On the incidence–prevalence relation and length‐biased sampling

For many diseases, logistic constraints render large incidence studies difficult to carry out. This becomes a drawback, particularly when a new study is needed each time the incidence rate is investigated in a new population. By carrying out a prevalent cohort study with follow‐up it is possible to estimate the incidence rate if it is constant. The authors derive the maximum likelihood estimator (MLE) of the overall incidence rate, λ, as well as age‐specific incidence rates, by exploiting the epidemiologic relationship, (prevalence odds) = (incidence rate) × (mean duration) (P/[1 ? P] = λ × µ). The authors establish the asymptotic distributions of the MLEs and provide approximate confidence intervals for the parameters. Moreover, the MLE of λ is asymptotically most efficient and is the natural estimator obtained by substituting the marginal maximum likelihood estimators for P and µ into P/[1 ? P] = λ × µ. Following‐up the subjects allows the authors to develop these widely applicable procedures. The authors apply their methods to data collected as part of the Canadian Study of Health and Ageing to estimate the incidence rate of dementia amongst elderly Canadians. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Which countries protect intellectual property? The case of software piracy

Using data on software piracy, we examine how protection of intellectual property varies across countries. Consistent with other studies, we find that intellectual property receives greater protection in developed economies; high-income countries have lower piracy rates. We also find that protection depends on cultural factors. Countries with an individualist culture have lower piracy rates than do countries with a collectivist culture. Piracy rates are also lower in countries that have strong institutions that enforce contracts and protect property from expropriation. These results suggest that national policies toward intellectual property reflect not only economic concerns but also national culture and institutions.     

Parametric modelling of prevalent cohort data with uncertainty in the measurement of the initial onset date

In prevalent cohort studies with follow-up, if disease duration is the focus, the date of onset must be obtained retrospectively. For some diseases, such as Alzheimer’s disease, the very notion of a date of onset is unclear, and it can be assumed that the reported date of onset acts only as a proxy for the unknown true date of onset. When adjusting for onset dates reported with error, the features of left-truncation and potential right-censoring of the failure times must be modeled appropriately. Under the assumptions of a classical measurement error model for the onset times and an underlying parametric failure time model, we propose a maximum likelihood estimator for the failure time distribution parameters which requires only the observed backward recurrence times. Costly and time-consuming follow-up may therefore be avoided. We validate the maximum likelihood estimator on simulated datasets under varying parameter combinations and apply the proposed method to the Canadian Study of Health and Aging dataset.

     

Estimation in the multipath change point problem for correlated data

In many experiments, several measurements on the same variable are taken over time, a geographic region, or some other index set. It is often of interest to know if there has been a change over the index set in the parameters of the distribution of the variable. Frequently, the data consist of a sequence of correlated random variables, and there may also be several experimental units under observation, each providing a sequence of data. A problem in ascertaining the boundaries between the layers in geological sedimentary beds is used to introduce the model and then to illustrate the proposed methodology. It is assumed that, conditional on the change point, the data from each sequence arise from an autoregressive process that undergoes a change in one or more of its parameters. Unconditionally, the model then becomes a mixture of nonstationary autoregressive processes. Maximum-likelihood methods are used, and results of simulations to evaluate the performance of these estimators under practical conditions are given.     

Population and poverty in sub-Saharan Africa

The intricate interrelationships between population and development in sub-Saharan Africa are examined and the prospects are considered for converting the abundant human resources into an effective development asset. The demographic trends that characterize the sub-Saharan region at this time differ markedly from what is happening in other parts of the developing world. In Africa, death rates have come down slightly (17/1000 in 1980-85 in contrast to 20/1000 in 1970-75); there has been practically no change in the birthrate. Consequently, population growth rates are on the rise throughout Africa although there are differences within the regions. The various factors responsible for high fertility in African societies and the consequences of the continuing high fertility often are mutually reinforcing. For example, low health and educational standards are likely to lead women to have large numbers of children, but these conditions are themselves the result of the population growth, which requires an expansion of health care and educational facilities that hard-pressed national budgets cannot provide. In Africa, the growth rate of the youth population is increasing even faster than that of the population as a whole -- from 3.1% in 1980-85 to an estimated 3.4% in 1990-95. The most critical problem posed by such growth rates is an increased demand for food. Countries which cannot adequately feed their growing populations are unlikely to be significantly more successful in satisfying their other basic needs. Whether educated or healthy or not, Africa's growing numbers of children represent major economic problems for countries with a low level of economic growth. There is little hope of effectively absorbing all the new entrants who swell the labor market each year, and the indirect consequences for the economy of rapid demographic growth are no less serious. Presently, Africa is the scene of major and particularly distressing movements of population as the drought has forced people to move long distances in search of food relief. It is too soon to tell whether or how much of the lands left behind can be rehabilitated and again become productive. The question arises as to whether appropriate policies, supported by adequate funds and technical know-how, can convert Africa's millions of young people from being a brake on development into a resource for the future. Policies and strategies that may be most appropriate to this end are: to take sufficient cognizance of the interrelationship between population and development and hence to be prepared to take the necessary steps to ensure that the two remain in balance; to realize that family planning programs mean more than a reduction in fertility but also the possibility of reducing infant and maternal mortality and morbidity; to back whatever family planning programs governments introduce; to plan comprehensively; and to effectively carry out the development strategies.     

Bayesian demography: projecting the Iraqi Kurdish population, 1977-1990

"Projecting populations that have sparse or unreliable data, such as those of many developing countries, presents a challenge to demographers. The assumptions that they make to project data-poor populations frequently fall into the realm of ?educated guesses', and the resulting projections, often regarded as forecasts, are valid only to the extent that the assumptions on which they are based reasonably represent the past or future, as the case may be. These traditional projection techniques do not incorporate a demographer's assessment of uncertainty in the assumptions. Addressing the challenges of forecasting a data-poor population, we project the Iraqi Kurdish population using a Bayesian approach. This approach incorporates a demographer's uncertainty about past and future characteristics of the population in the form of elicited prior distributions."     

Estimation in multi-path change-point problems

The current literature deals with the change-point problem only in the context of the obser¬vation of a single sequence. In this paper, inference will be based on the observation of TV sequences of random variables, each sequence containing one change-point. This extension allows the effective use of bootstrap and empirical Bayes methods, both of which are not feasible in the single-path context. Two classes of these “multi-path” change-point problems are considered. If the change-point is assumed to occur at the the same position in each sequence, then the terminology “fixed-tau multi-path change-point” will be used. In other cases, one may expect the change-point to occur at random positions in each sequence, according to some distribution, a “random-tau multi-path change-point” problem. Examples and simulations are given.     

Bayesian optimal design for changepoint problems

We investigate Bayesian optimal designs for changepoint problems. We find robust optimal designs which allow for arbitrary distributions before and after the change, arbitrary prior densities on the parameters before and after the change, and any log‐concave prior density on the changepoint. We define a new design measure for Bayesian optimal design problems as a means of finding the optimal design. Our results apply to any design criterion function concave in the design measure. We illustrate our results by finding the optimal design in a problem motivated by a previous clinical trial. The Canadian Journal of Statistics 37: 495–513; 2009 © 2009 Statistical Society of Canada