In the case-crossover design, only cases are sampled and the hazard ratio is estimated from within-subject comparisons of exposures at the event time and in M control periods prior to the event. We consider the effect of within-subject dependence of exposures in successive time periods. We show that estimates obtained from the conditional logistic model are biased. This bias disappears if the distribution of exposures in the M+1 successive time intervals is exchangeable. In contrast, the Mantel-Haenszel estimator for the odds ratio is approximately unbiased provided that exposures are stationary. Suitable methods of analysis of case-crossover designs using maximum likelihood may be derived from cohort rather than case-control models.

We introduce an algorithm for producing simple approximate principal components directly from a variance±covariance matrix. At the heart of the algorithm is a series of`simplicity preserving' linear transformations. Each transformation seeks a direction within a two-dimensional subspace that has maximum variance. However, the choice of directions is limited so that the direction can be represented by a vector of integers whenever the subspace can also be represented by vectors of integers. The resulting approximate components can therefore always be represented by integers. Furthermore the elements of these integer vectors are often small, particularly for the ®rst few components. We demonstrate the performance of this algorithm on two data sets and show that good approximations to the principal components that are also clearly simple and interpretable can result.

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The short insulin tolerance test is a simple method of estimating insulin resistance by measuring the rate of fall of blood glucose following the intravenous administration of insulin. To determine its reproducibility, 18 healthy subjects underwent duplicate insulin tolerance tests separated by at least 1 week. Intravenous insulin (0.05 units kg-1) was administered into an antecubital vein and arterialized venous samples were obtained from a retrogradely cannulated vein on the dorsum of the hand on the same side. The test was terminated with an intravenous glucose injection 15 min after the administration of insulin. The mean whole blood glucose concentration fell from 4.6 mmol l-1 to 2.8 mmol l-1 while plasma insulin concentrations rose to supraphysiological levels and declined exponentially. The glucose disappearance rate (Kitt) calculated from the slope of the fall in log transformed blood glucose between 3 and 15 min after insulin injection ranged from 2.1 to 6.5 (mean 4.4) % min-1 during the first visit and 1.7 to 7.4 (mean 4.4) % min-1 during the second. The ratio of the within-subject to between-subject variance of the test was 0.24, the within-subject coefficient of variation was 13% and the between-subject coefficient of variation 26%. The short insulin tolerance test is reproducible and could be used to measure insulin resistance in large-scale epidemiological studies.