Robust response transformations based on optimal prediction

Nonlinear regression problems can often be reduced to linearity by transforming the response variable (e.g., using the Box-Cox family of transformations). The classic estimates of the parameter defining the transformation as well as of the regression coefficients are based on the maximum likelihood criterion, assuming homoscedastic normal errors for the transformed response. These estimates are nonrobust in the presence of outliers and can be inconsistent when the errors are nonnormal or heteroscedastic. This article proposes new robust estimates that are consistent and asymptotically normal for any unimodal and homoscedastic error distribution. For this purpose, a robust version of conditional expectation is introduced for which the prediction mean squared error is replaced with an M scale. This concept is then used to develop a nonparametric criterion to estimate the transformation parameter as well as the regression coefficients. A finite sample estimate of this criterion based on a robust version of smearing is also proposed. Monte Carlo experiments show that the new estimates compare favorably with respect to the available competitors.

Robust T1-Weighted Structural Brain Imaging and Morphometry at 7T Using MP2RAGE.

PURPOSE: To suppress the noise, by sacrificing some of the signal homogeneity for numerical stability, in uniform T1 weighted (T1w) images obtained with the magnetization prepared 2 rapid gradient echoes sequence (MP2RAGE) and to compare the clinical utility of these robust T1w images against the uniform T1w images. MATERIALS AND METHODS: 8 healthy subjects (29.0±4.1 years; 6 Male), who provided written consent, underwent two scan sessions within a 24 hour period on a 7T head-only scanner. The uniform and robust T1w image volumes were calculated inline on the scanner. Two experienced radiologists qualitatively rated the images for: general image quality; 7T specific artefacts; and, local structure definition. Voxel-based and volume-based morphometry packages were used to compare the segmentation quality between the uniform and robust images. Statistical differences were evaluated by using a positive sided Wilcoxon rank test. RESULTS: The robust image suppresses background noise inside and outside the skull. The inhomogeneity introduced was ranked as mild. The robust image was significantly ranked higher than the uniform image for both observers (observer 1/2, p-value = 0.0006/0.0004). In particular, an improved delineation of the pituitary gland, cerebellar lobes was observed in the robust versus uniform T1w image. The reproducibility of the segmentation results between repeat scans improved (p-value = 0.0004) from an average volumetric difference across structures of ≈6.6% to ≈2.4% for the uniform image and robust T1w image respectively. CONCLUSIONS: The robust T1w image enables MP2RAGE to produce, clinically familiar T1w images, in addition to T1 maps, which can be readily used in uniform morphometry packages.

Quantitative estimation of foot-flat and stance phase of gait using foot-worn inertial sensors.

Time periods composing stance phase of gait can be clinically meaningful parameters to reveal differences between normal and pathological gait. This study aimed, first, to describe a novel method for detecting stance and inner-stance temporal events based on foot-worn inertial sensors; second, to extract and validate relevant metrics from those events; and third, to investigate their suitability as clinical outcome for gait evaluations. 42 subjects including healthy subjects and patients before and after surgical treatments for ankle osteoarthritis performed 50-m walking trials while wearing foot-worn inertial sensors and pressure insoles as a reference system. Several hypotheses were evaluated to detect heel-strike, toe-strike, heel-off, and toe-off based on kinematic features. Detected events were compared with the reference system on 3193 gait cycles and showed good accuracy and precision. Absolute and relative stance periods, namely loading response, foot-flat, and push-off were then estimated, validated, and compared statistically between populations. Besides significant differences observed in stance duration, the analysis revealed differing tendencies with notably a shorter foot-flat in healthy subjects. The result indicated which features in inertial sensors' signals should be preferred for detecting precisely and accurately temporal events against a reference standard. The system is suitable for clinical evaluations and provides temporal analysis of gait beyond the common swing/stance decomposition, through a quantitative estimation of inner-stance phases such as foot-flat.

iLOGP: A Simple, Robust, and Efficient Description of n-Octanol/Water Partition Coefficient for Drug Design Using the GB/SA Approach.

The n-octanol/water partition coefficient (log Po/w) is a key physicochemical parameter for drug discovery, design, and development. Here, we present a physics-based approach that shows a strong linear correlation between the computed solvation free energy in implicit solvents and the experimental log Po/w on a cleansed data set of more than 17,500 molecules. After internal validation by five-fold cross-validation and data randomization, the predictive power of the most interesting multiple linear model, based on two GB/SA parameters solely, was tested on two different external sets of molecules. On the Martel druglike test set, the predictive power of the best model (N = 706, r = 0.64, MAE = 1.18, and RMSE = 1.40) is similar to six well-established empirical methods. On the 17-drug test set, our model outperformed all compared empirical methodologies (N = 17, r = 0.94, MAE = 0.38, and RMSE = 0.52). The physical basis of our original GB/SA approach together with its predictive capacity, computational efficiency (1 to 2 s per molecule), and tridimensional molecular graphics capability lay the foundations for a promising predictor, the implicit log P method (iLOGP), to complement the portfolio of drug design tools developed and provided by the SIB Swiss Institute of Bioinformatics.

Achievement of at least very good partial response is a simple and robust prognostic factor in patients with multiple myeloma treated with high-dose therapy: long-term analysis of the IFM 99-02 and 99-04 Trials.

PURPOSE: The prognostic impact of complete response (CR) achievement in multiple myeloma (MM) has been shown mostly in the context of autologous stem-cell transplantation. Other levels of response have been defined because, even with high-dose therapy, CR is a relatively rare event. The purpose of this study was to analyze the prognostic impact of very good partial response (VGPR) in patients treated with high-dose therapy. PATIENTS AND METHODS: All patients were included in the Intergroupe Francophone du Myelome 99-02 and 99-04 trials and treated with vincristine, doxorubicin, and dexamethasone (VAD) induction therapy followed by double autologous stem-cell transplantation (ASCT). Best post-ASCT response assessment was available for 802 patients. RESULTS: With a median follow-up of 67 months, median event-free survival (EFS) and 5-year EFS were 42 months and 34%, respectively, for 405 patients who achieved at least VGPR after ASCT versus 32 months and 26% in 288 patients who achieved only partial remission (P = .005). Five-year overall survival (OS) was significantly superior in patients achieving at least VGPR (74% v 61% P = .0017). In multivariate analysis, achievement of less than VGPR was an independent factor predicting shorter EFS and OS. Response to VAD had no impact on EFS and OS. The impact of VGPR achievement on EFS and OS was significant in patients with International Staging System stages 2 to 3 and for patients with poor-risk cytogenetics t(4;14) or del(17p). CONCLUSION: In the context of ASCT, achievement of at least VGPR is a simple prognostic factor that has importance in intermediate and high-risk MM and can be informative in more patients than CR.

HIERFSTAT, a package for R to compute and test hierarchical F-statistics

The package HIERFSTAT for the statistical software R, created by the R Development Core Team, allows the estimate of hierarchical F-statistics from a hierarchy with any numbers of levels. In addition, it allows testing the statistical significance of population differentiation for these different levels, using a generalized likelihood-ratio test. The package HIERFSTAT is available at http://www.unil.ch/popgen/softwares/hierfstat.htm.

Comparison of the polynomial model against explicit measurements of noise components for different mammography systems.

Given the adverse impact of image noise on the perception of important clinical details in digital mammography, routine quality control measurements should include an evaluation of noise. The European Guidelines, for example, employ a second-order polynomial fit of pixel variance as a function of detector air kerma (DAK) to decompose noise into quantum, electronic and fixed pattern (FP) components and assess the DAK range where quantum noise dominates. This work examines the robustness of the polynomial method against an explicit noise decomposition method. The two methods were applied to variance and noise power spectrum (NPS) data from six digital mammography units. Twenty homogeneously exposed images were acquired with PMMA blocks for target DAKs ranging from 6.25 to 1600 µGy. Both methods were explored for the effects of data weighting and squared fit coefficients during the curve fitting, the influence of the additional filter material (2 mm Al versus 40 mm PMMA) and noise de-trending. Finally, spatial stationarity of noise was assessed.Data weighting improved noise model fitting over large DAK ranges, especially at low detector exposures. The polynomial and explicit decompositions generally agreed for quantum and electronic noise but FP noise fraction was consistently underestimated by the polynomial method. Noise decomposition as a function of position in the image showed limited noise stationarity, especially for FP noise; thus the position of the region of interest (ROI) used for noise decomposition may influence fractional noise composition. The ROI area and position used in the Guidelines offer an acceptable estimation of noise components. While there are limitations to the polynomial model, when used with care and with appropriate data weighting, the method offers a simple and robust means of examining the detector noise components as a function of detector exposure.

Which is the optimal sampling strategy for habitat suitability modelling

Designing an efficient sampling strategy is of crucial importance for habitat suitability modelling. This paper compares four such strategies, namely, 'random', 'regular', 'proportional-stratified' and 'equal -stratified'- to investigate (1) how they affect prediction accuracy and (2) how sensitive they are to sample size. In order to compare them, a virtual species approach (Ecol. Model. 145 (2001) 111) in a real landscape, based on reliable data, was chosen. The distribution of the virtual species was sampled 300 times using each of the four strategies in four sample sizes. The sampled data were then fed into a GLM to make two types of prediction: (1) habitat suitability and (2) presence/ absence. Comparing the predictions to the known distribution of the virtual species allows model accuracy to be assessed. Habitat suitability predictions were assessed by Pearson's correlation coefficient and presence/absence predictions by Cohen's K agreement coefficient. The results show the 'regular' and 'equal-stratified' sampling strategies to be the most accurate and most robust. We propose the following characteristics to improve sample design: (1) increase sample size, (2) prefer systematic to random sampling and (3) include environmental information in the design'

Chemical labelling of oyster shells used for time-calibrated high-resolution Mg/Ca ratios: A tool for estimation of past seasonal temperature variations

The geochemical compositions of biogenic carbonates are increasingly used for palaeoenvironmental reconstructions. The skeletal delta O-18 temperature relationship is dependent on water salinity, so many recent studies have focused on the Mg/Ca and Sr/Ca ratios because those ratios in water do not change significantly on short time scales. Thus, those elemental ratios are considered to be good palaeotemperature proxies in many biominerals, although their use remains ambiguous in bivalve shells. Here, we present the high-resolution Mg/Ca ratios of two modern species of juvenile and adult oyster shells, Crassostrea gigas and Ostrea edulis. These specimens were grown in controlled conditions for over one year in two different locations. In situ monthly Mn-marking of the shells has been used for day calibration. The daily Mg/Ca.ratios in the shell have been measured with an electron microprobe. The high frequency Mg/Ca variation of all specimens displays good synchronism with lunar cycles, suggesting that tides strongly influence the incorporation of Mg/Ca into the shells. Highly significant correlation coefficients (0.70<R<0.83, p<0.0001) between the Mg/Ca ratios and the seawater temperature are obtained only for juvenile C. gigas samples, while metabolic control of Mg/Ca incorporation and lower shell growth rates preclude the use of the Mg/Ca ratio in adult shells as a palaeothermometer. Data from three juvenile C. gigas shells from the two study sites are selected to establish a relationship: T = 3.77Mg/Ca + 1.88, where T is in degrees C and Mg/Ca in mmol/mol. (c) 2012 Elsevier B.V. All rights reserved.

Estimation of percentage body fat in 6- to 13-year-old children by skinfold thickness, body mass index and waist circumference.

We evaluated the accuracy of skinfold thicknesses, BMI and waist circumference for the prediction of percentage body fat (PBF) in a representative sample of 372 Swiss children aged 6-13 years. PBF was measured using dual-energy X-ray absorptiometry. On the basis of a preliminary bootstrap selection of predictors, seven regression models were evaluated. All models included sex, age and pubertal stage plus one of the following predictors: (1) log-transformed triceps skinfold (logTSF); (2) logTSF and waist circumference; (3) log-transformed sum of triceps and subscapular skinfolds (logSF2); (4) log-transformed sum of triceps, biceps, subscapular and supra-iliac skinfolds (logSF4); (5) BMI; (6) waist circumference; (7) BMI and waist circumference. The adjusted determination coefficient (R² adj) and the root mean squared error (RMSE; kg) were calculated for each model. LogSF4 (R² adj 0.85; RMSE 2.35) and logSF2 (R² adj 0.82; RMSE 2.54) were similarly accurate at predicting PBF and superior to logTSF (R² adj 0.75; RMSE 3.02), logTSF combined with waist circumference (R² adj 0.78; RMSE 2.85), BMI (R² adj 0.62; RMSE 3.73), waist circumference (R² adj 0.58; RMSE 3.89), and BMI combined with waist circumference (R² adj 0.63; RMSE 3.66) (P < 0.001 for all values of R² adj). The finding that logSF4 was only modestly superior to logSF2 and that logTSF was better than BMI and waist circumference at predicting PBF has important implications for paediatric epidemiological studies aimed at disentangling the effect of body fat on health outcomes.