Stochastic search for semiparametric linear regression models

This paper introduces and analyzes a stochastic search method for parameter estimation in linear regression models in the spirit of Beran and Millar [Ann. Statist. 15(3) (1987) 1131–1154]. The idea is to generate a random finite subset of a parameter space which will automatically contain points which are very close to an unknown true parameter. The motivation for this procedure comes from recent work of Dümbgen et al. [Ann. Statist. 39(2) (2011) 702–730] on regression models with log-concave error distributions.

The Blinder-Oaxaca decomposition for linear regression models

The counterfactual decomposition technique popularized by Blinder (1973, Journal of Human Resources, 436–455) and Oaxaca (1973, International Economic Review, 693–709) is widely used to study mean outcome differences between groups. For example, the technique is often used to analyze wage gaps by sex or race. This article summarizes the technique and addresses several complications, such as the identification of effects of categorical predictors in the detailed decomposition or the estimation of standard errors. A new command called oaxaca is introduced, and examples illustrating its usage are given.

Effect of vascular targeting agent in rat tumor model: dynamic contrast-enhanced versus diffusion-weighted MR imaging

PURPOSE: To compare dynamic contrast material-enhanced magnetic resonance (MR) imaging and diffusion-weighted MR imaging for noninvasive evaluation of early and late effects of a vascular targeting agent in a rat tumor model. MATERIALS AND METHODS: The study protocol was approved by the local ethics committee for animal care and use. Thirteen rats with one rhabdomyosarcoma in each flank (26 tumors) underwent dynamic contrast-enhanced imaging and diffusion-weighted echo-planar imaging in a 1.5-T MR unit before intraperitoneal injection of combretastatin A4 phosphate and at early (1 and 6 hours) and later (2 and 9 days) follow-up examinations after the injection. Histopathologic examination was performed at each time point. The apparent diffusion coefficient (ADC) of each tumor was calculated separately on the basis of diffusion-weighted images obtained with low b gradient values (ADC(low); b = 0, 50, and 100 sec/mm(2)) and high b gradient values (ADC(high); b = 500, 750, and 1000 sec/mm(2)). The difference between ADC(low) and ADC(high) was used as a surrogate measure of tissue perfusion (ADC(low) - ADC(high) = ADC(perf)). From the dynamic contrast-enhanced MR images, the volume transfer constant k and the initial slope of the contrast enhancement-time curve were calculated. For statistical analyses, a paired two-tailed Student t test and linear regression analysis were used. RESULTS: Early after administration of combretastatin, all perfusion-related parameters (k, initial slope, and ADC(perf)) decreased significantly (P < .001); at 9 days after combretastatin administration, they increased significantly (P < .001). Changes in ADC(perf) were correlated with changes in k (R(2) = 0.46, P < .001) and the initial slope (R(2) = 0.67, P < .001). CONCLUSION: Both dynamic contrast-enhanced MR imaging and diffusion-weighted MR imaging allow monitoring of perfusion changes induced by vascular targeting agents in tumors. Diffusion-weighted imaging provides additional information about intratumoral cell viability versus necrosis after administration of combretastatin.

Living Renal Allograft Transplantation: Diffusion-weighted MR Imaging in Longitudinal Follow-up of the Donated and the Remaining Kidney.

Purpose To determine whether diffusion-weighted (DW) magnetic resonance (MR) imaging in living renal allograft donation allows monitoring of potential changes in the nontransplanted remaining kidney of the donor because of unilateral nephrectomy and changes in the transplanted kidney before and after transplantation in donor and recipient, respectively, and whether DW MR parameters are correlated in the same kidney before and after transplantation. Materials and Methods The study protocol was approved by the local ethics committee; written informed consent was obtained. Thirteen healthy kidney donors and their corresponding recipients prospectively underwent DW MR imaging (multiple b values) in donors before donation and in donors and recipients at day 8 and months 3 and 12 after donation. Total apparent diffusion coefficient (ADCT) values were determined; contribution of microcirculation was quantified in perfusion fraction (FP). Longitudinal changes of diffusion parameters were compared (repeated-measures one-way analysis of variance with post hoc pairwise comparisons). Correlations were tested (linear regression). Results ADCT values in nontransplanted kidney of donors increased from a preexplantation value of (188 ± 9 [standard deviation]) to (202 ± 11) × 10(-5) mm(2)/sec in medulla and from (199 ± 11) to (210 ± 13) × 10(-5) mm(2)/sec in cortex 1 week after donation (P < .004). Medullary, but not cortical, ADCT values stayed increased up to 1 year. ADCT values in allografts in recipients were stable. Compared with values obtained before transplantation in donors, the corticomedullary difference was reduced in allografts (P < .03). Cortical ADCT values correlated with estimated glomerular filtration rate in recipients (R = 0.56, P < .001) but not donors. Cortical ADCT values in the same kidney before transplantation in donors correlated with those in recipients on day 8 after transplantation (R = 0.77, P = .006). FP did not show significant changes. Conclusion DW MR imaging depicts early adaptations in the remaining nontransplanted kidney of donors after nephrectomy. All diffusion parameters remained constant in allograft recipients after transplantation. This method has potential monitoring utility, although assessment of clinical relevance is needed. © RSNA, 2013 Online supplemental material is available for this article.

A prediction model for assessing residential radon concentration in Switzerland

Indoor radon is regularly measured in Switzerland. However, a nationwide model to predict residential radon levels has not been developed. The aim of this study was to develop a prediction model to assess indoor radon concentrations in Switzerland. The model was based on 44,631 measurements from the nationwide Swiss radon database collected between 1994 and 2004. Of these, 80% randomly selected measurements were used for model development and the remaining 20% for an independent model validation. A multivariable log-linear regression model was fitted and relevant predictors selected according to evidence from the literature, the adjusted R², the Akaike's information criterion (AIC), and the Bayesian information criterion (BIC). The prediction model was evaluated by calculating Spearman rank correlation between measured and predicted values. Additionally, the predicted values were categorised into three categories (50th, 50th-90th and 90th percentile) and compared with measured categories using a weighted Kappa statistic. The most relevant predictors for indoor radon levels were tectonic units and year of construction of the building, followed by soil texture, degree of urbanisation, floor of the building where the measurement was taken and housing type (P-values <0.001 for all). Mean predicted radon values (geometric mean) were 66 Bq/m³ (interquartile range 40-111 Bq/m³) in the lowest exposure category, 126 Bq/m³ (69-215 Bq/m³) in the medium category, and 219 Bq/m³ (108-427 Bq/m³) in the highest category. Spearman correlation between predictions and measurements was 0.45 (95%-CI: 0.44; 0.46) for the development dataset and 0.44 (95%-CI: 0.42; 0.46) for the validation dataset. Kappa coefficients were 0.31 for the development and 0.30 for the validation dataset, respectively. The model explained 20% overall variability (adjusted R²). In conclusion, this residential radon prediction model, based on a large number of measurements, was demonstrated to be robust through validation with an independent dataset. The model is appropriate for predicting radon level exposure of the Swiss population in epidemiological research. Nevertheless, some exposure misclassification and regression to the mean is unavoidable and should be taken into account in future applications of the model.

Blood lead level association with lower body weight in NHANES 1999-2006

BACKGROUND Lead exposure is associated with low birth-weight. The objective of this study is to determine whether lead exposure is associated with lower body weight in children, adolescents and adults. METHODS We analyzed data from NHANES 1999-2006 for participants aged ≥3 using multiple logistic and multivariate linear regression. Using age- and sex-standardized BMI Z-scores, overweight and obese children (ages 3-19) were classified by BMI ≥85 th and ≥95 th percentiles, respectively. The adult population (age ≥20) was classified as overweight and obese with BMI measures of 25-29.9 and ≥30, respectively. Blood lead level (BLL) was categorized by weighted quartiles. RESULTS Multivariate linear regressions revealed a lower BMI Z-score in children and adolescents when the highest lead quartile was compared to the lowest lead quartile (β (SE)=-0.33 (0.07), p<0.001), and a decreased BMI in adults (β (SE)=-2.58 (0.25), p<0.001). Multiple logistic analyses in children and adolescents found a negative association between BLL and the percentage of obese and overweight with BLL in the highest quartile compared to the lowest quartile (OR=0.42, 95% CI: 0.30-0.59; and OR=0.67, 95% CI: 0.52-0.88, respectively). Adults in the highest lead quartile were less likely to be obese (OR=0.42, 95% CI: 0.35-0.50) compared to those in the lowest lead quartile. Further analyses with blood lead as restricted cubic splines, confirmed the dose-relationship between blood lead and body weight outcomes. CONCLUSIONS BLLs are associated with lower body mass index and obesity in children, adolescents and adults.

ROBREG: Stata module providing robust regression estimators

robreg provides a number of robust estimators for linear regression models. Among them are the high breakdown-point and high efficiency MM-estimator, the Huber and bisquare M-estimator, and the S-estimator, each supporting classic or robust standard errors. Furthermore, basic versions of the LMS/LQS (least median of squares) and LTS (least trimmed squares) estimators are provided. Note that the moremata package, also available from SSC, is required.

Determinants of renal tissue oxygenation as measured with BOLD-MRI in chronic kidney disease and hypertension in humans.

Experimentally renal tissue hypoxia appears to play an important role in the pathogenesis of chronic kidney disease (CKD) and arterial hypertension (AHT). In this study we measured renal tissue oxygenation and its determinants in humans using blood oxygenation level-dependent magnetic resonance imaging (BOLD-MRI) under standardized hydration conditions. Four coronal slices were selected, and a multi gradient echo sequence was used to acquire T2* weighted images. The mean cortical and medullary R2* values ( = 1/T2*) were calculated before and after administration of IV furosemide, a low R2* indicating a high tissue oxygenation. We studied 195 subjects (95 CKD, 58 treated AHT, and 42 healthy controls). Mean cortical R2 and medullary R2* were not significantly different between the groups at baseline. In stimulated conditions (furosemide injection), the decrease in R2* was significantly blunted in patients with CKD and AHT. In multivariate linear regression analyses, neither cortical nor medullary R2* were associated with eGFR or blood pressure, but cortical R2* correlated positively with male gender, blood glucose and uric acid levels. In conclusion, our data show that kidney oxygenation is tightly regulated in CKD and hypertensive patients at rest. However, the metabolic response to acute changes in sodium transport is altered in CKD and in AHT, despite preserved renal function in the latter group. This suggests the presence of early renal metabolic alterations in hypertension. The correlations between cortical R2* values, male gender, glycemia and uric acid levels suggest that these factors interfere with the regulation of renal tissue oxygenation.

Modeling absolute differences in life expectancy with a censored skew-normal regression approach.

Parameter estimates from commonly used multivariable parametric survival regression models do not directly quantify differences in years of life expectancy. Gaussian linear regression models give results in terms of absolute mean differences, but are not appropriate in modeling life expectancy, because in many situations time to death has a negative skewed distribution. A regression approach using a skew-normal distribution would be an alternative to parametric survival models in the modeling of life expectancy, because parameter estimates can be interpreted in terms of survival time differences while allowing for skewness of the distribution. In this paper we show how to use the skew-normal regression so that censored and left-truncated observations are accounted for. With this we model differences in life expectancy using data from the Swiss National Cohort Study and from official life expectancy estimates and compare the results with those derived from commonly used survival regression models. We conclude that a censored skew-normal survival regression approach for left-truncated observations can be used to model differences in life expectancy across covariates of interest.

Climate-pollen relationships AD 1901-1996 in two small mires near the forest limit in the northern and central Swiss Alps

Climatic relationships were established in two 210Pb dated pollen sequences from small mires closely surrounded by forest just below actual forest limits (but about 300 m below potential climatic forest limits) in the northern Swiss Alps (suboceanic in climate; mainly with Picea) and the central Swiss Alps (subcontinental; mainly Pinus cembra and Larix) at annual or near-annual resolution from ad 1901 to 1996. Effects of vegetational succession were removed by splitting the time series into early and late periods and by linear detrending. Both pollen concentrations detrended by the depth-age model and modified percentages (in which counts of dominant pollen types are down-weighted) are correlated by simple linear regression with smoothed climatic parameters with one-and two-year timelags, including average monthly and April/September daylight air temperatures and with seasonal and annual precipitation sums. Results from detrended pollen concentrations suggest that peat accumulation is favoured in the northern-Alpine mire either by early snowmelt or by summer precipitation, but in the central-Alpine mire by increased precipitation and cooler summers, suggesting a position of the northern-Alpine mire near the upper altitudinal limit of peat formation, but of the central-Alpine mire near the lower limit. Results from modified pollen percentages indicate that pollen pro duction by plants growing near their upper altitudinal limit is limited by insufficient warmth in summer, and pollen production by plants growing near their lower altitudinal limit is limited by too-high temperatures. Only weakly significant pollen/climate relationships were found for Pinus cembra and Larix, probably because they experience little climatic stress growing 300 m below the potential climatic forest limit.