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Consistent estimators are derived for the age-specific and lifetime incidence rates of late-onset diseases from censored, biased samples, using a discrete time model and a traditional assumption for size-biased sampling. The estimators are alternatives to the so-called index case estimators often used by epidemiologists under similar circumstances. The asymptotic normality of the proposed estimators is established and an adaptation of Greenwood's formula is given for estimating and comparing their asymptotic variances. We show that index case estimators can be inconsistent and find a necessary and sufficient condition for their consistency. The results are applicable in the study of familial aggregation of diseases that are not manifest at birth when the sample consists of families identified through a family member who has the disease of interest. A survey of families of nursing home patients with a narrowly defined form of Alzheimer's disease, undertaken to clarify its mode of inheritance is an...

The work described here concerns some mathematical questions related to parasitology. It has its roots in a paper by Macdonald (1965) on helminthic infections where the author stresses the importance of the parasite’s sexuality in its transmission dynamics. Anyone who wants to capture quantitatively the life-cycle of a parasite has to deal, at some point, with its reproductive strategy. More precisely, it is impossible to avoid computation of the number of fertilized eggs if one wants to get an estimate of the parasite’s progeny. Assuming homogeneity, in the case of helminthic infections the quantity of interest will be proportional to the number of ovipositing worms.

The kinetics of complexation at 25°C of nickel malonate in water-glycerine mixtures has been studied by the pressure-jump relaxation technique. For the water-glycerine mixtures, the ratio kf/KF, (namely the ratio between the forward rate constant kf and the pre-equilibration constant for the bimolecular diffusion step KF), shows a decrease within a factor of two from pure water to 49% glycerine in water. This decrease, if significant, is at variance with the apparently random scatter of the same data for water-fructose mixtures. In order to decide whether these changes in kf/KF reflect solvation of nickel ion, or modification of the chelation mechanism, the complexation of Ni(NCS)2 at 10°C in the same solvent of composition 49% glycerine has been studied. It is proposed that the changes in kf/KF, may be caused by the changes in the KF with solvent composition, namely with changes in the ion-pair distance rather than with changes in the reaction mechanism. This is reflected in the constancy of the kf's with solvent composition.

Relaxation times, determined by the pressure-jump technique, for the kinetics of chelation of nickel (II) by malonate ion are significantly prolonged by the addition of β-cyclodextrin to aqueous solutions. The effect is due to inclusion of the malonate into the β-cyclodextrin cavity. In fact addition of glucose in a 7:1 ratio to malonate ion does not affect the kinetics of complexation with Ni 2+ . The effect is also specific to the size of the ring since α-cyclodextrin and γ-cyclodextrin do not show any effect on the above relaxation times. The kinetic data are interpreted to indicate a competitive inhibition process. β-cyclodextrin is bound to the anion and prevents its chelation reaction with Ni 2+ . The mechanism treats the data quantitatively with an inclusion formation constant between malonate and β-cyclodextrin of the order of 10 2 M −1 .

A fundamental unsolved problem in the programming area is one in which various activities have fixed charges (e.g., set-up time charges) if operating at a positive level. Properties of a general solution to this type problem are discussed in this paper. Under special circumstances it is shown that a fixed charge problem can be reduced to an ordinary linear programming problem.

The following is a summary of the biomedical content of the paper presented (by the first author) at the NATO Conference, Istanbul. For precise mathematical formulations and details the reader is referred to (6].