For hyperspectral compressed sensing method on linear mixed spectrum model

Compressive sensing (CS) has been employed to compress and store hyperspectral images (HSI) to transfer extensive data efficiently, and obtaining high-quality reconstructed images is crucial for subsequent applications. Model-based methods usually capture the priors of HSI, including sparsity, global and nonlocal low-rankness, nonlocal self-similarity and global correlation. However, it is challenging to reasonably integrate different regularizations in a united framework and exploit various priors mentioned to reconstruct high-quality images. In this paper, a tensor optimization model based on the low-rank coefficient tensor and global prior (LRCTGP) is proposed for HSI reconstruction. Complementary regularization terms are integrated into a united framework and effectively promote the reconstruction results. First, we apply the mode- tensor-matrix product to decompose the original HSI rather than employing the regularization to capture the spectral low-rankness and simultaneously constrain the original and feature HSI. Then, tensor ring decomposition is employed to constrain the coefficient tensor with fewer bands, which is more efficient in the low-rank approximation and has smaller calculation costs than applying it to the original HSI. Moreover, integrating BM3D as a regularizer is more efficient than other patch-based models. Finally, considering the smoothness and global correlation, spatial-spectral total variation (SSTV) is applied to compensate for the shortcomings after decomposing the original and feature HSI, which complements the overall structure and details of reconstructed images and improves the reconstruction quality. Alternating direction method of multipliers (ADMM) is used to optimize the proposed model. Experimental results of the LRCTGP model on different HSI datasets are better than existing state-of-the-art approaches, which proves the superiority.

A simulation study was conducted to assess Type I error and statistical power of linear mixed models, generalized linear mixed models, and linear quantile mixed models for the analysis of longitudinal cytometry by time-of-flight data. Findings indicate that, while generalized linear mixed models have superior statistical power, they also suffer from inflated Type I error rates. Linear mixed models can have substantially lower statistical power than the other methods at larger effect sizes. While linear quantile mixed models have slightly lower statistical power at smaller effect sizes, they have intermediate statistical power at larger effect sizes and good Type I error control. Taken altogether, these results generally recommend the use of linear quantile mixed models for longitudinal datasets such as for cytometry by time-of-flight data, although linear mixed models may be slightly more useful at small effect sizes and sample sizes.

A central point of disagreement, in certain long-standing discussions about a particular whaling dataset in the Scientific Committee of the International Whaling Commission, has directly involved model selection issues for linear mixed effect models. The biological question under discussion is associated with a clearly defined parameter of primary interest, a focus parameter, which makes model selection with the Focused Information Criterion (FIC) more appropriate than other selection methods. Since the existing FIC methodology has not covered the case of linear mixed effects models, this article sets up the required framework and develops the necessary formulae for the relevant FIC. Our new criterion requires the asymptotic distribution of estimators derived for a given candidate linear mixed model but with behaviour examined under a wider linear mixed model. These results, needed here to build our FIC, also have independent interest.

Earlier studies to assess the effects of risk factors on child nutritional status in Bangladesh have used conventional regression models that are inadequate to capture a complete scenario of effects. Therefore, this study aimed to evaluate the heterogeneous effects of factors at different points of conditional height-for-age Z-score (HAZ) distribution accounting for cluster-level variation using linear quantile mixed model (LQMM) and to compare them with a linear mixed model (LMM). In addition, an unconditional quantile model (UQM) was used to measure the effect of factors on the unconditional (marginal) HAZ distribution. A total of 6340 children aged 0–59 months extracted from the 2014 Bangladesh Demographic and Health Survey. Different factors – maternal characteristics (age, occupation, nutritional status, parity, birth interval), parental education, child age, breastfeeding status, and morbidity had significant heterogeneous effects on HAZ distribution. For example, secondary or higher educated parents had substantial differential impacts on the lower tail and upper tail of the child HAZ distribution, which was masked by LMM estimate. Moreover, significant cluster-level variations found across all quantiles of child HAZ. During intervention design, heterogeneous effects of factors and cluster variation ought to consider addressing the undernutrition problem in Bangladesh.

Bootstrap is a widely applicable computational statistical method. The focus of this paper lies in developing a bootstrap method for linear mixed models under homoscedasticity violation (heteroscedasticity) in variance of errors. We assume that the form of heteroscedasticity is unknown. To generate bootstrap response data as close as possible to the actual response data, we transform the marginal residuals to ensure that the variance of the modified marginal residuals in bootstrap samples is an unbiased estimator for the variance of the response variable in the linear mixed models. The consistency is proved, implying that the parameter estimators by the proposed method are asymptotically unbiased. The simulations are conducted with varying error terms and sample sizes to show improvement of the proposed method in parameter estimation. The simulation results are compared to demonstrate that the proposed method outperforms the other considered approaches including the wild method in the heteroscedastic linear mixed models under small samples and performs competitively with the parametric method and both methods outperform the other considered methods in homoscedastic linear mixed models. The proposed bootstrap method is applied to squid data for illustration of its effectiveness.

We study model selection for clustered data, when the focus is on cluster specific inference. Such data are often modelled using random effects, and conditional Akaike information was proposed in Vaida & Blanchard (2005) and used to derive an information criterion under linear mixed models. Here we extend the approach to generalized linear and proportional hazards mixed models. Outside the normal linear mixed models, exact calculations are not available and we resort to asymptotic approximations. In the presence of nuisance parameters, a profile conditional Akaike information is proposed. Bootstrap methods are considered for their potential advantage in finite samples. Simulations show that the performance of the bootstrap and the analytic criteria are comparable, with bootstrap demonstrating some advantages for larger cluster sizes. The proposed criteria are applied to two cancer datasets to select models when the cluster-specific inference is of interest.

Article Figures and data Abstract eLife digest Introduction Results Discussion Materials and methods Data availability References Decision letter Author response Article and author information Metrics Abstract End-stage kidney disease (ESKD) patients are at high risk of severe COVID-19. We measured 436 circulating proteins in serial blood samples from hospitalised and non-hospitalised ESKD patients with COVID-19 (n = 256 samples from 55 patients). Comparison to 51 non-infected patients revealed 221 differentially expressed proteins, with consistent results in a separate subcohort of 46 COVID-19 patients. Two hundred and three proteins were associated with clinical severity, including IL6, markers of monocyte recruitment (e.g. CCL2, CCL7), neutrophil activation (e.g. proteinase-3), and epithelial injury (e.g. KRT19). Machine-learning identified predictors of severity including IL18BP, CTSD, GDF15, and KRT19. Survival analysis with joint models revealed 69 predictors of death. Longitudinal modelling with linear mixed models uncovered 32 proteins displaying different temporal profiles in severe versus non-severe disease, including integrins and adhesion molecules. These data implicate epithelial damage, innate immune activation, and leucocyte–endothelial interactions in the pathology of severe COVID-19 and provide a resource for identifying drug targets. eLife digest COVID-19 varies from a mild illness in some people to fatal disease in others. Patients with severe disease tend to be older and have underlying medical problems. People with kidney failure have a particularly high risk of developing severe or fatal COVID-19. Patients with severe COVID-19 have high levels of inflammation, causing damage to tissues around the body. Many drugs that target inflammation have already been developed for other diseases. Therefore, to repurpose existing drugs or design new treatments, it is important to determine which proteins drive inflammation in COVID-19. Here, Gisby, Clarke, Medjeral-Thomas et al. measured 436 proteins in the blood of patients with kidney failure and compared the levels between patients who had COVID-19 to those who did not. This revealed that patients with COVID-19 had increased levels of hundreds of proteins involved in inflammation and tissue injury. Using a combination of statistical and machine learning analyses, Gisby et al. probed the data for proteins that might predict a more severe disease progression. In total, over 200 proteins were linked to disease severity, and 69 with increased risk of death. Tracking how levels of blood proteins changed over time revealed further differences between mild and severe disease. Comparing this data with a similar study of COVID-19 in people without kidney failure showed many similarities. This suggests that the findings may apply to COVID-19 patients more generally. Identifying the proteins that are a cause of severe COVID-19 – rather than just correlated with it – is an important next step that could help to select new drugs for severe COVID-19. Introduction Coronavirus disease (COVID-19), caused by the SARS-CoV-2 virus, displays wide clinical heterogeneity from asymptomatic to fatal disease. Patients with severe disease exhibit marked inflammatory responses and immunopathology. The mechanisms underlying this remain incompletely characterised, and the key molecular mediators are yet to be determined. The first treatment shown to reduce mortality from COVID-19 in randomised trials was dexamethasone (Horby et al., 2020), a corticosteroid that has broad non-specific effects on the immune system. Even with corticosteroid treatment, mortality in severe COVID-19 remains significant. There is a wide armamentarium of existing drugs that target inflammation more selectively, providing potential repurposing opportunities for the treatment of COVID-19. Recently, the REMAP-CAP trial has demonstrated efficacy of anti-IL6 receptor blockade in patients admitted to intensive care units with severe disease (Gordon et al., 2021). In order to select the most promising agents for future trials, we urgently need to better understand the molecular drivers of severe disease. Proteins are the effector molecules of biology and the targets of most drugs. Therefore, proteomic profiling to identify the key mediators of severe disease provides a valuable tool for identifying and prioritising potential drug targets (Suhre et al., 2021). Risk factors for severe or fatal COVID-19 include age, male sex, non-European ancestry, obesity, diabetes mellitus, cardiovascular disease, and immunosuppression (Williamson et al., 2020). End-stage kidney disease (ESKD) is one of the strongest risk factors for severe COVID-19 (estimated hazard ratio for death 3.69) (Williamson et al., 2020), and ESKD patients hospitalised with COVID-19 have a mortality of approximately 30% (Docherty et al., 2020; Corbett et al., 2020; Ng et al., 2020; Valeri et al., 2020). ESKD patients have a high prevalence of vascular and cardiometabolic disease (e.g. hypertension, ischaemic heart disease, diabetes), either as a result of the underlying cause of their renal disease or as a consequence of renal failure. In addition, ESKD results in both relative immunosuppression and chronic low-grade inflammation, which may impact viral defence and the host inflammatory response. Here we performed proteomic profiling of serial blood samples of ESKD patients with COVID-19, leveraging the unique opportunity for longitudinal sampling in both the outpatient and inpatient settings afforded by a large multi-ethnic haemodialysis cohort (Figure 1a). These data revealed 221 proteins that are dysregulated in COVID-19 versus matched non-infected ESKD patients. Using linear mixed models, joint models, and machine learning, we identified proteins that are markers of COVID-19 severity and risk of death. Finally, we characterised the temporal dynamics of the blood proteomic response during COVID-19 infection in ESKD patients, uncovering 32 proteins that display altered trajectories in patients with severe versus non-severe disease. Figure 1 with 1 supplement see all Download asset Open asset Study design. (a) Schematic representing a summary of the patient cohorts, sampling, and the major analyses. Blue and red stick figures represent outpatients and hospitalised patients, respectively. (b) Timing of serial blood sampling in relation to clinical course of COVID-19 (subcohort A). Black asterisks indicate when samples were obtained. Three patients were already in hospital prior to COVID-19 diagnosis (indicated by red bars). Results We recruited 55 ESKD patients with COVID-19 (subcohort A; Table 1). All patients were receiving haemodialysis prior to acquiring COVID-19. Blood samples were taken as soon as feasible following COVID-19 diagnosis. At time of initial sample, 30 patients were outpatients attending haemodialysis sessions and 25 were hospitalised inpatients (see Materials and methods, Figure 1). Following the initial blood sample, serial sampling was performed for 51/55 patients. We also recruited 51 non-infected haemodialysis patients as ESKD controls, mirroring the age, sex, and ethnicity distribution of the COVID-19 cases (Figure 1—figure supplement 1a–c). We used the Olink proteomics platform to measure 436 proteins (Supplementary file 1a) in 256 plasma samples from the COVID-19 patients and the 51 control samples. The proteins measured consisted of five multiplex 'panels' focussed on proteins relevant to immuno-inflammation, cardiovascular, and cardiometabolic disease. The 436 proteins assayed showed strong enrichment for immune-related proteins (Supplementary file 1b). Table 1 Characteristics of subcohort A. COVID-19-positive ESKD patients (n = 55)ESKD controls (n = 51) OverallPeak severity mild or moderate (n = 28)Peak severity severe or critical (n = 27)Age Median (IQR)72.2 62.5–77.373.4 65.5–76.468.5 61.8–78.870.1 62.2–75.1Sex M F39 (70.9%) 16 (29.1%)18 (64.3%) 10 (35.7%)21 (77.8%) 6 (22.2%)36 (70.6%) 15 (29.4%)Ethnicity White Black South Asian Asian (other) Other16 (29.1%) 8 (14.5%) 18 (32.7%) 4 (7.3%) 9 (16.4%)5 (17.9%) 5 (17.9%) 10 (35.7%) 1 (3.6%) 7 (25.0%)11 (40.7%) 3 (11.1%) 8 (29.6%) 3 (11.1%) 2 (7.4%)13 (25.5%) 8 (15.7%) 20 (39.2%) 3 (5.9%) 7 (13.7%)Diabetes34 (61.8%)*16 (57.1%)18 (66.7%)24 (47.1%)*Current smoker1 (1.8%)1 (3.6%)00ESKD cause DN Genetic GN HTN/vascular Other Unknown29 (52.7%) 1 (1.8%) 3 (5.5%) 5 (9.1%) 8 (14.5%) 9 (16.4%)14 (50.0%) 1 (3.6%) 1 (3.6%) 3 (10.7%) 5 (17.9%) 4 (14.3%)15 (55.6%) 0 2 (7.4%) 2 (7.4%) 3 (11.1%) 5 (18.5%)20 (39.2%) 1 (2.0%) 9 (17.6%) 7 (13.7%) 4 (7.8%) 10 (19.6%)Hospitalisation due to COVID-19†33 (60%)6 (21.4%)27 (100%)N/AFatal COVID-199 (16.3%)0 (0%)9 (33.3%)N/A DN = diabetic nephropathy. GN = glomerulonephritis. HTN = hypertension. IQR = inter-quartile range. 'South Asian' represents individuals with Indian, Pakistani, or Bangladeshi ancestry. Subsets defined according to peak WHO severity over the course of the illness. N/A = not applicable. *One patient had type 1 diabetes, the remainder type 2. †3 patients were hospitalised prior to COVID-19 diagnosis. 8 patients diagnosed with COVID-19 as outpatients subsequently deteriorated were hospitalised. In addition, we performed the Olink proteomic assays in 52 serum samples from a separate set of 46 COVID-19-positive ESKD patients (subcohort B) and 11 serum samples from ESKD COVID-19-negative controls (a subset of the controls described above). For the large majority of patients in subcohort B, only a single timepoint was available. A higher proportion of these patients (41/46, 89%) were hospitalised and had severe disease (Table 2) than in subcohort A (Figure 1, Table 1). Table 2 Characteristics of subcohort B. COVID-19-positive ESKD patients (n = 46)COVID-19-negative ESKD controls (n = 11)*Age Median (IQR)64.3 60.3–73.071.6 (61.7–73.9)Sex M F32 (69.6%) 14 (30.4%)8 (72.3%) 3 (27.3%)Ethnicity White Black South Asian Asian (other) Other11 (23.9%) 8 (17.4%) 12 (26.1%) 7 (15.2%) 8 (17.4%)3 (27.3%) 3 (27.3%) 3 (27.3%) 0 2 (18.2%)Diabetes29 (63.0%)6 (54.5%)Current smoker2 (4.3%)0 (%)ESKD cause DN Genetic GN HTN/vascular Other Unknown19 (41.3%) 1 (2.2%) 7 (15.2%) 3 (6.5%) 3 (6.5%) 13 (28.3%)5 (45.5%) 0 1 (9.1%) 1 (9.1%) 2 (18.2%) 2 (18.2%)Hospitalisation due to COVID-1941 (89.1%)N/ASevere or critical COVID-1933 (71.7%)N/AFatal COVID-199 (19.6%)N/A DN = diabetic nephropathy. GN = glomerulonephritis. HTN = hypertension. IQR = inter-quartile range. 'South Asian' represents individuals with Indian, Pakistani, or Bangladeshi ancestry. Subsets defined according to peak WHO severity over the course of the illness. N/A = not applicable. *These 11 controls are a subset of the control patients used in subcohort A. Proteomic differences between COVID-19-positive and -negative ESKD patients Principal component analysis (PCA) of proteomic data from subcohort A demonstrated differences between samples from COVID-19-positive cases and controls, although the two groups did not separate into discrete clusters (Figure 2a,b). To examine the effects of COVID-19 on the plasma proteome, we performed a differential expression analysis in subcohort A between COVID-19 cases (n = 256 samples passing quality control [QC] from 55 patients) and non-infected ESKD controls (n = 51) using linear mixed models, which account for serial samples from the same individual (see Materials and methods). This revealed 221 proteins associated with COVID-19 (5% false discovery rate, FDR); the vast majority were upregulated, with only 40 downregulated (Figure 3a, Supplementary file 1c). In order to provide a succinct and standardised nomenclature, we report proteins by the symbols of the genes encoding them (see Supplementary file 1a for a mapping of symbols to full protein names). The most strongly upregulated proteins (in terms of fold change) were DDX58, CCL7, IL6, CXCL11, KRT19, and CXCL10, and the most strongly downregulated were SERPINA5, CCL16, FABP2, PON3, ITGA11, and MMP12 (Figure 3—figure supplement 1). Notably, many of the upregulated proteins were chemotaxins. Figure 2 with 2 supplements see all Download asset Open asset Principal component analysis. PC = principal component. Each point represents a sample. Colouring indicates COVID-19 status. The directions and relative sizes of the six largest PC loadings are plotted as arrows (middle column). (a, b) Subcohort A. Due to serial sampling, there are multiple samples for most patients. The proportion of variance explained in subcohort A by each PC is shown in parentheses on the axis labels. (c, d) Subcohort B. Samples are projected into the PCA coordinates from subcohort A. Figure 3 with 4 supplements see all Download asset Open asset Identification of dysregulated proteins. (a) Proteins upregulated (red) or downregulated (blue) in COVID-19-positive patients versus COVID-19-negative ESKD patients n = 256 plasma samples from 55 COVID-19-positive patients, versus n = 51 ESKD controls (one sample per control patient). (b) Proteins associated with disease severity associations of protein levels against WHO severity score at the time of sampling. Linear gradient indicates the effect size. A positive effect size (red) indicates that an increase in protein level is associated with increasing disease severity and a negative gradient (blue) the opposite. n = 256 plasma samples from 55 COVID-19-positive patients. For (a, b), p-values from linear mixed models after Benjamini–Hochberg adjustment; significance threshold = 5% FDR; dark-grey = non-significant. (c) Heatmap showing protein levels for selected proteins with strong associations with severity. Each column represents a sample (n = 256 COVID-19 samples and 51 non-infected samples). Each row represents a protein. Proteins are annotated using the symbol of their encoding gene. For the purposes of legibility, not all significantly associated proteins are shown; the heatmap is limited to the 17% most up- or downregulated proteins (by effect size) of those with a significant association. Proteins are ordered by hierarchical clustering. Samples are ordered by WHO severity at the time of blood sample ('Severity'). 'Overall course' indicates the peak WHO severity over the course of the illness. We observed that a high proportion of the measured proteins were associated with COVID-19. Given the highly targeted nature of the Olink panels that we used (enriched for immune and inflammation-related proteins), this was not surprising. Nevertheless, to ensure that the Benjamini–Hochberg adjustment of p-values was controlling the FDR at the 5% level, we performed two additional analyses (see Materials and methods). First, we estimated the FDR using an alternative method (the plug-in procedure ; Hastie et al., 2001); this confirmed appropriate FDR control. Second, we used permutation to estimate the distribution of the number of proteins expected to be declared significant under the null hypothesis of no association between any proteins and COVID-19. This showed that the probability of observing the number of differentially abundant proteins we identified was highly unlikely under the null (empirical p<1×10−5; Figure 3—figure supplement 2). Although our COVID-19-negative controls were well matched in terms of age, sex, and ethnicity (Figure 1—figure supplement 1a–c), perfect matching of comorbidities was not feasible in the context of the healthcare emergency at the time of patient recruitment. There was a higher prevalence of diabetes in the COVID-19 cases compared to the controls (61.8% versus 47.1%, respectively; Table 1). To evaluate whether differing rates of diabetes had impacted the proteins identified as differentially abundant between cases and controls, we performed a sensitivity analysis adding diabetes as an additional covariate in the linear mixed model. This did not materially affect our findings; estimated effect sizes and –log10 p-values from models with and without the inclusion of diabetes were highly correlated (Pearson r > 0.99, and r = 0.95, respectively; Figure 3—figure supplement 3a,b). Full results from both models are shown in Supplementary file 1c. Similarly, there were also differences in the underlying cause of ESKD in cases compared to controls (Table 1). We therefore performed a further sensitivity analysis adjusting for underlying cause of renal failure. This did not make any meaningful difference to our results (Figure 3—figure supplement 3c,d, Supplementary file 1c). We also considered the possibility that timing of haemodialysis might affect the plasma proteome. To minimise the impact of this, all samples were taken prior to haemodialysis. For the large majority (86.6%) of samples, the most recent haemodialysis was between 48 and 72 hr prior to blood draw. This consistency in timing of blood sampling reduces the potential for impact of this issue. Nevertheless, to evaluate whether timing of haemodialysis might have impacted our results, we performed a sensitivity analysis including time from last haemodialysis as a covariate. Our results were not materially affected by this, with −log10 p-values and estimated effect sizes very highly correlated with those obtained without inclusion of this covariate (Pearson r > 0.99 for effect size estimates and for −log10 p-values; Figure 3—figure supplement 4a,b, Supplementary file 1c). We used the smaller subcohort B (n = 52 serum samples from 46 patients with COVID-19; see Materials and methods) for validation. We first projected the data from subcohort B into the PCA space of subcohort A to examine how well the separation of cases and controls in the PCA space replicated (see Materials and methods). This revealed clearer separation of infected and non-infected patients than in subcohort A (Figure 2c,d), perhaps reflecting the higher proportion of hospitalised patients (41 of 46 patients) in subcohort B (Table 2). We next performed differential abundance analysis in subcohort B and found 201 proteins that were dysregulated in cases versus controls (5% FDR) (Supplementary file 1c). Of the 221 differentially abundant proteins from subcohort A, 150 (69.7%) were also identified in subcohort B at 5% FDR (Figure 4a). Effect sizes in each dataset showed a strong correlation (r = 0.80, Figure 4b). This demonstrates that our findings are highly reproducible despite differences in sample sizes and blood materials (plasma versus serum in subcohorts A and B, respectively). Figure 4 with 1 supplement see all Download asset Open asset Validation. (a) Overlap between the significant associations in the differential abundance analysis between ESKD patients with and without COVID-19 in subcohorts A and B. 5% FDR was used as the significance threshold in both analyses. (b) Comparison of estimated effect sizes for all 436 proteins in the differential abundance analyses (COVID-19 positive versus negative) in subcohort A and B. Each point represents a protein. Pearson's r is shown. Differential abundance analyses were performed using linear mixed models. Subcohort A analysis (plasma samples): 256 samples from 55 COVID-19 patients versus 51 non-infected patient samples (single time-point). Subcohort B (serum samples): 52 samples from 55 COVID-19 patients and 11 non-infected patient samples (single timepoint). Proteins associated with COVID-19 severity Examination of the principal components plot labelling samples by clinical severity at the time of sampling (defined by WHO severity scores, graded as mild, moderate, severe, or critical) demonstrated a gradient of COVID-19 severity, best captured by principal components 1 and 3 (Figure 2—figure supplement 1a). To determine the proteomic effects of COVID-19 severity, we tested for associations between proteins and WHO severity score at the time of blood sampling, using linear mixed models with severity encoded as an ordinal predictor (see Materials and methods). This analysis revealed 203 proteins associated with severity (Figure 3b, Supplementary file 1d). The majority of these were upregulated in more severe disease, with only 42 downregulated. A sensitivity analysis adjusting for time since last haemodialysis made no significant impact on our results (Figure 3—figure supplement 4c,d, Supplementary file 1d). Consistent with previous reports, we found that severe COVID-19 was characterised by elevated IL6. In addition, we observed a signature of upregulated monocyte chemokines (e.g. CCL2, CCL7, CXCL10), neutrophil activation and degranulation (e.g. PRTN3, MPO), and epithelial injury (e.g. KRT19, AREG, PSIP1, GRN). (Figures 3b,c and 5). SERPINA5 and leptin showed the greatest downregulation as COVID-19 severity increased (Figure 3b,c). Figure 5 Download asset Open asset proteins strongly associated with COVID-19 severity. showing distribution of plasma protein levels according to COVID-19 at the time of blood draw. indicate and inter-quartile range. n = 256 samples from 55 COVID-19 patients and 51 samples from non-infected patients. WHO severity indicates the clinical severity score of the patient at the time the sample was n = moderate n = severe n = critical n = 15 samples. monocyte markers of epithelial injury. two neutrophil and IL6. We next how the COVID-19 severity protein signature to the proteins that are differentially abundant between cases and The majority of proteins were also identified as differentially abundant in the COVID-19-positive versus -negative analysis (Figure fold for proteins in COVID-19 versus non-infected patients were correlated with effect sizes in the severity that the proteins most upregulated in cases versus controls also to the greatest in severe disease (Figure there were some (e.g. that were strongly associated with severity, not differentially expressed in infected versus non-infected patients (Figure Figure 6 Download asset Open asset Comparison of proteins differentially expressed in COVID-19 with those associated with clinical severity. (a) Overlap between the proteins significantly differentially expressed in COVID-19 (n = 256 COVID-19 samples and 51 non-infected versus those associated with severity n = 256 (subcohort A). 5% FDR was used as the significant in both analyses. (b) Comparison of effect sizes for each protein in the COVID-19-positive versus -negative analysis and severity analysis Each point represents a protein. Pearson's r is shown. (c) of proteins associated with severity, not significantly differentially abundant in the of all cases versus showing distribution of plasma protein levels according to COVID-19 at the time of blood draw. indicate and inter-quartile range. n = 256 samples from 55 COVID-19 patients and 51 samples from non-infected patients. WHO severity indicates the clinical severity score of the patient at the time the sample was n = moderate n = severe n = critical n = 15 samples. learning to predict COVID-19 severity PCA revealed that some samples from patients who had mild or moderate disease at the time of sampling with samples from patients with severe disease (Figure 2—figure supplement 1a). Examination of the same PCA plot labelling samples according to the clinical course by peak WHO severity score over the of the (Figure 2—figure supplement revealed that these samples from individuals who subsequently developed severe or critical disease. This that molecular may clinical To evaluate this we used learning to whether the proteomic signature of the first blood sample for each patient in our dataset could identify whether the patient either had severe COVID-19 at the time of sampling or severe disease in the differential expression analyses each protein of all proteins in the Using we a on the first sample for each COVID-19 patient to predict the clinical defined by peak WHO severity. For the purposes of this we clinical course into either WHO or The method in peak severity. using only predictors and clinical the method in peak severity. clinical proteins did not compared to using proteomic predictors that the information in the clinical predictors is captured at the proteomic we not that proteomic profiling is to clinical for risk during this the selected by the proteins of We therefore the to identify key proteins by (see Materials and methods, Supplementary file The most important proteins for the of or future severe disease were IL18BP, GDF15, KRT19, and (Figure is that this as a key of severe disease. Figure 7 with 1 supplement see all Download asset Open asset of severe COVID-19 and death. (a) The 12 most important proteins for clinical course (defined by peak COVID-19 WHO using a is important for it is to in many of and be to the have a The all was used as the (b) Proteins that are significant predictors of death n = 256 samples from 55 COVID-19-positive patients, of Risk estimates are from a joint model. indicate For proteins with a positive risk a higher to a high risk of and for proteins with negative Proteins associated with risk of death of 55 patients in subcohort A We therefore to identify proteins associated with risk of death. To the nature of protein for of we joint models, which linear mixed models and models et al., (see Materials and methods). This analysis identified proteins for which increased was associated with increased risk of death (Figure Supplementary file including and and 25 proteins for which increased was associated with risk of including and with clinical A number of clinical have associations with COVID-19 (e.g. elevated inflammatory and et al., 2020). We therefore compared our proteomic data from COVID-19 patients at each timepoint to clinical using linear mixed models (see Materials and methods). We found associations between plasma proteins and all clinical (Figure Supplementary file Many of these proteins were also markers of severity (e.g. IL6, KRT19, and were strongly associated with and and Of CCL7, a monocyte that was also identified as an important of severity by the was associated with monocyte and inflammatory neutrophil was associated with which IL6, and and with the and Figure 8 Download asset Open asset of clinical markers with plasma proteins. Proteins that are (red) or (blue) associated with clinical (5% p-values from differential abundance analysis using linear mixed models after Benjamini–Hochberg = non-significant. Two associations were found for shown – see Supplementary file Longitudinal analysis proteins with temporal profiles according to severity The immune response to infection is and therefore provide only the serial sampling in our dataset (Figure we the temporal of each protein and whether or not any protein trajectories in patients with a versus clinical This was a

Linear mixed effects models are highly flexible in handling a broad range of data types and are therefore widely used in applications. A key part in the analysis of data is model selection, which often aims to choose a parsimonious model with other desirable properties from a possibly very large set of candidate statistical models. Over the last 5–10 years the literature on model selection in linear mixed models has grown extremely rapidly. The problem is much more complicated than in linear regression because selection on the covariance structure is not straightforward due to computational issues and boundary problems arising from positive semidefinite constraints on covariance matrices. To obtain a better understanding of the available methods, their properties and the relationships between them, we review a large body of literature on linear mixed model selection. We arrange, implement, discuss and compare model selection methods based on four major approaches: information criteria such as AIC or BIC, shrinkage methods based on penalized loss functions such as LASSO, the Fence procedure and Bayesian techniques.

The adequacy of quantification of the components in non-homogeneous pharmaceutical tablets using near infrared (NIR) linear hyperspectral unmixing has been studied with and without the presence of the tablet coating and an inefficient blending process. NIR images of six coated tablets of different formulations and of sections thereof, extracted at specific depths, were acquired. The quantification of the compounds present was performed via the classical least squares criterion. The results presented show that given the low depth of penetration of the NIR radiation, the coating represents as much as 30% of the mass fraction of the sampled tablet, even though it is commonly less than 3% of the mass fraction of the total tablet. This deviation negatively impacts the estimates of the compounds of interest. Estimates of the compounds obtained in sections approached the true values and were consistent at each depth. Both scenarios (coated and uncoated) were found to be well explained by a linear mixing model, as the errors in spectral estimates were small. The pixels showing the highest fraction of energy not explained by the linear model were found to be spatially located in areas where the surface curvature was high and a high reflectivity was observed; factors known to contribute non-linearities to the mixing scenario. The outcomes of this study have practical importance for the pharmaceutical industry: first, tablets should always be uncoated or microtomed before being imaged, in order to remove the high contribution of the coating and to obtain a flat surface. These steps reduce the above-mentioned non-linearities that introduce errors when using a linear mixing model. Second, the mixing scale shall be taken into account, as a poor blending may not show a similar in-depth pattern and thus provide different estimates at each depth and, on the other hand, over-blending may lead to a non-linear mixing scenario, depending on the spatial resolution used. An appropriate prior study will direct analysis either to linear or non-linear approaches.

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

In this paper, we propose a new wideband digital receiver based on the modulated wideband converter (MWC) discrete compressed sampling (CS) structure, and we further propose a uniform linear array (ULA)-based MWC discrete CS structure to estimate the carrier frequency and angle-of-arrival (AOA). The proposed receiver and ULA-based system use a bank of pseudorandom sequences to mix signals to baseband and other sub-bands. The product is then low-pass filtered and down-sampled at a low rate to obtain the baseband CS data. Meanwhile, the cross-channel signal problem can be solved flexibly, since the frequency spectrum of the cross-channel signal is all mixed to the baseband. And the sensitivity can be increased a lot, because the bandwidth of the baseband is very small. However, the CS data lose the true carrier frequency and phase differences information, because of the mixing operation.Therefore, we propose to utilize the cyclic-shifted pseudorandom sequences in the ULA-based system in order to design a special phase relationship for the CS data, and on this basis, we can get the carrier frequency estimation. Then, we correct the phase differences of the CS data to estimate AOA. Finally, simulation experiments show that the proposed systems are effective and demonstrate the superior estimation performance in the case of small numbers of snapshots and low signal-to-noise ratios.

In the past decade, the compressive sensing (CS) based ISAR imaging methods have gained much interest due to the capability of obtaining high-quality images with under-sampled data. However, both the performance and the application of CS ISAR imaging methods are limited by sparse representations and iterative reconstruction algorithms where the former may be hard to find and the latter may lead to low imaging efficiency. The deep-network (DN) based image reconstruction methods appeared in recent years have been shown to be able to dramatically reduce the computational complexity and ensure the image reconstruction at the same time. The Deep-ADMM-Net (DAN) is a network constructed by iterative steps of the traditional optimization algorithm, Alternating Direction Method of Multipliers (ADMM). The mainly characteristic of DAN is that it is interpretable and efficient. We propose a DAN based ISAR imaging method. The well trained DAN can reconstruct high-quality ISAR image using much fewer measurements than CS based imaging methods. Experimental results show that our proposed imaging method is superior to the existing CS method in both image reconstruction quality and computational efficiency

Privileged by rapid increase in available epigenomic data, epigenome‐wide association studies (EWAS) are to make a profound contribution to understand the molecular mechanism of DNA methylation in cognitive aging. Current statistical methods used in EWAS are dominated by models based on multiple assumptions, for example, linear relationship between molecular profiles and phenotype, normal distribution for the methylation data and phenotype. In this study, we applied an assumption‐free method, the generalized correlation coefficient (GCC), and compare it to linear models, namely the linear mixed model and kinship model. We use DNA methylation associated with a cognitive score in 400 and 206 twins as discovery and replication samples respectively. DNA methylation associated with cognitive function using GCC, linear mixed model, and kinship model, identified 65 CpGs (p < 1e‐04) from discovery sample displaying both nonlinear and linear correlations. Replication analysis successfully replicated 9 of these top CpGs. When combining results of GCC and linear models to cover diverse patterns of relationships, we identified genes like KLHDC4, PAPSS2, and MRPS18B as well as pathways including focal adhesion, axon guidance, and some neurological signaling. Genomic region‐based analysis found 15 methylated regions harboring 11 genes, with three verified in gene expression analysis, also the 11 genes were related to top functional clusters including neurohypophyseal hormone and maternal aggressive behaviors. The GCC approach detects valuable methylation sites missed by traditional linear models. A combination of methylation markers from GCC and linear models enriched biological pathways sensible in neurological function that could implicate cognitive performance and cognitive aging.

Hyperspectral data are often modeled using either a linear mixture or a statistical classification approach. The linear mixture model describes each spectral vector as a constrained linear combination of end-member spectra, whereas the classification approach models each spectra as a realization of a random vector having one of several normal distributions. In this work we describe a stochastic compositional model that synthesizes these two viewpoints and models each spectra as a constrained linear combination of random vectors. Maximum likelihood methods of estimating the parameters of the model, assuming normally distributed random vectors, are described, and anomaly and likelihood ratio detection statistics are defined. Detection algorithms derived from the classification, linear mixing, and stochastic compositional models are defined. Detection algorithms derived from the classification, linear mixing, and stochastic compositional models are compared using data consisting of ocean hyperspectral imagery to which the signature of a personal flotation device has been added at pixel fill fractions (PFF) of five and ten percent. These results show that detection algorithms based on the stochastic compositional model may significantly improve detection performance. For example, this study shows that, at a 5% PFF and a probability of detection of 0.8, the false alarm probabilities of anomaly and likelihood detection algorithms based on the stochastic compositional model are more than an order of magnitude lower than the false alarm probabilities of comparable algorithms based on either a linear unmixing algorithm or a Gaussian mixture model.

This paper presents the latest results of a series of experiments deigned to identify situations in which linear and nonlinear mixing models are expect to occur. It continues to investigate the possibility that there may be naturally occurring situation in which the typically used linear mixture model may not provide the most accurate spectrum. It has already been shown that for specific situations, in binary mixing cases, the nonlinear mixing model can produce more accurate endmember abundance estimates. These results are extended to include ternary and quaternary mixtures, as well as hyperspectral imagery collected over Cuprite, Nevada. In order to test these hypotheses, laboratory endmember and mixture data are collected in various scenarios for analysis. As shown in experiments, ternary and quaternary mixtures are more complicated than binary mixtures and the nonlinear mixing is more likely to occur in ternary and quaternary mixtures than in binary mixtures.© (2002) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.