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.

Accounting for risk aversion in repeated prisoners’ dilemma games: an experimental test

We apply experimental methods to study the role of risk aversion on players’ behavior in repeated prisoners’ dilemma games. Faced with quantitatively equal discount factors, the most risk-averse players will choose Nash strategies more often in the presence of uncertainty than when future profits are discounted in a deterministic way. Overall, we find that risk aversion relates negatively with the frequency of collusive outcomes.

The influence of time on lead toxicity and bioaccumulation determined by the OECD earthworm toxicity test

Internationally agreed standard protocols for assessing chemical toxicity of contaminants in soil to worms assume that the test soil does not need to equilibrate with the chemical to be tested prior to the addition of the test organisms and that the chemical will exert any toxic effect upon the test organism within 28 days. Three experiments were carried out to investigate these assumptions. The first experiment was a standard toxicity test where lead nitrate was added to a soil in solution to give a range of concentrations. The mortality of the worms and the concentration of lead in the survivors were determined. The LC(50)s for 14 and 28 days were 5311 and 5395 mug(Pb) g(soil)(-1) respectively. The second experiment was a timed lead accumulation study with worms cultivated in soil containing either 3000 or 5000 mug(Pb) g(soil)(-1). The concentration of lead in the worms was determined at various sampling times. Uptake at so' Sol both concentrations was linear with time. Worms in the 5000 mug g(-1) soil accumulated lead at a faster rate (3.16 mug Pb g(tissue)(-1) day(-1)) tiss than those in the 3000 mug g(-1) soil (2.21 mug Pb-tissue g(-1) day(-1)). The third experiment was a timed experiment with worms cultivated in tiss soil containing 7000 mugPb g(soil)(-1). Soil and lead nitrate solution were mixed and stored at 20 degreesC. Worms were added at various times over a 35-day period. The time to death increased from 23 h, when worms were added directly after the lead was added to the soil, to 67 It when worms were added after the soil had equilibrated with the lead for 35 days. In artificially Pb-amended soils the worms accumulate Pb over the duration of their exposure to the Pb. Thus time limited toxicity tests may be terminated before worm body load has reached a toxic level. This could result in under-estimates of the toxicity of Pb to worms. As the equilibration time of artificially amended Pb-bearing soils increases the bioavailability of Pb decreases. Thus addition of worms shortly after addition of Pb to soils may result in the over-estimate of Pb toxicity to worms. The current OECD acute worm toxicity test fails to take these two phenomena into account thereby reducing the environmental relevance of the contaminant toxicities it is used to calculate. (C) 2002 Elsevier Science Ltd. All rights reserved.

A test of the master gene hypothesis for interspersed repetitive DNA sequences

Many families of interspersed repetitive DNA elements, including human Alu and LINE (Long Interspersed Element) elements, have been proposed to have accumulated through repeated copying from a single source locus: the "master gene." The extent to which a master gene model is applicable has implications for the origin, evolution, and function of such sequences. One repetitive element family for which a convincing case for a master gene has been made is the rodent ID (identifier) elements. Here we devise a new test of the master gene model and use it to show that mouse ID element sequences are not compatible with a strict master gene model. We suggest that a single master gene is rarely, if ever, likely to be responsible for the accumulation of any repeat family.

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.