The mode of a distribution provides an important summary of data and is often estimated based on some non-parametric kernel density estimator. This article develops a new data analysis tool called modal linear regression in order to explore highdimensional data. Modal linear regression models the conditional mode of a response Y given a set of predictors x as a linear function of x. Modal linear regression differs from standard linear regression in that standard linear regression models the conditional mean (as opposed to mode) of Y as a linear function of x. We propose an Expectation-Maximization algorithm in order to estimate the regression coefficients of modal linear regression. We also provide asymptotic properties for the proposed estimator without the symmetric assumption of the error density. Our empirical studies with simulated data and real data demonstrate that the proposed modal regression gives shorter predictive intervals than mean linear regression, median linear regression, and MM-estimators.
The principal impetus for the fabrication of functional nanotube materials comes from the promise of discovering unique structure-dependant properties and superior performance that are derived from their intrinsic nanotubular architecture. [1][2][3][4] 1D TiO 2 nanotube arrays prepared by the electrochemical anodization of self-organized porous structures on Ti foil [5][6][7] have attracted great research interest in recent years owing to their peculiar architecture, remarkable properties, and potential for wide-ranging applications. Uniform TiO 2 nanotubes are quite remarkably different in structure from other forms of TiO 2 , and are highly ordered, high-aspect-ratio structures with nanocrystalline walls perpendicular to electrically conductive Ti substrates, thereby naturally forming a Schottky-type contact. Moreover, these structures can be directly used as electrodes for photoelectric applications since the size of the nanotubes is very precisely controllable. The technological applications of TiO 2 nanotube arrays are still at an early stage, but these remarkable structures have already been shown to be very promising for applications in sensing, [8] catalysis, [9] photovoltaics, [10] photoelectrolysis, [11] and nanotemplating. [12] The electrical resistance of the TiO 2 nanotubes changes by almost 7 orders of magnitude upon exposure to 1000 ppm H 2 , [13] the largest ever reported sensitivity of a material to a gas. Furthermore, the H 2 evolution rate of TiO 2 nanotube arrays has been reported to be 76 mL hw -1 , [11] which is the highest reported H 2 generation rate for any oxide system upon photoelectrolysis. TiO 2 nanotube arrays have also attracted great interest for enhancing the photocatalytic degradation of various organics, which makes them promising materials for the detection of pollutants. Given the increasing quantities of pollutants that are being dumped into water bodies, environmental monitoring and control have become issues of global concern. Chemical oxygen demand (COD) is one of the most widely used metrics in the field of water-quality analysis in many countries, and is frequently used as an important index for controlling the operation of wastewater treatment plants, wastewater effluent monitoring, and taxation of wastewater pollution. [14] or ultrasound-assisted oxidation.[15]Other alternative assays have also been developed such as electrocatalytic determination using PbO 2 or Cu sensors in thin-cell reactors, [16,17] and photocatalytic and photoelectrocatalytic methods based on TiO 2 nanomaterial sensors. [18,19] However, all these modified K 2 Cr 2 O 7 methods are still plagued by the secondary pollution caused by highly toxic Cr(VI) ions, and moreover, the PbO 2 sensors pose the risk of the potential release of hazardous Pb during the preparation and disposal of the active material of the sensors. As compared to traditional analytical methods, photoelectrocatalytic approaches are more promising because of the superior oxidative abilities of illuminated TiO 2 . Furthermore, TiO 2 ...
BackgroundFalls pose major health problems to the middle-aged and older adults and may potentially lead to various levels of injuries. Sleep duration and disturbances have been shown to be associated with falls in literature; however, studies of the joint and distinct effects of those sleep problems are still sparse. To fill this gap, we aimed to determine the association between sleep duration, sleep disturbances and falls among middle-aged and older adults in China controlling for psychosocial, lifestyle, socio-demographical factors and comorbidity.MethodsData were derived from the China Health and Retirement Longitudinal Study (CHARLS) based on multi-stage sampling designs, with respondents aged 50 and older. Associations were evaluated by using multiple logistic regression adjusting for confounders and complex survey design. To further determine if the association of sleep duration/disturbance and falls depends on age groups, the study data were divided into two samples (age 50–64 vs. age 65+) and comparison was made between the two age groups.ResultsOf the 12,759 respondents, 2172 (17%) had falls within the last 2 years. Our findings indicated that the participants who had nighttime sleep duration ≤5 were more likely to report falls than those who had nighttime sleep duration ≥6 h; whereas no association between nighttime sleep duration > 8 h and falls. Participants having sleep disturbances 1–2 days, or 3–4 days, and 5–7 days per week were also more likely to report falls than those who had no sleep disturbance. The nap sleep duration was not significantly associated with falls. Although the combined sample found both sleep duration and sleep disturbance to be strongly associated with falls after adjusting for various confounders, sleep disturbance was not significantly related to falls among participants aged 65 + .ConclusionsOur study suggested that there is an independent association between falls and short sleep duration and disturbed sleep among middle-aged and older adults in China. Findings underscore the need for evidence-based prevention and interventions targeting sleep duration and disturbance among this study population.
Looking at predictive accuracy is a traditional method for comparing models. A natural method for approximating out-of-sample predictive accuracy is leave-one-out crossvalidation (LOOCV) -we alternately hold out each case from a full data set and then train a Bayesian model using Markov chain Monte Carlo (MCMC) without the held-out; at last we evaluate the posterior predictive distribution of all cases with their actual observations. However, actual LOOCV is time-consuming. This paper introduces two methods, namely iIS and iWAIC, for approximating LOOCV with only Markov chain samples simulated from a posterior based on a full data set. iIS and iWAIC aim at improving the approximations given by importance sampling (IS) and WAIC in Bayesian models with possibly correlated latent variables. In iIS and iWAIC, we first integrate the predictive density over the distribution of the latent variables associated with the held-out without reference to its observation, then apply IS and WAIC approximations to the integrated predictive density. We compare iIS and iWAIC with other approximation methods in three kinds of models: finite mixture models, models with correlated spatial effects, and a random effect logistic regression model. Our empirical results show that iIS and iWAIC give substantially better approximates than non-integrated IS and WAIC and other methods.
Identification of effective biomarkers is crucial for monitoring the treatment and remission of colorectal cancer (CRC) and improving survival. It is particularly important to diagnose CRC before the tumor metastasizes (stage I–II disease) where possible, to provide the greatest opportunity for patient recovery. Here, we evaluated the clinical value of serum chemokine (C-X-C) ligand 7 (CXCL7) concentration as a biomarker for CRC diagnosis. An enzyme-linked immunosorbent assay was used to measure CXCL7 concentration in 560 serum samples from patients with CRC and controls. Logistic regression and receiver operating characteristic (ROC) curve analysis was used to assess the diagnostic efficacy and build mathematical diagnostic models. The concentration of CXCL7 in the CRC group was significantly higher than that in the control group (P < 0.001), with an area under the ROC curve (AUC) value of 0.862 [95% confidence interval (CI): 0.831–0.890]. Further, the AUC of a regression model including the markers carcinoembryonic antigen (CEA), carbohydrate antigen 19-9 (CA19-9), and carbohydrate antigen 125 (CA125), along with CXCL7, was 0.933 (95% CI: 0.909–0.952). For stage I–II tumors, CXCL7 had the highest AUC (0.823, 95% CI: 0.783–0.858) among the four individual biomarkers. The AUC value for combination model analysis of samples from patients with stage I–II tumors was 0.904 (95% CI: 0.872–0.930), with a sensitivity of 82.76% and a specificity of 87.14%, and an optimal cut-off value of 2.66. AUC values for application of the regression model in subgroup analysis were 0.947 (0.917–0.968) and 0.919 (0.874–0.951) for males and females, respectively. These results suggest that CXCL7 has potential as a serum diagnostic biomarker for detection of CRC. Importantly, the combination of CXCL7, CEA, CA125, and CA19-9 may facilitate diagnosis of CRC with relatively high sensitivity and specificity.Clinical Trial Registration Number: LS2017001.
Background: Examining residuals is a crucial step in statistical analysis to identify the discrepancies between models and data, and assess the overall model goodness-of-fit. In diagnosing normal linear regression models, both Pearson and deviance residuals are often used, which are equivalently and approximately standard normally distributed when the model fits the data adequately. However, when the response vari*able is discrete, these residuals are distributed far from normality and have nearly parallel curves according to the distinct discrete response values, imposing great challenges for visual inspection. Methods: Randomized quantile residuals (RQRs) were proposed in the literature by Dunn and Smyth (1996) to circumvent the problems in traditional residuals. However, this approach has not gained popularity partly due to the lack of investigation of its performance for count regression including zero-inflated models through simulation studies. Therefore, we assessed the normality of the RQRs and compared their performance with traditional residuals for diagnosing count regression models through a series of simulation studies. A real data analysis in health care utilization study for modeling the number of repeated emergency department visits was also presented. Results: Our results of the simulation studies demonstrated that RQRs have low type I error and great statistical power in comparisons to other residuals for detecting many forms of model misspecification for count regression models (non-linearity in covariate effect, over-dispersion, and zero inflation). Our real data analysis also showed that RQRs are effective in detecting misspecified distributional assumptions for count regression models. Conclusions: Our results for evaluating RQRs in comparison with traditional residuals provide further evidence on its advantages for diagnosing count regression models.
ObjectiveThe present study was designed to investigate the role of the chemokine CXCL7 in angiogenesis and explore its prognostic value in colorectal cancer (CRC).MethodsA total of 160 CRC patients who had undergone surgery were included in this study, and staged according to the guidelines of the AJCC, 7th Edition. Expression of CXCL7 and VEGF was detected by immunohistochemical (IHC) staining and divided into high and low expression subgroups. The correlation between CXCL7 and VEGF expression was evaluated by Spearman’s rank-correlation coefficient. Prognosis based on CXCL7 and VEGF was evaluated using the Cox proportional hazards regression model and a nomogram of 5-year overall survival (OS) time.ResultsCXCL7 was highly expressed in tumor tissues (65.63% vs 25.00% in paracancerous tissue, P < 0.001), as was VEGF. CXCL7 and VEGF expression correlated well with N and TNM stage cancers (all P < 0.001). Importantly, CXCL7 was positively correlated with VEGF expression in CRC tissues. CXCL7 was an independent predictor of poor OS of CRC patients (HR = 2.216, 95% CI: 1.069-4.593, P = 0.032), and co-expression of CXCL7 and VEGF of predicted poor OS of 56.96 months.ConclusionExpression of CXCL7 correlated with VEGF and was associated with poor clinical outcomes in CRC patients.
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