Systematic review and meta-analysis of the growth and rupture rates of small abdominal aortic aneurysms: implications for surveillance intervals and their cost-effectiveness.

BACKGROUND: Small abdominal aortic aneurysms (AAAs; 3.0-5.4 cm in diameter) are usually asymptomatic and managed by regular ultrasound surveillance until they grow to a diameter threshold (commonly 5.5 cm) at which surgical intervention is considered. The choice of appropriate surveillance intervals is governed by the growth and rupture rates of small AAAs, as well as their relative cost-effectiveness. OBJECTIVES: The aim of this series of studies was to inform the evidence base for small AAA surveillance strategies. This was achieved by literature review, collation and analysis of individual patient data, a focus group and health economic modelling. DATA SOURCES: We undertook systematic literature reviews of growth rates and rupture rates of small AAAs. The databases MEDLINE, EMBASE on OvidSP, Cochrane Central Register of Controlled Trials 2009 Issue 4, ClinicalTrials.gov, and controlled-trials.com were searched from inception up until the end of 2009. We also obtained individual data on 15,475 patients from 18 surveillance studies. REVIEW METHODS: Systematic reviews of publications identified 15 studies providing small AAA growth rates, and 14 studies with small AAA rupture rates, up to December 2009 (later updated to September 2012). We developed statistical methods to analyse individual surveillance data, including the effects of patient characteristics, to inform the choice of surveillance intervals and provide inputs for health economic modelling. We updated an existing health economic model of AAA screening to address the cost-effectiveness of different surveillance intervals. RESULTS: In the literature reviews, the mean growth rate was 2.3 mm/year and the reported rupture rates varied between 0 and 1.6 ruptures per 100 person-years. Growth rates increased markedly with aneurysm diameter, but insufficient detail was available to guide surveillance intervals. Based on individual surveillance data, for each 0.5-cm increase in AAA diameter, growth rates increased by about 0.5 mm/year and rupture rates doubled. To control the risk of exceeding 5.5 cm to below 10% in men, on average a 7-year surveillance interval is sufficient for a 3.0-cm aneurysm, whereas an 8-month interval is necessary for a 5.0-cm aneurysm. To control the risk of rupture to below 1%, the corresponding estimated surveillance intervals are 9 years and 17 months. Average growth rates were higher in smokers (by 0.35 mm/year) and lower in patients with diabetes (by 0.51 mm/year). Rupture rates were almost fourfold higher in women than men, doubled in current smokers and increased with higher blood pressure. Increasing the surveillance interval from 1 to 2 years for the smallest aneurysms (3.0-4.4 cm) decreased costs and led to a positive net benefit. For the larger aneurysms (4.5-5.4 cm), increasing surveillance intervals from 3 to 6 months led to equivalent cost-effectiveness. LIMITATIONS: There were no clear reasons why the growth rates varied substantially between studies. Uniform diagnostic criteria for rupture were not available. The long-term cost-effectiveness results may be susceptible to the modelling assumptions made. CONCLUSIONS: Surveillance intervals of several years are clinically acceptable for men with AAAs in the range 3.0-4.0 cm. Intervals of around 1 year are suitable for 4.0-4.9-cm AAAs, whereas intervals of 6 months would be acceptable for 5.0-5.4-cm AAAs. These intervals are longer than those currently employed in the UK AAA screening programmes. Lengthening surveillance intervals for the smallest aneurysms was also shown to be cost-effective. Future work should focus on optimising surveillance intervals for women, studying whether or not the threshold for surgery should depend on patient characteristics, evaluating the usefulness of surveillance for those with aortic diameters of 2.5-2.9 cm, and developing interventions that may reduce the growth or rupture rates of small AAAs. FUNDING: The National Institute for Health Research Health Technology Assessment programme

Prediction intervals for reliability growth models with small sample sizes

Engineers and practitioners contribute to society through their ability to apply basic scientific principles to real problems in an effective and efficient manner. They must collect data to test their products every day as part of the design and testing process and also after the product or process has been rolled out to monitor its effectiveness. Model building, data collection, data analysis and data interpretation form the core of sound engineering practice.After the data has been gathered the engineer must be able to sift them and interpret them correctly so that meaning can be exposed from a mass of undifferentiated numbers or facts. To do this he or she must be familiar with the fundamental concepts of correlation, uncertainty, variability and risk in the face of uncertainty. In today's global and highly competitive environment, continuous improvement in the processes and products of any field of engineering is essential for survival. Many organisations have shown that the first step to continuous improvement is to integrate the widespread use of statistics and basic data analysis into the manufacturing development process as well as into the day-to-day business decisions taken in regard to engineering processes.The Springer Handbook of Engineering Statistics gathers together the full range of statistical techniques required by engineers from all fields to gain sensible statistical feedback on how their processes or products are functioning and to give them realistic predictions of how these could be improved

Confidence intervals for reliability growth models with small sample sizes

Fully Bayesian approaches to analysis can be overly ambitious where there exist realistic limitations on the ability of experts to provide prior distributions for all relevant parameters. This research was motivated by situations where expert judgement exists to support the development of prior distributions describing the number of faults potentially inherent within a design but could not support useful descriptions of the rate at which they would be detected during a reliability-growth test. This paper develops inference properties for a reliability-growth model. The approach assumes a prior distribution for the ultimate number of faults that would be exposed if testing were to continue ad infinitum, but estimates the parameters of the intensity function empirically. A fixed-point iteration procedure to obtain the maximum likelihood estimate is investigated for bias and conditions of existence. The main purpose of this model is to support inference in situations where failure data are few. A procedure for providing statistical confidence intervals is investigated and shown to be suitable for small sample sizes. An application of these techniques is illustrated by an example

Stages of steady diffusion growth of a gas bubble in strongly supersaturated gas-liquid solution

Gas bubble growth as a result of diffusion flux of dissolved gas molecules from the surrounding supersaturated solution to the bubble surface is studied. The condition of the flux steadiness is revealed. A limitation from below on the bubble radius is considered. Its fulfillment guarantees the smallness of fluctuation influence on bubble growth and irreversibility of this process. Under the conditions of steadiness of diffusion flux three stages of bubble growth are marked out. With account for Laplace forces in the bubble intervals of bubble size change and time intervals of these stages are found. The trend of the third stage towards the self-similar regime of the bubble growth, when Laplace forces in the bubble are completely neglected, is described analytically.Comment: 22 page

A Threshold Model of Real US GDP and the Problem of Constructing Confidence Intervals in TAR Models

We estimate real U.S. GDP growth as a threshold autoregressive process, and construct confidence intervals for the parameter estimates. However, there are various approaches that can be used in constructing the confidence intervals. Specifically, standard- t , bootstrap- t , and bootstrap-percentile confidence intervals are simulated for the slope coefficients and the estimated threshold. However, the results for the different methods have very different economic implications. We perform a Monte Carlo experiment to evaluate the various methods.Bootstrap GDP; Threshold Autoregression; Bootstrap Confidence Intervals

Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion

The Negative Binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard Normal approximation often does not provide adequate inferences about the data's mean in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's Inequality. We now propose growth estimators of the Negative Binomial mean. Under high dispersion, zero values are likely to be overrepresented in the data. A growth estimator constructs a Normal-style confidence interval by effectively removing a small, pre--determined number of zeros from the data. We propose growth estimators based upon multiplicative adjustments of the sample mean and direct removal of zeros from the sample. These methods do not require estimating the nuisance dispersion parameter. We will demonstrate that the growth estimators' confidence intervals provide improved coverage over a wide range of parameter values and asymptotically converge to the sample mean. Interestingly, the proposed methods succeed despite adding both bias and variance to the Normal approximation

Intervals of permutation class growth rates

We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is θB ≈ 2.35526, and that it also contains every value at least λB ≈ 2.35698. These results improve on a theorem of Vatter, who determined that there are permutation classes of every growth rate at least λA ≈ 2.48187. Thus, we also refute his conjecture that the set of growth rates below λA is nowhere dense. Our proof is based upon an analysis of expansions of real numbers in non-integer bases, the study of which was initiated by Rényi in the 1950s. In particular, we prove two generalisations of a result of Pedicini concerning expansions in which the digits are drawn from sets of allowed values

Stochastic growth equations on growing domains

The dynamics of linear stochastic growth equations on growing substrates is studied. The substrate is assumed to grow in time following the power law $t^\gamma$, where the growth index $\gamma$ is an arbitrary positive number. Two different regimes are clearly identified: for small $\gamma$ the interface becomes correlated, and the dynamics is dominated by diffusion; for large $\gamma$ the interface stays uncorrelated, and the dynamics is dominated by dilution. In this second regime, for short time intervals and spatial scales the critical exponents corresponding to the non-growing substrate situation are recovered. For long time differences or large spatial scales the situation is different. Large spatial scales show the uncorrelated character of the growing interface. Long time intervals are studied by means of the auto-correlation and persistence exponents. It becomes apparent that dilution is the mechanism by which correlations are propagated in this second case.Comment: Published versio

Intervals of permutation class growth rates

We prove that the set of growth rates of permutation classes includes an infinite sequence of intervals whose infimum is $\theta_B\approx2.35526$, and that it also contains every value at least $\lambda_B\approx2.35698$. These results improve on a theorem of Vatter, who determined that there are permutation classes of every growth rate at least $\lambda_A\approx2.48187$. Thus, we also refute his conjecture that the set of growth rates below $\lambda_A$ is nowhere dense. Our proof is based upon an analysis of expansions of real numbers in non-integer bases, the study of which was initiated by R\'enyi in the 1950s. In particular, we prove two generalisations of a result of Pedicini concerning expansions in which the digits are drawn from sets of allowed values.Comment: 20 pages, 10 figures, ancillary files containing computer-aided calculations include

Growth and emigration of white shimp, Litopenaeus vannamei, in the Mar Muerto Lagoon, Southern Mexico

Microcohorts of white shrimp, Litopenaeus vannamei, were sampled with a cast net at fortnightly intervals in the Mar Muerto Lagoon, Southern Mexico. Shrimp recruited to the lagoon throughout the sampling period (January to August 1993). Mean growth rates of microcohorts ranged from 0.21 to 1.21 mm total length (TL) per day. Juvenile shrimp mainly between the sizes of 70 to 80 mm TL emigrated from the lagoon. Growth and the onset of emigration appeared to be related to water salinity