Revisiting proportion estimators

Proportion estimators are quite frequently used in many application areas. The conventional proportion estimator (number of events divided by sample size) encounters a number of problems when the data are sparse as will be demonstrated in various settings. The problem of estimating its variance when sample sizes become small is rarely addressed in a satisfying framework. Specifically, we have in mind applications like the weighted risk difference in multicenter trials or stratifying risk ratio estimators (to adjust for potential confounders) in epidemiological studies. It is suggested to estimate p using the parametric family (see PDF for character) and p(1 - p) using (see PDF for character), where (see PDF for character). We investigate the estimation problem of choosing c 0 from various perspectives including minimizing the average mean squared error of (see PDF for character), average bias and average mean squared error of (see PDF for character). The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be independent of n and equals c = 1. The optimal value of c for minimizing the average mean squared error of (see PDF for character) is found to be dependent of n with limiting value c = 0.833. This might justifiy to use a near-optimal value of c = 1 in practice which also turns out to be beneficial when constructing confidence intervals of the form (see PDF for character).

Some general comparative points on Chao's and Zelterman's estimators of the population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

Estimators in capture-recapture studies with two sources

This paper investigates the applications of capture-recapture methods to human populations. Capture-recapture methods are commonly used in estimating the size of wildlife populations but can also be used in epidemiology and social sciences, for estimating prevalence of a particular disease or the size of the homeless population in a certain area. Here we focus on estimating the prevalence of infectious diseases. Several estimators of population size are considered: the Lincoln-Petersen estimator and its modified version, the Chapman estimator, Chao's lower bound estimator, the Zelterman's estimator, McKendrick's moment estimator and the maximum likelihood estimator. In order to evaluate these estimators, they are applied to real, three-source, capture-recapture data. By conditioning on each of the sources of three source data, we have been able to compare the estimators with the true value that they are estimating. The Chapman and Chao estimators were compared in terms of their relative bias. A variance formula derived through conditioning is suggested for Chao's estimator, and normal 95% confidence intervals are calculated for this and the Chapman estimator. We then compare the coverage of the respective confidence intervals. Furthermore, a simulation study is included to compare Chao's and Chapman's estimator. Results indicate that Chao's estimator is less biased than Chapman's estimator unless both sources are independent. Chao's estimator has also the smaller mean squared error. Finally, the implications and limitations of the above methods are discussed, with suggestions for further development.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Educational and psychosocial programmes for adolescents with diabetes: approaches, outcomes and cost-effectiveness

Diabetes incurs heavy personal and health system costs. Self-management is required if complications are to be avoided. Adolescents face particular challenges as they learn to take responsibility for their diabetes. A systematic review of educational and psychosocial programmes for adolescents with diabetes was undertaken. This aimed to: identify and categorise the types of programmes that have been evaluated; assess the cost-effectiveness of interventions; identify areas where further research is required. Sixty-two papers were identified and Subjected to a narrative review. Generic programmes focus on knowledge/skills, psychosocial issues, and behaviour/self-management. They result in modest improvements across a range of outcomes but improvements are often not sustained, suggesting a need for continuous support, possibly integrated into normal care. In-hospital education at diagnosis confers few advantages over home treatment. The greatest returns may be obtained by targeting poorly controlled individuals. Few studies addressed resourcing issues and robust cost-effectiveness appraisals are required to identify interventions that generate the greatest returns on expenditure. (C) 2004 Elsevier Ireland Ltd. All rights reserved.

Efficient and cost-effective experimental determination of kinetic constants and data: the success of a Bayesian systematic approach to drug transport, receptor binding, continuous culture and cell transport kinetics

Details about the parameters of kinetic systems are crucial for progress in both medical and industrial research, including drug development, clinical diagnosis and biotechnology applications. Such details must be collected by a series of kinetic experiments and investigations. The correct design of the experiment is essential to collecting data suitable for analysis, modelling and deriving the correct information. We have developed a systematic and iterative Bayesian method and sets of rules for the design of enzyme kinetic experiments. Our method selects the optimum design to collect data suitable for accurate modelling and analysis and minimises the error in the parameters estimated. The rules select features of the design such as the substrate range and the number of measurements. We show here that this method can be directly applied to the study of other important kinetic systems, including drug transport, receptor binding, microbial culture and cell transport kinetics. It is possible to reduce the errors in the estimated parameters and, most importantly, increase the efficiency and cost-effectiveness by reducing the necessary amount of experiments and data points measured. (C) 2003 Federation of European Biochemical Societies. Published by Elsevier B.V. All rights reserved.

Exposing the myth of the 1:5:200 ratio relating initial cost, maintenance and staffing costs of office buildings

In an attempt to focus clients' minds on the importance of considering the construction and maintenance costs of a commercial office building (both as a factor in staff productivity and as a fraction of lifetime staff costs) there is an often-quoted ratio of costs of 1:5:200, where for every one pound spent on construction cost, five are spent on maintenance and building operating costs and 200 on staffing and business operating costs. This seems to stem from a paper published by the Royal Academy of Engineering, in which no data is given and no derivation or defence of the ratio appears. The accompanying belief that higher quality design and construction increases staff productivity, and simultaneously reduces maintenance costs, how ever laudable, appears unsupported by research, and carries all the hallmarks of an "urban myth". In tracking down data about real buildings, a more realistic ratio appears to depend on a huge variety of variables, as well as the definition of the number of "lifetime" years. The ill-defined origins of the original ratio (1:5:200) describing these variables have made replication impossible. However, by using published sources of data, we have found that for three office buildings, a more realistic ratio is 1:0.4:12. As there is nothing in the public domain about what comprised the original research that gave rise to 1:5:200, it is not possible to make a true comparison between these new calculations and the originals. Clients and construction professionals stand to be misled because the popularity and widespread use of the wrong ratio appears to be mis-informing important investment and policy decisions.

Techno-economic modelling and cost functions of CO2 capture processes

The paper presents the techno-economic modelling of CO2 capture process in coal-fired power plants. An overall model is being developed to compare carbon capture and sequestration options at locations within the UK, and for studies of the sensitivity of the cost of disposal to changes in the major parameters of the most promising solutions identified. Technological options of CO2 capture have been studied and cost estimation relationships (CERs) for the chosen options calculated. Created models are related to the capital, operation and maintenance cost. A total annualised cost of plant electricity output and amount of CO2 avoided have been developed. The influence of interest rates and plant life has been analysed as well. The CERs are included as an integral part of the overall model.