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.

The influence of muscle strength on the gait profile score (GPS) across different patients

BACKGROUND Muscle strength greatly influences gait kinematics. The question was whether this association is similar in different diseases. METHODS Data from instrumented gait analysis of 716 patients were retrospectively assessed. The effect of muscle strength on gait deviations, namely the gait profile score (GPS) was evaluated by means of generalised least square models. This was executed for seven different patient groups. The groups were formed according to the type of disease: orthopaedic/neurologic, uni-/bilateral affection, and flaccid/spastic muscles. RESULTS Muscle strength had a negative effect on GPS values, which did not significantly differ amongst the different patient groups. However, an offset of the GPS regression line was found, which was mostly dependent on the basic disease. Surprisingly, spastic patients, who have reduced strength and additionally spasticity in clinical examination, and flaccid neurologic patients showed the same offset. Patients with additional lack of trunk control (Tetraplegia) showed the largest offset. CONCLUSION Gait kinematics grossly depend on muscle strength. This was seen in patients with very different pathologies. Nevertheless, optimal correction of biomechanics and muscle strength may still not lead to a normal gait, especially in that of neurologic patients. The basic disease itself has an additional effect on gait deviations expressed as a GPS-offset of the linear regression line.

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.

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.