Tom Fearn

On orthogonal signal correction

Abstract A new algorithm for orthogonal signal correction is presented, compared with existing algorithms, and illustrated on an example from near infrared spectroscopy. Given a matrix X of spectral or other high dimensional data and a vector or matrix Y of concentrations or other reference measurements on the same samples, orthogonal signal correction subtracts from X factors that account for as much as possible of the variance in X and are orthogonal to Y. The aim is to improve the performance of a subsequent partial least squares (PLS) regression of Y on X.

Multivariate Bayesian variable selection and prediction

The multivariate regression model is considered with p regressors. A latent vector with p binary entries serves to identify one of two types of regression coefficients: those close to 0 and those not. Specializing our general distributional setting to the linear model with Gaussian errors and using natural conjugate prior distributions, we derive the marginal posterior distribution of the binary latent vector. Fast algorithms aid its direct computation, and in high dimensions these are supplemented by a Markov chain Monte Carlo approach to sampling from the known posterior distribution. Problems with hundreds of regressor variables become quite feasible. We give a simple method of assigning the hyperparameters of the prior distribution. The posterior predictive distribution is derived and the approach illustrated on compositional analysis of data involving three sugars with 160 near infra-red absorbances as regressors.

Risk of lung cancer associated with residential radon exposure in south-west England: a case-control study.

Studies of underground miners occupationally exposed to radon have consistently demonstrated an increased risk of lung cancer in both smokers and non-smokers. Radon exposure also occurs elsewhere, especially in houses, and estimates based on the findings for miners suggest that residential radon is responsible for about one in 20 lung cancers in the UK, most being caused in combination with smoking. These calculations depend, however, on several assumptions and more direct evidence on the magnitude of the risk is needed. To obtain such evidence, a case-control study was carried out in south-west England in which 982 subjects with lung cancer and 3185 control subjects were interviewed. In addition, radon concentrations were measured at the addresses at which subjects had lived during the 30-year period ending 5 years before the interview. Lung cancer risk was examined in relation to residential radon concentration after taking into account the length of time that subjects had lived at each address and adjusting for age, sex, smoking status, county of residence and social class. The relative risk of lung cancer increased by 0.08 (95% CI -0.03, 0.20) per 100 Bq m(-3) increase in the observed time-weighted residential radon concentration. When the analysis was restricted to the 484 subjects with lung cancer and the 1637 control subjects with radon measurements available for the entire 30-year period of interest, the corresponding increase was somewhat higher at 0.14 per 100 Bq m(-3) (95% CI 0.01, 0.29), although the difference between this group and the remaining subjects was not statistically significant. When the analysis was repeated taking into account uncertainties in the assessment of radon exposure, the estimated increases in relative risk per 100 Bq m(-3) were larger, at 0.12 (95% CI -0.05, 0.33) when all subjects were included and 0.24 (95% CI -0.01, 0.56) when limited to subjects with radon measurements available for all 30 years. These results are consistent with those from studies of residential radon carried out in other countries in which data on individual subjects have been collected. The combined evidence suggests that the risk of lung cancer associated with residential radon exposure is about the size that has been postulated on the basis of the studies of miners exposed to radon.

Standardisation and Calibration Transfer for near Infrared Instruments: A Review:

Transferring calibrations between near infrared instruments is not always straightforward, even when the instruments are nominally the same. Problems can include both wavelength shifts and differences in absorbance response between instruments. This review describes a number of chemometric methods that have been developed to aid calibration transfer. The approaches are classified under three headings: making robust calibrations, adjusting calibrations and adjusting spectra. Calibrations can be made more robust, and more transferable, by the appropriate use of spectral pre-treatments that reduce between-instrument variability. Robust calibrations can also be made by pooling data from several instruments when calibrating. Calibrations can be adjusted using skew and bias corrections estimated from a modest number of samples with known reference values. Under the third heading, adjusting spectra, come methods such as piecewise direct standardisation and the patented method of Shenk and Westerhaus that use spectral information from samples measured on two instruments to match the spectral response of the instruments.

Bayesian Wavelet Regression on Curves With Application to a Spectroscopic Calibration Problem

Motivated by calibration problems in near-infrared (NIR) spectroscopy, we consider the linear regression setting in which the many predictor variables arise from sampling an essentially continuous curve at equally spaced points and there may be multiple predictands. We tackle this regression problem by calculating the wavelet transforms of the discretized curves, then applying a Bayesian variable selection method using mixture priors to the multivariate regression of predictands on wavelet coefficients. For prediction purposes, we average over a set of likely models. Applied to a particular problem in NIR spectroscopy, this approach was able to find subsets of the wavelet coefficients with overall better predictive performance than the more usual approaches. In the application, the available predictors are measurements of the NIR reflectance spectrum of biscuit dough pieces at 256 equally spaced wavelengths. The aim is to predict the composition (i.e., the fat, flour, sugar, and water content) of the dough pieces using the spectral variables. Thus we have a multivariate regression of four predictands on 256 predictors with quite high intercorrelation among the predictors. A training set of 39 samples is available to fit this regression. Applying a wavelet transform replaces the 256 measurements on each spectrum with 256 wavelet coefficients that carry the same information. The variable selection method could use subsets of these coefficients that gave good predictions for all four compositional variables on a separate test set of samples. Selecting in the wavelet domain rather than from the original spectral variables is appealing in this application, because a single wavelet coefficient can carry information from a band of wavelengths in the original spectrum. This band can be narrow or wide, depending on the scale of the wavelet selected.

Bayes model averaging with selection of regressors

When a number of distinct models contend for use in prediction, the choice of a single model can offer rather unstable predictions. In regression, stochastic search variable selection with Bayesian model averaging offers a cure for this robustness issue but at the expense of requiring very many predictors. Here we look at Bayes model averaging incorporating variable selection for prediction. This offers similar mean-square errors of prediction but with a vastly reduced predictor space. This can greatly aid the interpretation of the model. It also reduces the cost if measured variables have costs. The development here uses decision theory in the context of the multivariate general linear model. In passing, this reduced predictor space Bayes model averaging is contrasted with single-model approximations. A fast algorithm for updating regressions in the Markov chain Monte Carlo searches for posterior inference is developed, allowing many more variables than observations to be contemplated. We discuss the merits of absolute rather than proportionate shrinkage in regression, especially when there are more variables than observations. The methodology is illustrated on a set of spectroscopic data used for measuring the amounts of different sugars in an aqueous solution. Copyright 2002 Royal Statistical Society.

Elastic scattering spectroscopy accurately detects high grade dysplasia and cancer in Barrett's oesophagus

Background and aims: Endoscopic surveillance of Barrett’s oesophagus currently relies on multiple random biopsies. This approach is time consuming, has a poor diagnostic yield, and significant interobserver variability. Elastic scattering spectroscopy is a real time in vivo optical technique which detects changes in the physical properties of cells. The aim of this study was to assess the potential for elastic scattering to detect high grade dysplasia or cancer within Barrett’s oesophagus. Methods: Elastic scattering spectroscopy measurements collected in vivo were matched with histological specimens taken from identical sites within Barrett’s oesophagus. All biopsies were reviewed by three gastrointestinal pathologists and defined as either “low risk” (non-dysplastic or low grade dysplasia) or “high risk” (high grade dysplasia or cancer). Two different statistical approaches (leave one out and block validation) were used to validate the model. Results: A total of 181 matched biopsy sites from 81 patients, where histopathological consensus was reached, were analysed. There was good pathologist agreement in differentiating high grade dysplasia and cancer from other pathology (kappa = 0.72). Elastic scattering spectroscopy detected high risk sites with 92% sensitivity and 60% specificity and differentiated high risk sites from inflammation with a sensitivity and specificity of 79%. If used to target biopsies during endoscopy, the number of low risk biopsies taken would decrease by 60% with minimal loss of accuracy. A negative spectroscopy result would exclude high grade dysplasia or cancer with an accuracy of >99.5%. Conclusions: These preliminary results show that elastic scattering spectroscopy has the potential to target conventional biopsies in Barrett’s surveillance saving significant endoscopist and pathologist time with consequent financial savings. This technique now requires validation in prospective studies.

Comparison of cervical magnetic stimulation and bilateral percutaneous electrical stimulation of the phrenic nerves in normal subjects

Cervical magnetic stimulation is a new technique for stimulating the phrenic nerves, and may offer an alternative to percutaneous electrical stimulation for assessing diaphragmatic strength in normal subjects and patients in whom electrical stimulation is technically difficult or poorly tolerated. We compared cervical magnetic stimulation with conventional supramaximal bilateral percutaneous electrical stimulation in nine normal subjects. We measured oesophageal pressure (Poes), gastric pressure (Pgas) and transdiaphragmatic pressure (Pdi). The maximal relaxation rate (MRR) was also measured. The mean magnetic twitch Pdi was 36.5 cmH2O (range 27-48 cmH2O), significantly larger than electrical twitch Pdi, mean 29.7 cmH2O (range 22-40 cmH2O). The difference in twitch Pdi was explained entirely by twitch Poes, and it is possible that the magnetic technique stimulates some of the nerves to the upper chest wall muscles as well as the phrenic nerves. We compared bilateral, rectified, integrated, diaphragm surface electromyographic (EMG) responses in three subjects and found results within 10% in each subject, indicating similar diaphragmatic activation. The within occasion coefficient of variation, i.e. same subject/same session, was 6.7% both for magnetic and electrical twitch Pdi. The between occasion coefficient of variation, i.e. same subject/different days, was 6.6% for magnetic stimulation and 8.8% for electrical. There was no difference between relaxation rates measured with either technique. We conclude that magnetic stimulation is a reproducible and acceptable technique for stimulating the phrenic nerves, and that it provides a potentially useful alternative to conventional electrical stimulation as a nonvolitional test of diaphragm strength.

A Misuse of Ridge Regression in the Calibration of a Near Infrared Reflectance Instrument

SUMMARY An example is presented of regression data which, despite high correlations between the explanatory variables, are not suitable for the application of ridge regression. This is because the relevant information in the explanatory variables is associated with small eigenvalues of their correlation matrix.

Leukemia mortality after X-ray treatment for ankylosing spondylitis.

Leukemia mortality has been studied in 14,767 adult ankylosing spondylitis patients diagnosed between 1935 and 1957 in the United Kingdom, of whom 13,914 patients received X-ray treatment. By 1 January 1992, there were 60 leukemia deaths among the irradiated patients, almost treble that expected from national rates. Leukemia mortality was not increased among unirradiated patients. Among those irradiated, the ratio of observed to expected deaths for leukemia other than chronic lymphocytic leukemia was greatest in the period 1-5 years after the first treatment (ratio = 11.01, 95% confidence interval 5.26-20.98) and decreased to 1.87 (95% confidence interval 0.94-3.36) in the 25+ year period. There was no significant variation in this ratio with sex or age at first treatment. The ratio for chronic lymphocytic leukemia was slightly but not significantly raised (ratio = 1.44, 95% confidence interval 0.62-2.79). Most irradiated patients received all their exposure within a year. Based on a 1 in 15 random sample, the mean total marrow dose was 4.38 Gy. Doses were nonuniform, with heaviest doses to the lower spine. The risk for nonchronic lymphocytic leukemia was adequately described by a linear-exponential model that allowed for cell sterilization in heavily exposed parts of the marrow and time since exposure. Ten years after first exposure, the linear component of excess relative risk was 12.37 per Gy (95% confidence interval 2.25-52.07), and it was estimated that cell sterilization reduced the excess relative risk by 47% at 1 Gy (95% confidence interval 17%-79%). The average predicted relative risk in the period 1-25 years after exposure to a uniform dose of 1 Gy was 7.00.