A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

We propose a likelihood ratio test ( LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrapbased approach. LRT is shown to be significantly faster and statistically powerful even within non- Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided.

Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

Improved testing inference in mixed linear models

Mixed linear models are commonly used in repeated measures studies. They account for the dependence amongst observations obtained from the same experimental unit. Often, the number of observations is small, and it is thus important to use inference strategies that incorporate small sample corrections. In this paper, we develop modified versions of the likelihood ratio test for fixed effects inference in mixed linear models. In particular, we derive a Bartlett correction to such a test, and also to a test obtained from a modified profile likelihood function. Our results generalize those in [Zucker, D.M., Lieberman, O., Manor, O., 2000. Improved small sample inference in the mixed linear model: Bartlett correction and adjusted likelihood. Journal of the Royal Statistical Society B, 62,827-838] by allowing the parameter of interest to be vector-valued. Additionally, our Bartlett corrections allow for random effects nonlinear covariance matrix structure. We report simulation results which show that the proposed tests display superior finite sample behavior relative to the standard likelihood ratio test. An application is also presented and discussed. (C) 2008 Elsevier B.V. All rights reserved.

Correction to “The Importance of Convexity in Learning With Squared Loss” [Sep 98 1974-1980]

The paper "the importance of convexity in learning with squared loss" gave a lower bound on the sample complexity of learning with quadratic loss using a nonconvex function class. The proof contains an error. We show that the lower bound is true under a stronger condition that holds for many cases of interest.

Three Bartlett-type corrections for score statistics in symmetric nonlinear regression models

We present simple matrix formulae for corrected score statistics in symmetric nonlinear regression models. The corrected score statistics follow more closely a chi (2) distribution than the classical score statistic. Our simulation results indicate that the corrected score tests display smaller size distortions than the original score test. We also compare the sizes and the powers of the corrected score tests with bootstrap-based score tests.

Radiographic outcomes over time after endoscopic anterior scoliosis correction

A prospective, consecutive series of 106 patients receiving endoscopic anterior scoliosis correction. The aim was to analyse changes in radiographic parameters and rib hump in the two years following surgery. Endoscopic anterior scoliosis correction is a level sparing approach, therefore it is important to assess the amount of decompensation which occurs after surgery. All patients received a single anterior rod and vertebral body screws using a standard compression technique. Cleared disc spaces were packed with either mulched femoral head allograft or rib head/iliac crest autograft. Radiographic parameters (major, instrumented, minor Cobb, T5-T12 kyphosis) and rib hump were measured at 2,6,12 and 24 months after surgery. Paired t-tests and Wilcoxon signed ranks tests were used to assess the statistical significant of changes between adjacent time intervals.----- Results: Mean loss of major curve correction from 2 to 24 months after surgery was 4 degrees. Mean loss of rib hump correction was 1.4 degrees. Mean sagittal kyphosis increased from 27 degrees at 2 months to 30.6 degrees at 24 months. Rod fractures and screw-related complications resulted in several degrees less correction than patients without complications, but overall there was no clinically significant decompensation following complications. The study concluded that there are small changes in deformity measures after endoscopic anterior scoliosis surgery, which are statistically significant but not clinically significant.

The anatomical and biomechanical consequences of anterior vertebral stapling for the fusionless correction of scoliosis

Fusionless scoliosis surgery is an emerging treatment for idiopathic scoliosis as it offers theoretical advantages over current forms of treatment. Anterior vertebral stapling using a nitinol staple is one such treatment. Despite increasing interest in this technique, little is known about the effects on the spine following insertion, or the mechanism of action of the staple. The aims of this study were threefold; (1) to measure changes in the bending stiffness of a single motion segment following staple insertion, (2) to describe the forces that occur within the staple during spinal movement, and (3) to describe the anatomical changes that occur following staple insertion. Results suggest that staple insertion consistently decreased stiffness in all directions of motion. An explanation for the finding may be found in the outcomes of the strain gauge testing and micro-CT scan. The strain gauge testing showed that once inserted, the staple tips applied a baseline compressive force to the surrounding trabecular bone and vertebral end-plate. This finding would be consistent with the current belief that the clinical effect of the staples is via unilateral compression of the physis. Interestingly however, as each specimen progressed through the five cycles of each test, the baseline load on the staple tips gradually decreased, implying that the force at the staple tip-bone interface was decreasing. We believe that this was likely occurring as a result of structural damage to the trabecular bone and vertebral end-plate by the staple effectively causing ‘loosening’ of the staple. This hypothesis is further supported by the findings of the micro-CT scan. The pictures depict significant trabecular bone and physeal injury around the staple blades. These results suggest that the current hypothesis that stapling modulates growth through physeal compression may be incorrect, but rather the effect occurs through mechanical disruption of the vertebral growth plate.

Effect of bone graft type on fusion rates following endoscopic anterior scoliosis correction

Bone graft is generally considered fundamental in achieving solid fusion in scoliosis correction and pseudarthrosis following instrumentation may predispose to implant failure. In endoscopic anterior-instrumented scoliosis surgery, autologous rib or iliac crest graft has been utilised traditionally but both techniques increase operative duration and cause donor site morbidity. Allograft bone and bone- morphogenetic-protein alternatives may improve fusion rates but this remains controversial. This study's objective was to compare two-year postoperative fusion rates in a series of patients who underwent endoscopic anterior instrumentation for thoracic scoliosis utilising various bone graft types. Significantly better rates of fusion occurred in endoscopic anterior instrumented scoliosis correction using femoral allograft compared to autologous rib-heads and iliac crest graft. This may be partly explained by the difficulty obtaining sufficient quantities of autologous graft. Lower fusion rates in the autologous graft group appeared to predispose to rod fracture although the clinical consequence of implant failure is uncertain.

The relationship between deformity correction and clinical outcomes after thoracoscopic scoliosis surgery

Surgical treatment of scoliosis is quantitatively assessed in the clinic using radiographic measures of deformity correction, as well as the rib hump, but it is important to understand the extent to which these quantitative measures correlate with self-reported improvements in patients’ quality of life following surgery. The purpose of this prospective study was to evaluate the relationship between clinical outcomes of thoracoscopic anterior scoliosis surgery and deformity correction using the Scoliosis Research Society questionnaire (SRS-24). Patients undergoing thoracoscopic anterior scoliosis correction report good SRS scores which are comparable to those reported in previous studies for both open and thoracoscopic scoliosis correction procedures. Major Cobb correction is a significant predictor of patient satisfaction when comparing subgroups of patients with the highest and lowest major curve corrections.

The measurement of applied forces during anterior single rod correction of adolescent idiopathic scoliosis

Adolescent idiopathic scoliosis (AIS) is the most common form of spinal deformity in paediatrics, prevalent in approximately 2-4% of the general population. While it is a complex three-dimensional deformity, it is clinically characterised by an abnormal lateral curvature of the spine. The treatment for severe deformity is surgical correction with the use of structural implants. Anterior single rod correction employs a solid rod connected to the anterior spine via vertebral body screws. Correction is achieved by applying compression between adjacent vertebral body screws, before locking each screw onto the rod. Biomechanical complication rates have been reported as high as 20.8%, and include rod breakage, screw pull-out and loss of correction. Currently, the corrective forces applied to the spine are unknown. These forces are important variables to consider in understanding the biomechanics of scoliosis correction. The purpose of this study was to measure these forces intra-operatively during anterior single rod AIS correction.

The effect of bone graft type on fusion rates following anterior thoracoscopic scoliosis correction

Bone graft is generally considered fundamental in achieving solid fusion in scoliosis correction and pseudarthrosis following instrumentation may predispose to implant failure. In thoracoscopic anterior-instrumented scoliosis surgery, autologous rib or iliac crest graft has been utilised traditionally but both techniques increase operative duration and cause donor site morbidity. Allograft bone and bone morphogenetic protein (BMP) alternatives may improve fusion rates but this remains controversial. This study's objective was to compare two-year postoperative fusion rates in a series of patients who underwent thoracoscopic anterior instrumentation for thoracic scoliosis utilising various bone graft types.