The use of information from flanking markers to estimate the position and size of the effect of a quantitative trait locus (QTL) lying between two markers is shown to be affected by QTLs lying in neighbouring regions of the chromosome. In some situations the effects of two QTLs lying outside the flanked region are reinforced in such a way that a 'ghost' QTL may be mistakenly identified as a real QTL. These problems are discussed in the framework of a backcross using a regression model as the analytical tool to present the theoretical results. Regression models that use information obtained from three or more nearby markers are shown to be useful in separating the effects of QTLs in neighbouring regions. A simulated data set exemplifies the problem and is analysed by the interval mapping method as well as by the regression model.

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Natural exposure to prion disease is likely to occur throughout successive challenges, yet most experiments focus on single large doses of infectious material. We analyze the results from an experiment in which rodents were exposed to multiple doses of feed contaminated with the scrapie agent. We formally define hypotheses for how the doses combine in terms of statistical models. The competing hypotheses are that only the total dose of infectivity is important (cumulative model), doses act independently, or a general alternative that interaction between successive doses occurs (to raise or lower the risk of infection). We provide sample size calculations to distinguish these hypotheses. In the experiment, a fixed total dose has a significantly reduced probability of causing infection if the material is presented as multiple challenges, and as the time between challenges lengthens. Incubation periods are shorter and less variable if all material is consumed on one occasion. We show that the probability of infection is inconsistent with the hypothesis that each dose acts as a cumulative or independent challenge. The incubation periods are inconsistent with the independence hypothesis. Thus, although a trend exists for the risk of infection with prion disease to increase with repeated doses, it does so to a lesser degree than is expected if challenges combine independently or in a cumulative manner.