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.     

Comparison of three estimators of the number of species

We consider estimation of the number of cells in a multinomial distribution. This is one version of the species problem: there are many applications, such as the estimation of the number of unobserved species of animals; estimation of vocabulary size, etc. We describe the results of a simulation comparison of three principal frequent-ist' procedures for estimating the number of cells (or species). The first procedure postulates a functional form for the cell probabilities; the second procedure approxi mates the distribution of the probabilities by a parametric probability density function; and the third procedure is based on an estimate of the sample coverage, i.e. the sum of the probabilities of the observed cells. Among the procedures studied, we find that the third (non-parametric) method is globally preferable; the second (functional parametric) method cannot be recommended; and that, when based on the inverse Gaussian density, the first method is competitive in some cases with the third method. We also discuss Sichel's recent generalized inverse Gaussian-based procedure which, with some refine ment, promises to perform at least as well as the non-parametric method in all cases.     

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.     

HIV-infected woman. Illness cognition assessment.

1. Special attention is particularly important in addressing the mental health needs of HIV-infected women. These needs may involve issues such as concerns about present or future pregnancy; child-rearing, often as single parents; poverty, illicit drug use or addiction; and the potential lack of support services. 2. Diagnosis of HIV infection in women may be overlooked, as the clinical signs that routinely trigger the suspicion of HIV illness in men are often interpreted to reflect depression or psychological factors, such as stress or overwork, rather than raise the suspicion of HIV infection in women. 3. Understanding a woman's illness cognition is an important component of designing strategies that can enhance coping. The picture a woman generates regarding her illness is a composite of her experiences and responses, and determines to a large extent what she will do in response to her illness.     

Implications of temporal aggregation on the relation between two time series

Using a simple theoretical model and giving an empirical example it is investigated if it matters whether we use (monthly) averages or end-of-period (month) data in performing Granger-causality tests. It is shown that no major problems are to be expected if the two series are temporally aggregated in the same way, but non-trivial problems can occur if the two series have different kinds of temporal aggregation.     

The effect of 1980s tort reform legislation on general liability and medical malpractice insurance

A large number of states adopted tort reforms in the mid-1980s to limit the dramatic surge in insurance losses and premiums. Evidence based on liability insurance data by state indicates that these reforms substantially influenced general liability insurance. The levels of losses, premiums, and loss ratios (a measure of insurance profitability) all reflected the impact of the reforms. The large-scale reform efforts in 1986 were particularly influential. Medical malpractice insurance was much less sensitive to the reform efforts.