The analysis of incomplete data using stochastic covariates

In the development of many diseases there are often associated random variables which continuously reflect the progress of a subject towards the final expression of the disease (failure). At any given time these processes, which we call stochastic covariates, may provide information about the current hazard and the remaining time to failure. Likewise, in situations when the specific times of key prior events are not known, such as the time of onset of an occult tumour or the time of infection with HIV-1, it may be possible to identify a stochastic covariate which reveals, indirectly, when the event of interest occurred. The analysis of carcinogenicity trials which involve occult tumours is usually based on the time of death or sacrifice and an indicator of tumour presence for each animal in the experiment. However, the size of an occult tumour observed at the endpoint represents data concerning tumour development which may convey additional information concerning both the tumour incidence rate and the rate of death to which tumour-bearing animals are subject. We develop a stochastic model for tumour growth and suggest different ways in which the effect of this growth on the hazard of failure might be modelled. Using a combined model for tumour growth and additive competing risks of death, we show that if this tumour size information is used, assumptions concerning tumour lethality, the context of observation or multiple sacrifice times are no longer necessary in order to estimate the tumour incidence rate. Parametric estimation based on the method of maximum likelihood is outlined and is applied to simulated data from the combined model. The results of this limited study confirm that use of the stochastic covariate tumour size results in more precise estimation of the incidence rate for occult tumours.     

Estimating the Rayleigh distribution scale parameter from doubly censored samples—Some comments

In a recent paper in this journal, Lee, Kapadia and Brock (1980) developed maximum likelihood (ML) methods for estimating the scale parameter of the Rayleigh distribution from doubly censored samples. They reported convergence difficulties in attempting to solve numerically the nonlinear likelihood equation (LE). To mitigate these difficulties, they employed approximations to simplify the LE, but found that the solution of the resulting simplified equation can give rise to parameter estimates of erratic accuracy. We show that the use of approximations to simplify the LE is unnecessary. In fact, under suitable parametric transformation, the log-likelihood function is strictly concave, the ML estimate always exists, is unique and finite. Furthermore, the LE is easy to solve numerically. A numerical example is given to illustrate the computations involved.     

Benefits of preventive dentistry in children: Cost factors and public policy

Dental caries in children is now recognized as a preventable disease. The use of fluoride and sealants has produced a major reduction in caries prevalence among school aged children in the United States and other countries. A portion of the child population who are educationally and socioeconomically disadvantaged are not fully receiving these benefits. Public policy, insurance and medicaid groups must be made aware of these preventative measures and strategies developed to implement them.     

MOVING OUT OF THE HOUSE: AN ANALYSIS OF CONGRESSIONAL QUITS

Despite extensive study concerning involuntary departures by U.S. House members, little has been said about voluntary departures from the House–-quit behavior. This paper has three primary purposes: (1) to establish a theoretical framework that models the full range of choices a representative faces in any given term, (2) to measure the impact of different variables that affect representatives' quit behavior, and (3) to explain why Republicans have been more likely to pursue higher office than their Democratic colleagues.     

The dilemma of recognition: Administrative categories and cultural diversity

Governments around the world combat inequality by means of group-specific redistribution. Some pursue redistribution that benefits groups, but also wish to avoid accentuating or even recognizing group distinctions. This poses a dilemma that they try to resolve by adjusting the category system used to target redistribution. There are three types of adjustment: accommodation (the multicultural approach), denial (the ideal-typical liberal solution), and replacement (a compromise). In replacement the targets of redistributive policies are constructed to avoid accentuation or recognition of inconvenient group distinctions, but still allow redistribution that benefits these groups. Replacement is increasingly in demand around the world because the disadvantages of multiculturalism are becoming apparent while denial is hard to sustain in the face of group inequality. The actual effect of replacement is little researched and less understood, however. Does it resolve the dilemma of recognition? Two examples–India and Nigeria–where replacement has been tried ever since the 1950s cast doubt on its viability.