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Simple and multiple linear regression models are considered between variables whose "values" are convex compact random sets in R p , (that is, hypercubes, spheres, and so on). We analyze such models within a set-arithmetic approach. Contrary to what happens for random variables, the least squares optimal solutions for the basic affine transformation model do not produce suitable estimates for the linear regression model. First, we derive least squares estimators for the simple linear regression model and examine them from a theoretical perspective. Moreover, the multiple linear regression model is dealt with and a stepwise algorithm is developed in order to find the estimates in this case. The particular problem of the linear regression with interval-valued data is also considered and illustrated by means of a real-life example.

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Docetaxel and paclitaxel administered weekly have discrete efficacy in patients with NSCLC previously treated with platinum-based chemotherapy. The higher non-haematological toxicity of docetaxel, particularly pulmonary toxicity and diarrhoea, is of concern and warrants further investigation.

The receiver operating characteristic curve is a popular graphical method frequently used in order to study the diagnostic capacity of continuous markers. It represents in a plot true-positive rates against the false-positive ones. Both the practical and theoretical aspects of the receiver operating characteristic curve have been extensively studied. Conventionally, it is assumed that the considered marker has a monotone relationship with the studied characteristic; i.e., the upper (lower) values of the (bio)marker are associated with a higher probability of a positive result. However, there exist real situations where both the lower and the upper values of the marker are associated with higher probability of a positive result. We propose a receiver operating characteristic curve generalization, [Formula: see text], useful in this context. All pairs of possible cut-off points, one for the lower and another one for the upper marker values, are taken into account and the best of them are selected. The natural empirical estimator for the [Formula: see text] curve is considered and its uniform consistency and asymptotic distribution are derived. Finally, two real-world applications are studied.