tapping tests outline: 8. Alternately tapping two fields (un-cued) with right hand 9. Same as 8 but using left hand 10. Tapping an active field (out of two) following a system-generated rhythm (increasing speed) with the dominant hand 11. Tapping an active field (out of four) that randomly changes location when tapped using the dominant hand Methods: 65 patients (currently on Duodopa, or candidates for this treatment) entered diary responses and performed tapping tests four times per day during one to six periods of seven days length. In total there were 224 test periods and 6039 test occasions. Speed for tapping test 10 was discardedand tests 8 and 9 were combined by taking means. Descriptive statistics were used to present the variation of the test variables in relation to self assessment (question 7). Pearson correlation coefficients between speed and accuracy (percent correct) in tapping tests and diary responses were calculated. Results: Mean compliance (percentage completed test occasions per test period) was 83% and the median was 93%. There were large differences in both mean tapping speed and accuracy between the different self-assessed states. Correlations between diary responses and tapping results were small (-0.2 to 0.3, negative values for off-time and dyskinetic-time that had opposite scale directions). Correlations between tapping results were all positive (0.1 to 0.6). Conclusions: The diary responses and tapping results provided different information. The low correlations can partly be explained by the fact that questions related to the past and by random variability, which could be reduced by taking means over test periods. Both tapping speed and accuracy reflect the motor function of the patient to a large extent.

A conditional likelihood ratio test for structural models

This paper develops a general method for constructing similar tests based on the conditional distribution of nonpivotal statistics in a simultaneous equations model with normal errors and known reducedform covariance matrix. The test based on the likelihood ratio statistic is particularly simple and has good power properties. When identification is strong, the power curve of this conditional likelihood ratio test is essentially equal to the power envelope for similar tests. Monte Carlo simulations also suggest that this test dominates the Anderson- Rubin test and the score test. Dropping the restrictive assumption of disturbances normally distributed with known covariance matrix, approximate conditional tests are found that behave well in small samples even when identification is weak.