Selection bias in gene extraction on the basis of microarray gene-expression data

In the context of cancer diagnosis and treatment, we consider the problem of constructing an accurate prediction rule on the basis of a relatively small number of tumor tissue samples of known type containing the expression data on very many (possibly thousands) genes. Recently, results have been presented in the literature suggesting that it is possible to construct a prediction rule from only a few genes such that it has a negligible prediction error rate. However, in these results the test error or the leave-one-out cross-validated error is calculated without allowance for the selection bias. There is no allowance because the rule is either tested on tissue samples that were used in the first instance to select the genes being used in the rule or because the cross-validation of the rule is not external to the selection process; that is, gene selection is not performed in training the rule at each stage of the cross-validation process. We describe how in practice the selection bias can be assessed and corrected for by either performing a cross-validation or applying the bootstrap external to the selection process. We recommend using 10-fold rather than leave-one-out cross-validation, and concerning the bootstrap, we suggest using the so-called. 632+ bootstrap error estimate designed to handle overfitted prediction rules. Using two published data sets, we demonstrate that when correction is made for the selection bias, the cross-validated error is no longer zero for a subset of only a few genes.

Practical scheme for error control using feedback

We describe a scheme for quantum-error correction that employs feedback and weak measurement rather than the standard tools of projective measurement and fast controlled unitary gates. The advantage of this scheme over previous protocols [for example, Ahn Phys. Rev. A 65, 042301 (2001)], is that it requires little side processing while remaining robust to measurement inefficiency, and is therefore considerably more practical. We evaluate the performance of our scheme by simulating the correction of bit flips. We also consider implementation in a solid-state quantum-computation architecture and estimate the maximal error rate that could be corrected with current technology.

Data analysis in multiple-frequency bioelectrical impedance analysis

The performance of three analytical methods for multiple-frequency bioelectrical impedance analysis (MFBIA) data was assessed. The methods were the established method of Cole and Cole, the newly proposed method of Siconolfi and co-workers and a modification of this procedure. Method performance was assessed from the adequacy of the curve fitting techniques, as judged by the correlation coefficient and standard error of the estimate, and the accuracy of the different methods in determining the theoretical values of impedance parameters describing a set of model electrical circuits. The experimental data were well fitted by all curve-fitting procedures (r = 0.9 with SEE 0.3 to 3.5% or better for most circuit-procedure combinations). Cole-Cole modelling provided the most accurate estimates of circuit impedance values, generally within 1-2% of the theoretical values, followed by the Siconolfi procedure using a sixth-order polynomial regression (1-6% variation). None of the methods, however, accurately estimated circuit parameters when the measured impedances were low (<20 Omega) reflecting the electronic limits of the impedance meter used. These data suggest that Cole-Cole modelling remains the preferred method for the analysis of MFBIA data.

Quantum error correction for continuously detected errors

We show that quantum feedback control can be used as a quantum-error-correction process for errors induced by a weak continuous measurement. In particular, when the error model is restricted to one, perfectly measured, error channel per physical qubit, quantum feedback can act to perfectly protect a stabilizer codespace. Using the stabilizer formalism we derive an explicit scheme, involving feedback and an additional constant Hamiltonian, to protect an (n-1)-qubit logical state encoded in n physical qubits. This works for both Poisson (jump) and white-noise (diffusion) measurement processes. Universal quantum computation is also possible in this scheme. As an example, we show that detected-spontaneous emission error correction with a driving Hamiltonian can greatly reduce the amount of redundancy required to protect a state from that which has been previously postulated [e.g., Alber , Phys. Rev. Lett. 86, 4402 (2001)].

Bayesian analysis of the error correction model

This paper presents a method for estimating the posterior probability density of the cointegrating rank of a multivariate error correction model. A second contribution is the careful elicitation of the prior for the cointegrating vectors derived from a prior on the cointegrating space. This prior obtains naturally from treating the cointegrating space as the parameter of interest in inference and overcomes problems previously encountered in Bayesian cointegration analysis. Using this new prior and Laplace approximation, an estimator for the posterior probability of the rank is given. The approach performs well compared with information criteria in Monte Carlo experiments. (C) 2003 Elsevier B.V. All rights reserved.

Serum triglycerides as a risk factor for cardiovascular diseases in the Asia-Pacific Region

Background-The importance of serum triglyceride levels as a risk factor for cardiovascular diseases is uncertain. Methods and Results-We performed an individual participant data meta-analysis of prospective studies conducted in the Asia-Pacific region. Cox models were applied to the combined data from 26 studies to estimate the overall and region-, sex-, and age-specific hazard ratios for major cardiovascular diseases by fifths of triglyceride values. During 796 671 person-years of follow-up among 96 224 individuals, 670 and 667 deaths as a result of coronary heart disease (CHD) and stroke, respectively, were recorded. After adjustment for major cardiovascular risk factors, participants grouped in the highest fifth of triglyceride levels had a 70% (95% CI, 47 to 96) greater risk of CHD death, an 80% (95% CI, 49 to 119) higher risk of fatal or nonfatal CHD, and a 50% (95% CI, 29% to 76%) increased risk of fatal or nonfatal stroke compared with those belonging to the lowest fifth. The association between triglycerides and CHD death was similar across subgroups defined by ethnicity, age, and sex. Conclusions-Serum triglycerides are an important and independent predictor of CHD and stroke risk in the Asia-Pacific region. These results may have clinical implications for cardiovascular risk prediction and the use of lipid-lowering therapy.

Hormone replacement therapy and breast cancer: estimate of risk: Education debate

The risk of breast cancer arises from a combination of genetic susceptibility and environmental factors. Recent studies show that type and duration of use of hormone replacement therapy affect a women's risk of developing breast cancer.1-7 The women's health initiative trial was stopped early because of excess adverse cardiovascular events and invasive breast cancer with oestrogen and progestogen.6 The publicity increased public awareness of the risks of hormone replacement therapy, and this was heightened by the publication of the million women study.2 However, the recently published oestrogen only arm of the women's health initiative trial suggests that this formulation may reduce the risk of breast cancer.8 To help make sense of the often confusing information,9 women and clinicians need individual rather than population risk data. We have produced estimates that can be used to calculate individual risk for women living up to the age of 79 and suggest the risk

Not so ancient: the extant crown group of Nothofagus represents a post-Gondwanan radiation

This study uses a molecular-dating approach to test hypotheses about the biogeography of Nothofagus. The molecular modelling suggests that the present-day subgenera and species date from a radiation that most likely commenced between 55 and 40 Myr ago. This rules out the possibility of a reconciled all-vicariance hypothesis for the biogeography of extant Nothofagus. However, the molecular dates for divergences between Australasian and South American taxa are consistent with the rifting of Australia and South America from Antarctica. The molecular dates further suggest a dispersal of subgenera Lophozonia and Fuscospora between Australia and New Zealand after the onset of the Antarctic Circumpolar Current and west wind drift. It appears likely that the New Caledonian lineage of subgenus Brassospora diverged from the New Guinean lineage elsewhere, prior to colonizing New Caledonia. The molecular approach strongly supports fossil-based estimates that Nothofagus diverged from the rest of Fagales more than 84 Myr ago. However, the mid-Cenozoic estimate for the diversification of the four extant subgenera conflicts with the palynological interpretation because pollen fossils, attributed to all four extant subgenera, were widespread across the Weddellian province of Gondwana about 71 Myr ago. The discrepancy between the pollen and molecular dates exists even when confidence intervals from several sources of error are taken into account. In contrast, the molecular age estimates are consistent with macrofossil dates. The incongruence between pollen fossils and molecular dates could be resolved if the early pollen types represent extinct lineages, with similar types later evolving independently in the extant lineages.

Anthropometric measures in relation to Basal Cell Carcinoma: a longitudinal study

Background: The relationship between anthropometric indices and risk of basal cell carcinoma ( BCC) is largely unknown. We aimed to examine the association between anthropometric measures and development of BCC and to demonstrate whether adherence to World Health Organisation guidelines for body mass index, waist circumference, and waist/ hip ratio was associated with risk of BCC, independent of sun exposure. Methods: Study participants were participants in a community- based skin cancer prevention trial in Nambour, a town in southeast Queensland ( latitude 26 degrees S). In 1992, height, weight, and waist and hip circumferences were measured for all 1621 participants and weight was remeasured at the end of the trial in 1996. Prevalence proportion ratios were calculated using a log- binomial model to estimate the risk of BCC prior to or prevalent in 1992, while Poisson regression with robust error variances was used to estimate the relative risk of BCC during the follow- up period. Results: At baseline, 94 participants had a current BCC, and 202 had a history of BCC. During the 5- year follow- up period, 179 participants developed one or more new BCCs. We found no significant association between any of the anthropometric measures or indices and risk of BCC after controlling for potential confounding factors including sun exposure. There was a suggestion that short- term weight gain may increase the risk of developing BCC for women only. Conclusion: Adherence to World Health Organisation guidelines for body mass index, waist circumference and waist/ hip ratio is not significantly associated with occurrence of basal cell carcinomas of the skin.

Estimating correlations from epidemiological data in the presence of measurement error

Analysis of a major multi-site epidemiologic study of heart disease has required estimation of the pairwise correlation of several measurements across sub-populations. Because the measurements from each sub-population were subject to sampling variability, the Pearson product moment estimator of these correlations produces biased estimates. This paper proposes a model that takes into account within and between sub-population variation, provides algorithms for obtaining maximum likelihood estimates of these correlations and discusses several approaches for obtaining interval estimates. (C) 1997 by John Wiley & Sons, Ltd.

Development of a genetic method to estimate effective spawner numbers in the NPF and Queensland tiger prawn fisheries

OBJECTIVES: 1. To critically evaluate a variety of mathematical methods of calculating effective population size (Ne) by conducting comprehensive computer simulations and by analysis of empirical data collected from the Moreton Bay population of tiger prawns. 2. To lay the groundwork for the application of the technology in the NPF. 3. To produce software for the calculation of Ne, and to make it widely available.