Evaluating Assumptions for Least Squares Analysis Using the General Linear Model: A Guide for the Pharmaceutical Industry Statistician

Abstract

A review of graphical and test based methods for evaluating assumptions underlying the use of least squares analysis with the general linear model is presented along with some discussion of robustness. Alternative analyses are described for situations where there is evidence that the assumptions are not reasonable. Evaluation of the assumptions is illustrated through the use of an example from a clinical trial used for US registration purposes. It is recommended that: (1) most assumptions required for the least squares analysis of data using the general linear model can be judged using residuals graphically without the need for formal testing, (2) it is more important to normalize data or to use nonparametric methods when there is heterogeneous variance between treatment groups, and (3) nonparametric analyses can be used to demonstrate robustness of results and that it is best to specify these analyses prior to unblinding.     

Machine learning for predicting levetiracetam treatment response in temporal lobe epilepsy

ObjectiveTo determine the predictive power for seizure-freedom of 19-channels EEG, measured both before and after three months the initiation of the use of Levetiracetam (LEV), in a cohort of people after a new diagnosis of temporal-lobe epilepsy (TLE) using a machine-learning approach.MethodsTwenty-three individuals with TLE were examined. We dichotomized clinical outcome into seizure-free (SF) and non-seizure-free (NSF) after two years of LEV. EEG effective power in different frequency bands was compared using baseline EEG (T0) and the EEG after three months of LEV therapy (T1) between SF and NSF patients. Partial Least Square (PLS) analysis was used to test and validate the prediction of the model for clinical outcome.ResultsA total of 152 features were extracted from the EEG recordings. When considering only the features calculated at T1, a predictive power for seizure-freedom (AUC = 0.750) was obtained. When employing both T0 and T1 features, an AUC = 0.800 was obtained.ConclusionsThis study provides a proof-of-concept pipeline for predicting the clinical response to anti-seizure medications in people with epilepsy.SignificanceFuture studies may benefit from the pipeline proposed in this study in order to develop a model that can match each patient to the most effective anti-seizure medication.     

Least squares for diffusion tensor estimation revisited: propagation of uncertainty with Rician and non-Rician signals

Least Squares (LS) and its minimum variance counterpart, Weighted Least Squares (WLS), have become very popular when estimating the Diffusion Tensor (DT), to the point that they are the standard in most of the existing software for diffusion MRI. They are based on the linearization of the Stejskal-Tanner equation by means of the logarithmic compression of the diffusion signal. Due to the Rician nature of noise in traditional systems, a certain bias in the estimation is known to exist. This artifact has been made patent through some experimental set-ups, but it is not clear how the distortion translates in the reconstructed DT, and how important it is when compared to the other source of error contributing to the Mean Squared Error (MSE) in the estimate, i.e. the variance. In this paper we propose the analytical characterization of log-Rician noise and its propagation to the components of the DT through power series expansions. We conclude that even in highly noisy scenarios the bias for log-Rician signals remains moderate when compared to the corresponding variance. Yet, with the advent of Parallel Imaging (pMRI), the Rician model is not always valid. We make our analysis extensive to a number of modern acquisition techniques through the study of a more general Non Central-Chi (nc-χ) model. Since WLS techniques were initially designed bearing in mind Rician noise, it is not clear whether or not they still apply to pMRI. An important finding in our work is that the common implementation of WLS is nearly optimal when nc-χ noise is considered. Unfortunately, the bias in the estimation becomes far more important in this case, to the point that it may nearly overwhelm the variance in given situations. Furthermore, we evidence that such bias cannot be removed by increasing the number of acquired gradient directions. A number of experiments have been conducted that corroborate our analytical findings, while in vivo data have been used to test the actual relevance of the bias in the estimation.     

基于小波变换的最佳融合算法

目的：实现图像的最大融合,增强隐藏图像的抗攻击能力。方法：用最小二乘原理得到与图像有关的置乱变换,提高算法的融合度。将融合因子与置乱操作所用矩阵及迭代次数作为密钥,增加算法的安全性。结果：实验证明该算法使图像的融合因子和融合度得到较大提高。结论：可广泛应用于电子图像的版权保护和加密信息的网络安全传输。     

Discrepancies between vertebral bone density values: the least dense vertebra

Vertebral bone mineral density (BMD) measurements by DXA are considered reliable indicators of local fracture risk in the absence of radiographic deformities. The clinical evaluation of one individual vertebra presenting a BMD value significantly less than the others is attempted in this study. For a period of 30 months, BMD measurements of L1–L4 vertebrae and femoral neck (FN) were performed by DXA in 817 postmenopausal women, aged under 65 years, with a BMI less than 33 kg/m². In 204 (25%) of these women (group A), the least dense vertebra (LDV) presented a BMD value lower than 92.4% from the immediate denser vertebra. The remaining 613 women comprised group B. Women with X-ray proven vertebral degenerative lesions or deformities were excluded from the study. Among the four measured vertebrae, L1 was the most frequent LDV (47%), whilst L3 was the most rare (2%). Absolute and age-adjusted BMD values of L1–L4 and FN, as well as the proportions of osteopenic or osteoporotic women, did not differ significantly between the two groups. A significant positive correlation was observed between either L1–L4 or LDV and FN BMD values in both groups, but stepwise multiple regression analysis revealed that in group A the LDV did not participate in the model explaining the variability of the FN BMD values. In group B, the least dense vertebra was the only variable participating in the respective model (adjusted-R² = 37.7%). It is concluded that in a significant proportion of relatively young postmenopausal women, a wide variance of BMD values exists between individual vertebral BMD values without radiographic background. L1 was the most frequent LDV and L3 the most rare. In such cases, the evaluation of the least dense vertebra seems to offer an alternative estimation of vertebral bone mass, instead of mean L1–L4.     

Decreased T-cell mediated hepatic injury in concanavalin A-treated PLRP2-deficient mice

Concanavalin A (Con A) activates innate immunity and causes liver damage mediated by cytotoxic T lymphocytes (CTL) in mice. The Pancreatic lipase-related protein 2 (PLRP2) is induced by interleukin (IL)-4 in vitro in CTLs and associated with CTL functions. We examined the role of PLRP2 in a mouse model of Con A-induced T cell-mediated hepatitis. PLRP2-knockout and wild-type (WT) mice were inoculated with 20 mg/kg Con A. Mice lacking PLRP2 reduced Con A-induced hepatitis, which was manifested by a decrease in serum aminotransferase and histopathological assessment. The expression and secretion of cytokines including tumor necrosis factor-alpha (TNF-α), interferon (IFN)-γ, IL-6, and IL-1β were suppressed in Con A-treated PLRP2-knockout mice. In PLRP2 knockout mice, Con A-induced liver chemokines and adhesion molecules (such as MIP-1α, MIP-1β, ICAM-1 and MCP-1) were also down regulated. In the WT liver treated with Con A, the number of T cells (CD4⁺ and CD8⁺) and macrophages (CD11b⁺ F4/80⁺) increased significantly, while the lack of PLRP2 reduced the number of T cells in the liver, but had no effect on macrophages. The shift of the metabolic profiles was impaired in Con A-treated PLRP2-knockout mice compared to WT mice. In conclusion, these results indicate that PLRP2 deficiency reduces T-cell mediated Con A-induced hepatitis, and suggest PLRP2 is a potential target of anti-inflammatory and immunomodulatory drugs to treat immune-mediated hepatitis.     

Fast Clustered Radial Basis Function Network as an adaptive predictive controller

This paper presents a novel artificial neural network with the Radial Basis Function (RBF) as an activation function of neurons and clustered neurons in the hidden layer which has a high learning speed, thus it is called Fast Clustered Radial Basis Function Network (FCRBFN). The weights of the network are determined by solving a number of linear equation systems. In addition, new training data can be given to the network on-line and the re-training is done at high speed using the Least Squares method. In order to test the validity of the FCRBFN, it is applied to 4 classical regression applications, and also used to build the functional adaptive predictive controller. Experimental results show that, compared with other methods, the FCRBFN with a small amount of hidden neurons could achieve good or better regression precision and generalization, as well as adaptive ability at a much faster learning speed.     

Clinical feasibility tests on a novel optical on-line blood monitoring sensor for cardiopulmonary systems

An on-line determination of the oxygen saturation and hematocrit (Hct) in cardiopulmonary systems is important for control of the oxygen supply to the body and the functionality of the oxygenation systems. A novel on-line spatially resolving sensor was investigated. Diffuse reflectance of circulating blood at 700 and 810 nm wavelength was detected at different distances from the light source. The sensor was connected to the venous side of an extracorporeal circulation unit. Blood samples were taken for reference measurement after every reflectance measurement. The 72 measurements obtained for 9 patients during heart lung surgery were processed by the “partial least squares regression”. These measurements, recorded during surgery, ranged between 15% and 31% for Hct and between 69% and 95% for oxygen saturation (SatO₂). Using the “leave-one-out” validation method, values for Hct and SatO₂ were determined with a predictive root mean square error (PRMSE) of 0.8% and 2.2%, respectively. No correlations were established between differences in predicted and reference values of the determined blood parameters and the parameters Hct, SatO₂, patient, blood flow, temperature or time of measurement. A cross validation with half the measurements has shown that the Hct and SatO₂ can be predicted with a PRMSE of 2.2% in both cases. As the accuracy achieved exceeds that of existing systems, this approach could provide a promising method for on-line blood monitoring of cardiopulmonary systems.