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.

Estimation of pelvic tilt on anteroposterior X-rays--a comparison of six parameters

OBJECTIVE: To compare six different parameters described in literature for estimation of pelvic tilt on an anteroposterior pelvic radiograph and to create a simple nomogram for tilt correction of prosthetic cup version in total hip arthroplasty. DESIGN: Simultaneous anteroposterior and lateral pelvic radiographs are taken routinely in our institution and were analyzed prospectively. The different parameters (including three distances and three ratios) were measured and compared to the actual pelvic tilt on the lateral radiograph using simple linear regression analysis. PATIENTS: One hundred and four consecutive patients (41 men, 63 women with a mean age of 31.7 years, SD 9.2 years, range 15.7-59.1 years) were studied. RESULTS: The strongest correlation between pelvic tilt and one of the six parameters for both men and women was the distance between the upper border of the symphysis and the sacrococcygeal joint. The correlation coefficient was 0.68 for men (P<0.001) and 0.61 for women (P<0.001). Based on this linear correlation, a nomogram was created that enables fast, tilt-corrected cup version measurements in clinical routine use. CONCLUSION: This simple method for correcting variations in pelvic tilt on plain radiographs can potentially improve the radiologist's ability to diagnose and interpret malformations of the acetabulum (particularly acetabular retroversion and excessive acetabular overcoverage) and post-operative orientation of the prosthetic acetabulum.

Migration and population expansion of Abies, Fagus, Picea, and Quercus since 15000 years in and across the Alps, based on pollen-percentage threshold values

Aims: The aim of this study is to explore the migration (colonization of new areas) and subsequent population expansion (within an area) since 15 ka cal BP of Abies, Fagus, Picea, and Quercus into and through the Alps solely on the basis of high-quality pollen data. Methods: Chronologies of 101 pollen sequences are improved or created. Data from the area delimited by 45.5–48.1°N and 6–14°E are summarized in three ways: (1) in a selection of pollen-percentage threshold maps (thresholds 0.5%, 1%, 2%, 4%, 8%, 16%, and 32% of land pollen); (2) in graphic summaries of 250-year time slices and geographic segments (lengthwise and transverse in relation to the main axis of the Alps) as pollen-percentage curves, pollen-percentage difference curves, and pollen-percentage threshold ages cal BP graphed against both the length and the transverse Alpine axes; and (3) in tables showing statistical relationships of either pollen-percentage threshold ages cal BP or pollen expansion durations (=time lapse between different pollen-percentage threshold ages cal BP) with latitude, longitude, and elevation; to establish these relationships we used both simple linear regression and multiple linear regression after stepwise-forward selection. Results: The statistical results indicate that (a) the use of pollen-percentage thresholds between 0.5% and 8% yield mostly similar directions of tree migration, so the method is fairly robust, (b) Abies migrated northward, Fagus southward, Picea westward, and Quercus northward; more detail does not emerge due to an extreme scarcity of high-quality data especially along the southern foothills of the Alps and in the eastern Alps. This scarcity allows the reconstruction of one immigration route only of Abies into the southern Alps. The speed of population expansion (following arrival) of Abies increased and of Picea decreased during the Holocene, of Fagus it decreased especially during the later Holocene, and of Quercus it increased especially at the start of the Holocene.

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.

Endocrine symptom assessment in women with breast cancer: what a simple "yes" means

GOALS OF WORK: To investigate the self-reported symptoms related to endocrine therapy in women with early or advanced breast cancer and the impact of these symptoms on quality of life (QL) indicators. MATERIALS AND METHODS: Symptom occurrence was assessed by the Checklist for Patients on Endocrine Therapy (C-PET) and symptom intensity was assessed by linear analogue self-assessment (LASA) indicators. Patients also responded to global LASA indicators for physical well-being, mood, coping effort and treatment burden. Associations between symptoms and these indicators were analysed by linear regression models. MAIN RESULTS: Among 373 women, the distribution of symptom intensity showed considerable variation in patients reporting a symptom as present. Even though patients recorded a symptom as absent, some patients reported having experienced that symptom when responding to symptom intensity, as seen for decreased sex drive, tiredness and vaginal dryness. Six of 13 symptoms and lower age had a detrimental impact on the global indicators, particularly tiredness and irritability. CONCLUSIONS: Patients' experience of endocrine symptoms needs to be considered both in patient care and research, when interpreting the association between symptoms and QL.

Simple Estimation of Incident HIV Infection Rates in Notification Cohorts Based on Window Periods of Algorithms for Evaluation of Line-Immunoassay Result Patterns

Background Tests for recent infections (TRIs) are important for HIV surveillance. We have shown that a patient's antibody pattern in a confirmatory line immunoassay (Inno-Lia) also yields information on time since infection. We have published algorithms which, with a certain sensitivity and specificity, distinguish between incident (< = 12 months) and older infection. In order to use these algorithms like other TRIs, i.e., based on their windows, we now determined their window periods. Methods We classified Inno-Lia results of 527 treatment-naïve patients with HIV-1 infection < = 12 months according to incidence by 25 algorithms. The time after which all infections were ruled older, i.e. the algorithm's window, was determined by linear regression of the proportion ruled incident in dependence of time since infection. Window-based incident infection rates (IIR) were determined utilizing the relationship ‘Prevalence = Incidence x Duration’ in four annual cohorts of HIV-1 notifications. Results were compared to performance-based IIR also derived from Inno-Lia results, but utilizing the relationship ‘incident = true incident + false incident’ and also to the IIR derived from the BED incidence assay. Results Window periods varied between 45.8 and 130.1 days and correlated well with the algorithms' diagnostic sensitivity (R2 = 0.962; P<0.0001). Among the 25 algorithms, the mean window-based IIR among the 748 notifications of 2005/06 was 0.457 compared to 0.453 obtained for performance-based IIR with a model not correcting for selection bias. Evaluation of BED results using a window of 153 days yielded an IIR of 0.669. Window-based IIR and performance-based IIR increased by 22.4% and respectively 30.6% in 2008, while 2009 and 2010 showed a return to baseline for both methods. Conclusions IIR estimations by window- and performance-based evaluations of Inno-Lia algorithm results were similar and can be used together to assess IIR changes between annual HIV notification cohorts.

Tidal volume single breath washout of two tracer gases--a practical and promising lung function test

Background Small airway disease frequently occurs in chronic lung diseases and may cause ventilation inhomogeneity (VI), which can be assessed by washout tests of inert tracer gas. Using two tracer gases with unequal molar mass (MM) and diffusivity increases specificity for VI in different lung zones. Currently washout tests are underutilised due to the time and effort required for measurements. The aim of this study was to develop and validate a simple technique for a new tidal single breath washout test (SBW) of sulfur hexafluoride (SF6) and helium (He) using an ultrasonic flowmeter (USFM). Methods The tracer gas mixture contained 5% SF6 and 26.3% He, had similar total MM as air, and was applied for a single tidal breath in 13 healthy adults. The USFM measured MM, which was then plotted against expired volume. USFM and mass spectrometer signals were compared in six subjects performing three SBW. Repeatability and reproducibility of SBW, i.e., area under the MM curve (AUC), were determined in seven subjects performing three SBW 24 hours apart. Results USFM reliably measured MM during all SBW tests (n = 60). MM from USFM reflected SF6 and He washout patterns measured by mass spectrometer. USFM signals were highly associated with mass spectrometer signals, e.g., for MM, linear regression r-squared was 0.98. Intra-subject coefficient of variation of AUC was 6.8%, and coefficient of repeatability was 11.8%. Conclusion The USFM accurately measured relative changes in SF6 and He washout. SBW tests were repeatable and reproducible in healthy adults. We have developed a fast, reliable, and straightforward USFM based SBW method, which provides valid information on SF6 and He washout patterns during tidal breathing.

A PRISMA assessment of the reporting quality of systematic reviews in orthodontics

Abstract Objectives: To assess the reporting quality of Cochrane and non-Cochrane systematic reviews (SR) in orthodontics and to compare the reporting quality (PRISMA score) with methodological quality (AMSTAR criteria). Materials and Methods: Systematic reviews (n  =  109) published between January 2000 and July 2011 in five leading orthodontic journals were identified and included. The quality of reporting of the included reviews was assessed by two authors in accordance with the PRISMA guidelines. Each article was assigned a cumulative grade based on fulfillment of the applicable criteria, and an overall percentage score was assigned. Descriptive statistics and simple and multiple linear regression analyses were undertaken. Results: The mean overall PRISMA score was 64.1% (95% confidence interval [CI], 62%-65%). The quality of reporting was considerably better in reviews published in the Cochrane Database of Systematic Reviews (P < .001) than in non-Cochrane reviews. Both multivariable and univariable analysis indicated that journal of publication and number of authors was significantly associated with the PRISMA score. The association between AMSTAR score and modified PRISMA score was also found to be highly statistically significant. Conclusion: Compliance of orthodontic SRs published in orthodontic journals with PRISMA guidelines was deficient in several areas. The quality of reporting assessed using PRISMA guidelines was significantly better in orthodontic SRs published in the Cochrane Database of Systematic Reviews.

Predicting spike timing of neocortical pyramidal neurons by simple threshold models

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current--is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of +/-2 ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold process.

Fluctuation analysis of lung function as a predictor of long-term response to beta2-agonists

The response to beta(2)-agonists differs between asthmatics and has been linked to subsequent adverse events, even death. Possible determinants include beta(2)-adrenoceptor genotype at position 16, lung function and airway hyperresponsiveness. Fluctuation analysis provides a simple parameter alpha measuring the complex correlation properties of day-to-day peak expiratory flow. The present study investigated whether alpha predicts clinical response to beta(2)-agonist treatment, taking into account other conventional predictors. Analysis was performed on previously published twice-daily peak expiratory flow measurements in 66 asthmatic adults over three 6-month randomised order treatment periods: placebo, salbutamol and salmeterol. Multiple linear regression was used to determine the association between alpha during the placebo period and response to treatment (change in the number of days with symptoms), taking into account other predictors namely beta(2)-adrenoceptor genotype, lung function and its variability, and airway hyperresponsiveness. The current authors found that alpha measured during the placebo period considerably improved the prediction of response to salmeterol treatment, taking into account genotype, lung function or its variability, or airway hyperresponsiveness. The present study provides further evidence that response to beta(2)-agonists is related to the time correlation properties of lung function in asthma. The current authors conclude that fluctuation analysis of lung function offers a novel predictor to identify patients who may respond well or poorly to treatment.

Assessing vegetation cover and biomass in restored erosion areas in Iceland using SPOT satellite data

Due to highly erodible volcanic soils and a harsh climate, livestock grazing in Iceland has led to serious soil erosion on about 40% of the country's surface. Over the last 100 years, various revegetation and restoration measures were taken on large areas distributed all over Iceland in an attempt to counteract this problem. The present research aimed to develop models for estimating percent vegetation cover (VC) and aboveground biomass (AGB) based on satellite data, as this would make it possible to assess and monitor the effectiveness of restoration measures over large areas at a fairly low cost. Models were developed based on 203 vegetation cover samples and 114 aboveground biomass samples distributed over five SPOT satellite datasets. All satellite datasets were atmospherically corrected, and digital numbers were converted into ground reflectance. Then a selection of vegetation indices (VIs) was calculated, followed by simple and multiple linear regression analysis of the relations between the field data and the calculated VIs. Best results were achieved using multiple linear regression models for both %VC and AGB. The model calibration and validation results showed that R2 and RMSE values for most VIs do not vary very much. For percent VC, R2 values range between 0.789 and 0.822, leading to RMSEs ranging between 15.89% and 16.72%. For AGB, R2 values for low-biomass areas (AGB < 800 g/m2) range between 0.607 and 0.650, leading to RMSEs ranging between 126.08 g/m2 and 136.38 g/m2. The AGB model developed for all areas, including those with high biomass coverage (AGB > 800 g/m2), achieved R2 values between 0.487 and 0.510, resulting in RMSEs ranging from 234 g/m2 to 259.20 g/m2. The models predicting percent VC generally overestimate observed low percent VC and slightly underestimate observed high percent VC. The estimation models for AGB behave in a similar way, but over- and underestimation are much more pronounced. These results show that it is possible to estimate percent VC with high accuracy based on various VIs derived from SPOT satellite data. AGB of restoration areas with low-biomass values of up to 800 g/m2 can likewise be estimated with high accuracy based on various VIs derived from SPOT satellite data, whereas in the case of high biomass coverage, estimation accuracy decreases with increasing biomass values. Accordingly, percent VC can be estimated with high accuracy anywhere in Iceland, whereas AGB is much more difficult to estimate, particularly for areas with high-AGB variability.

Effects of weight on blood pressure at rest and during exercise.

Body weight (BW) and blood pressure (BP) have a close relationship, which has been accounted for by hormonal changes. No previous study has evaluated the effect of wearing an external weight vest on BP to determine whether there is a simple mechanism between BW and BP. Seventeen healthy volunteers underwent weight reduction (WR) through caloric restriction. Before and after WR, BW, body fat percentage and BP at rest and during exercise were measured. Before and after WR, exercise testing was performed twice with the random allocation of a weight vest (10 kg) during one of the tests. Linear regression was used to detect independent associations between BP and the weight vest, BW and body fat percentage. BW decreased from 89.4 ± 15.4 kg to 79.1 ± 14.0 kg following WR (P<0.001). WR led to significant decreases in BP at rest (from 130.0/85.9 mm Hg to 112.5/77.8 mm Hg, P<0.001 for systolic and diastolic BPs) and during exercise. The weight vest significantly increased BP at rest (to 136.1/90.7 mm Hg before and 125.8/84.6 mm Hg after WR) and during exercise. Linear regression analysis identified an independent association between the weight vest and BP (P=0.006 for systolic BP and P=0.009 for diastolic BP at rest). This study demonstrates that wearing an external weight vest has immediate effects on BP at rest and during exercise independent of BW or body fat. More research is needed to understand the physiological mechanisms between weight and BP.

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.