Functional support vector machine.

Linear and generalized linear scalar-on-function modeling have been commonly used to understand the relationship between a scalar response variable (e.g. continuous, binary outcomes) and functional predictors. Such techniques are sensitive to model misspecification when the relationship between the response variable and the functional predictors is complex. On the other hand, support vector machines (SVMs) are among the most robust prediction models but do not take account of the high correlations between repeated measurements and cannot be used for irregular data. In this work, we propose a novel method to integrate functional principal component analysis with SVM techniques for classification and regression to account for the continuous nature of functional data and the nonlinear relationship between the scalar response variable and the functional predictors. We demonstrate the performance of our method through extensive simulation experiments and two real data applications: the classification of alcoholics using electroencephalography signals and the prediction of glucobrassicin concentration using near-infrared reflectance spectroscopy. Our methods especially have more advantages when the measurement errors in functional predictors are relatively large.

A sparse additive model for treatment effect-modifier selection.

Sparse additive modeling is a class of effective methods for performing high-dimensional nonparametric regression. This article develops a sparse additive model focused on estimation of treatment effect modification with simultaneous treatment effect-modifier selection. We propose a version of the sparse additive model uniquely constrained to estimate the interaction effects between treatment and pretreatment covariates, while leaving the main effects of the pretreatment covariates unspecified. The proposed regression model can effectively identify treatment effect-modifiers that exhibit possibly nonlinear interactions with the treatment variable that are relevant for making optimal treatment decisions. A set of simulation experiments and an application to a dataset from a randomized clinical trial are presented to demonstrate the method.

Serotonin transporter binding in major depressive disorder: impact of serotonin system anatomy.

Serotonin transporter (5-HTT) binding deficits are reported in major depressive disorder (MDD). However, most studies have not considered serotonin system anatomy when parcellating brain regions of interest (ROIs). We now investigate 5-HTT binding in MDD in two novel ways: (1) use of a 5-HTT tract-based analysis examining binding along serotonergic axons; and (2) using the Copenhagen University Hospital Neurobiology Research Unit (NRU) 5-HT Atlas, based on brain-wide binding patterns of multiple serotonin receptor types. [11C]DASB 5-HTT PET scans were obtained in 60 unmedicated participants with MDD in a current depressive episode and 31 healthy volunteers (HVs). Binding potential (BPP) was quantified with empirical Bayesian estimation in graphical analysis (EBEGA). Within the [11C]DASB tract, the MDD group showed significantly lower BPP compared with HVs (p = 0.02). This BPP diagnosis difference also significantly varied by tract location (p = 0.02), with the strongest MDD binding deficit most proximal to brainstem raphe nuclei. NRU 5-HT Atlas ROIs showed a BPP diagnosis difference that varied by region (p < 0.001). BPP was lower in MDD in 3/10 regions (p-values < 0.05). Neither [11C]DASB tract or NRU 5-HT Atlas BPP correlated with depression severity, suicidal ideation, suicide attempt history, or antidepressant medication exposure. Future studies are needed to determine the causes of this deficit in 5-HTT binding being more pronounced in proximal axon segments and in only a subset of ROIs for the pathogenesis of MDD. Such regional specificity may have implications for targeting antidepressant treatment, and may extend to other serotonin-related disorders.

Functional additive models for optimizing individualized treatment rules.

A novel functional additive model is proposed, which is uniquely modified and constrained to model nonlinear interactions between a treatment indicator and a potentially large number of functional and/or scalar pretreatment covariates. The primary motivation for this approach is to optimize individualized treatment rules based on data from a randomized clinical trial. We generalize functional additive regression models by incorporating treatment-specific components into additive effect components. A structural constraint is imposed on the treatment-specific components in order to provide a class of additive models with main effects and interaction effects that are orthogonal to each other. If primary interest is in the interaction between treatment and the covariates, as is generally the case when optimizing individualized treatment rules, we can thereby circumvent the need to estimate the main effects of the covariates, obviating the need to specify their form and thus avoiding the issue of model misspecification. The methods are illustrated with data from a depression clinical trial with electroencephalogram functional data as patients' pretreatment covariates.

Permutation-Based Inference for Function-on-Scalar Regression With an Application in PET Brain Imaging.

The density of various proteins throughout the human brain can be studied through the use of positron emission tomography (PET) imaging. We report here on data from a study of serotonin transporter (5-HTT) binding. While PET imaging data analysis is most commonly performed on data that are aggregated into several discrete a priori regions of interest, in this study, primary interest is on measures of 5-HTT binding potential that are made at many locations along a continuous anatomically defined tract, one that was chosen to follow serotonergic axons. Our goal is to characterize the binding patterns along this tract and also to determine how such patterns differ between control subjects and depressed patients. Due to the nature of our data, we utilize function-on-scalar regression modeling to make optimal use of our data. Inference on both main effects (position along the tract; diagnostic group) and their interactions is made using permutation testing strategies that do not require distributional assumptions. Also, to investigate the question of homogeneity we implement a permutation testing strategy, which adapts a "block bootstrapping" approach from time series analysis to the functional data setting.

Simultaneous multifactor Bayesian analysis (SiMBA) of PET time activity curve data.

Positron emission tomography (PET) is an in vivo imaging method essential for studying the neurochemical pathophysiology of psychiatric and neurological disease. However, its high cost and exposure of participants to radiation make it unfeasible to employ large sample sizes. The major shortcoming of PET imaging is therefore its lack of power for studying clinically-relevant research questions. Here, we introduce a new method for performing PET quantification and analysis called SiMBA, which helps to alleviate these issues by improving the efficiency of PET analysis by exploiting similarities between both individuals and regions within individuals. In simulated [11C]WAY100635 data, SiMBA greatly improves both statistical power and the consistency of effect size estimation without affecting the false positive rate. This approach makes use of hierarchical, multifactor, multivariate Bayesian modelling to effectively borrow strength across the whole dataset to improve stability and robustness to measurement error. In so doing, parameter identifiability and estimation are improved, without sacrificing model interpretability. This comes at the cost of increased computational overhead, however this is practically negligible relative to the time taken to collect PET data. This method has the potential to make it possible to test clinically-relevant hypotheses which could never be studied before given the practical constraints. Furthermore, because this method does not require any additional information over and above that required for traditional analysis, it makes it possible to re-examine data which has already previously been collected at great expense. In the absence of dramatic advancements in PET image data quality, radiotracer development, or data sharing, PET imaging has been fundamentally limited in the scope of research hypotheses which could be studied. This method, especially combined with the recent steps taken by the PET imaging community to embrace data sharing, will make it possible to greatly improve the research possibilities and clinical relevance of PET neuroimaging.

Source-to-Target Automatic Rotating Estimation (STARE) - A publicly-available, blood-free quantification approach for PET tracers with irreversible kinetics: Theoretical framework and validation for [18F]FDG.

INTRODUCTION: Full quantification of positron emission tomography (PET) data requires an input function. This generally means arterial blood sampling, which is invasive, labor-intensive and burdensome. There is no current, standardized method to fully quantify PET radiotracers with irreversible kinetics in the absence of blood data. Here, we present Source-to-Target Automatic Rotating Estimation (STARE), a novel, data-driven approach to quantify the net influx rate (Ki) of irreversible PET radiotracers, that requires only individual-level PET data and no blood data. We validate STARE with human [18F]FDG PET scans and assess its performance using simulations. METHODS: STARE builds upon a source-to-target tissue model, where the tracer time activity curves (TACs) in multiple "target" regions are expressed at once as a function of a "source" region, based on the two-tissue irreversible compartment model, and separates target region Ki from source Ki by fitting the source-to-target model across all target regions simultaneously. To ensure identifiability, data-driven, subject-specific anchoring is used in the STARE minimization, which takes advantage of the PET signal in a vasculature cluster in the field of view (FOV) that is automatically extracted and partial volume-corrected. To avoid the need for any a priori determination of a single source region, each of the considered regions acts in turn as the source, and a final Ki is estimated in each region by averaging the estimates obtained in each source rotation. RESULTS: In a large dataset of human [18F]FDG scans (N = 69), STARE Ki estimates were correlated with corresponding arterial blood-based Ki estimates (r = 0.80), with an overall regression slope of 0.88, and were precisely estimated, as assessed by comparing STARE Ki estimates across several runs of the algorithm (coefficient of variation across runs=6.74 ± 2.48%). In simulations, STARE Ki estimates were largely robust to factors that influence the individualized anchoring used within its algorithm. CONCLUSION: Through simulations and application to [18F]FDG PET data, feasibility is demonstrated for STARE blood-free, data-driven quantification of Ki. Future work will include applying STARE to PET data obtained with a portable PET camera and to other irreversible radiotracers.

Designing drug occupancy studies with PET neuroimaging: Sample size, occupancy ranges and analytical methods.

Molecular neuroimaging is today considered essential for evaluation of novel CNS drugs; it is used to quantify blood-brain barrier permeability, verify interaction with key target and determine the drug dose resulting in 50% occupancy, IC50. In spite of this, there has been limited data available to inform on how to optimize study designs. Through simulations, we here evaluate how IC50 estimation is affected by the (i) range of drug doses administered, (ii) number of subjects included, and (iii) level of noise in the plasma drug concentration measurements. Receptor occupancy is determined from PET distribution volumes using two different methods: the Lassen plot and Likelihood estimation of occupancy (LEO). We also introduce and evaluate a new likelihood-based estimator for direct estimation of IC50 from PET distribution volumes. For estimation of IC50, we find very limited added benefit in scanning individuals who are given drug doses corresponding to less than 40% receptor occupancy. In the range of typical PET sample sizes (5-20 subjects) each extra individual clearly reduces the error of the IC50 estimate. In all simulations, likelihood-based methods gave more precise IC50 estimates than the Lassen plot; four times the number of subjects were required for the Lassen plot to reach the same IC50 precision as LEO.

Serotonin 1A Receptor Binding of [11C]CUMI-101 in Bipolar Depression Quantified Using Positron Emission Tomography: Relationship to Psychopathology and Antidepressant Response.

BACKGROUND: The pathophysiology of bipolar disorder (BD) remains largely unknown despite it causing significant disability and suicide risk. Serotonin signaling may play a role in the pathophysiology, but direct evidence for this is lacking. Treatment of the depressed phase of the disorder is limited. Previous studies have indicated that positron emission tomography (PET) imaging of the serotonin 1A receptor (5HT1AR) may predict antidepressant response. METHODS: A total of 20 participants with BD in a current major depressive episode and 16 healthy volunteers had PET imaging with [11C]CUMI-101, employing a metabolite-corrected input function for quantification of binding potential to the 5HT1AR. Bipolar participants then received an open-labeled, 6-week clinical trial with a selective serotonin reuptake inhibitor (SSRI) in addition to their mood stabilizer. Clinical ratings were obtained at baseline and during SSRI treatment. RESULTS: Pretreatment binding potential (BPF) of [11C]CUMI-101 was associated with a number of pretreatment clinical variables within BD participants. Within the raphe nucleus, it was inversely associated with the baseline Montgomery Åsberg Rating Scale (P = .026), the Beck Depression Inventory score (P = .0023), and the Buss Durkee Hostility Index (P = .0058), a measure of lifetime aggression. A secondary analysis found [11C]CUMI-101 BPF was higher in bipolar participants compared with healthy volunteers (P = .00275). [11C]CUMI-101 BPF did not differ between SSRI responders and non-responders (P = .907) to treatment and did not predict antidepressant response (P = .580). Voxel-wise analyses confirmed the results obtained in regions of interest analyses. CONCLUSIONS: A disturbance of serotonin system function is associated with both the diagnosis of BD and its severity of depression. Pretreatment 5HT1AR binding did not predict SSRI antidepressant outcome.The study was listed on clinicaltrials.gov with identifier NCT02473250.

Brain 5-HT1A Receptor PET Binding, Cortisol Responses to Stress, and the Familial Transmission of Suicidal Behavior.

BACKGROUND: The serotonin 1A (5-HT1A) receptor has been implicated in depression and suicidal behavior. Lower resting cortisol levels are associated with higher 5-HT1A receptor binding, and both differentiate suicide attempters with depression. However, it is not clear whether 5-HT1A receptor binding and cortisol responses to stress are related to familial risk and resilience for suicidal behavior. METHODS: [11C]CUMI-101 positron emission tomography imaging to quantify regional brain 5-HT1A receptor binding was conducted in individuals considered to be at high risk for mood disorder or suicidal behavior on the basis of having a first- or second-degree relative(s) with an early onset mood disorder and history of suicidal behavior. These high-risk individuals were subdivided into the following groups: high risk resilient having no mood disorder or suicidal behavior (n = 29); high risk with mood disorder and no suicidal behavior history (n = 31); and high risk with mood disorder and suicidal behavior (n = 25). Groups were compared with healthy volunteers without a family history of mood disorder or suicidal behavior (n = 34). Participants underwent the Trier Social Stress Task (TSST). All participants were free from psychotropic medications at the time of the TSST and PET scanning. RESULTS: We observed no group differences in 5-HT1A receptor binding considering all regions simultaneously, nor did we observe heterogeneity of the effect of group across regions. These results were similar across outcome measures (BPND for all participants and BPp in a subset of the sample) and definitions of regions of interest (ROIs; standard or serotonin system-specific ROIs). We also found no group differences on TSST outcomes. Within the high risk with mood disorder and suicidal behavior group, lower BPp binding (ß = -0.084, SE = 0.038, P = .048) and higher cortisol reactivity to stress (ß = 9.25, 95% CI [3.27,15.23], P = .004) were associated with higher lethality attempts. There were no significant relationships between 5-HT1A binding and cortisol outcomes. CONCLUSIONS: 5-HT1A receptor binding in ROIs was not linked to familial risk or resilience protecting against suicidal behavior or mood disorder although it may be related to lethality of suicide attempt. Future studies are needed to better understand the biological mechanisms implicated in familial risk for suicidal behavior and how hypothalamic-pituitary-adrenal axis function influences such risk.

Effect of diet energy level and genomic residual feed intake on bred Holstein dairy heifer growth and feed efficiency.

The objective of this study was to determine growth, feed intake, and feed efficiency of postbred dairy heifers with different genomic residual feed intake (RFI) predicted as a lactating cow when offered diets differing in energy density. Postbred Holstein heifers (n = 128, ages 14-20 mo) were blocked by initial weight (high, medium-high, medium-low, and low) with 32 heifers per block. Each weight block was sorted by RFI (high or low) to obtain 2 pens of heifers with high and low genomically predicted RFI within each block (8 heifers per pen). Low RFI heifers were expected to have greater feed efficiency than high RFI heifers. Dietary treatments consisted of a higher energy control diet based on corn silage and alfalfa haylage [HE; 62.7% total digestible nutrients, 11.8% crude protein, and 45.6% neutral detergent fiber; dry matter (DM) basis], and a lower energy diet diluted with straw (LE; 57.0% total digestible nutrients, 11.7% crude protein, and 50.1% neutral detergent fiber; DM basis). Each pen within a block was randomly allocated a diet treatment to obtain a 2 × 2 factorial arrangement (2 RFI levels and 2 dietary energy levels). Diets were offered in a 120-d trial. Dry matter intake by heifers was affected by diet (11.0 vs. 10.0 kg/d for HE and LE, respectively) but not by RFI or the interaction of RFI and diet. Daily gain was affected by the interaction of RFI and diet, with low RFI heifers gaining more than high RFI heifers when fed LE (0.94 vs. 0.85 kg/d for low and high RFI, respectively), but no difference for RFI groups when fed HE (1.16 vs. 1.19 kg/d for low and high RFI, respectively). Respective feed efficiencies were improved for low RFI compared with high RFI heifers when fed LE (10.6 vs. 11.8 kg of feed DM/kg of gain), but no effect of RFI was found when fed HE (9.4 vs. 9.5 kg of DM/kg of gain for high and low RFI, respectively). No effect of RFI or diet on first-lactation performance through 150 DIM was observed. Based on these results, the feed efficiency of heifers having different genomic RFI may be dependent on diet energy level, whereby low RFI heifers utilized the LE diet more efficiently. The higher fiber straw (LE) diet controlled intake and maintained more desirable heifer weight gains. This suggests that selection for improved RFI in lactating cows may improve feed efficiency in growing heifers when fed to meet growth goals of 0.9 to 1.0 kg of gain/d.

A constrained single-index regression for estimating interactions between a treatment and covariates.

We consider a single-index regression model, uniquely constrained to estimate interactions between a set of pretreatment covariates and a treatment variable on their effects on a response variable, in the context of analyzing data from randomized clinical trials. We represent interaction effect terms of the model through a set of treatment-specific flexible link functions on a linear combination of the covariates (a single index), subject to the constraint that the expected value given the covariates equals 0, while leaving the main effects of the covariates unspecified. We show that the proposed semiparametric estimator is consistent for the interaction term of the model, and that the efficiency of the estimator can be improved with an augmentation procedure. The proposed single-index regression provides a flexible and interpretable modeling approach to optimizing individualized treatment rules based on patients' data measured at baseline, as illustrated by simulation examples and an application to data from a depression clinical trial.

Inference in functional mixed regression models with applications to Positron Emission Tomography imaging data.

In a function-on-scalar regression framework, we present some modeling strategies for functional mixed models and also some approaches for making inference about various aspects of the fixed effects. This is presented in the context of modeling positron emission tomography (PET) data in order to explore the density of various proteins of interest throughout the human brain. For this application, information about the density of the target protein in a given brain region is encapsulated in the impulse response function (IRF) of the region. Previous work on nonparametric estimation of the IRF is limited in that it is only able to model a single brain region at a time. We propose an extension, based on principles of functional data analysis, that will allow modeling of multiple brain regions simultaneously. Applicable more broadly to functional mixed regression modeling, we discuss two general approaches for permutation testing and describe valid strategies for identifying exchangeable units within the model and building corresponding permutation tests. We illustrate our methods with an application to PET data and explore the effects of depression and sex on the IRF.

Verbal estimation of the magnitude of time, number, and length.

Performance similarities on tasks requiring the processing of different domains of magnitude (e.g. time, numerosity, and length) have led to the suggestion that humans possess a common processing system for all domains of magnitude (Bueti and Walsh in Philos Trans R Soc B 364:1831-1840, 2009). In light of this, the current study examined whether Wearden's (Timing Time Percept 3:223-245, 2015) model of the verbal estimation of duration could be applied to verbal estimates of numerosity and length. Students (n = 23) verbally estimated the duration, number, or physical length of items presented in visual displays. Analysis of the mean verbal estimates indicated the data were typical of that found in other studies. Analysis of the frequency of individual verbal estimates produced suggested that the verbal responses were highly quantized for duration and length: that is, only a small number of estimates were used. Responses were also quantized for number but to a lesser degree. The data were modelled using Wearden's (2015) account of verbal estimation performance, which simulates quantization effects, and good fits could be obtained providing that stimulus durations were scaled as proportions (0.75, 1.06, and 0.92 for duration, number, and length, respectively) of their real magnitudes. The results suggest that despite previous reports of similarities in the processing of magnitude, there appear to be differences in the way in which the underlying representations of the magnitudes are scaled and then transformed into verbal outputs.

Prediction of lithium treatment response in bipolar depression using 5-HTT and 5-HT1A PET.

BACKGROUND: Lithium, one of the few effective treatments for bipolar depression (BPD), has been hypothesized to work by enhancing serotonergic transmission. Despite preclinical evidence, it is unknown whether lithium acts via the serotonergic system. Here we examined the potential of serotonin transporter (5-HTT) or serotonin 1A receptor (5-HT1A) pre-treatment binding to predict lithium treatment response and remission. We hypothesized that lower pre-treatment 5-HTT and higher pre-treatment 5-HT1A binding would predict better clinical response. Additional analyses investigated group differences between BPD and healthy controls and the relationship between change in binding pre- to post-treatment and clinical response. Twenty-seven medication-free patients with BPD currently in a depressive episode received positron emission tomography (PET) scans using 5-HTT tracer [11C]DASB, a subset also received a PET scan using 5-HT1A tracer [11C]-CUMI-101 before and after 8 weeks of lithium monotherapy. Metabolite-corrected arterial input functions were used to estimate binding potential, proportional to receptor availability. Fourteen patients with BPD with both [11C]DASB and [11C]-CUMI-101 pre-treatment scans and 8 weeks of post-treatment clinical scores were included in the prediction analysis examining the potential of either pre-treatment 5-HTT or 5-HT1A or the combination of both to predict post-treatment clinical scores. RESULTS: We found lower pre-treatment 5-HTT binding (p = 0.003) and lower 5-HT1A binding (p = 0.035) were both significantly associated with improved clinical response. Pre-treatment 5-HTT predicted remission with 71% accuracy (77% specificity, 60% sensitivity), while 5-HT1A binding was able to predict remission with 85% accuracy (87% sensitivity, 80% specificity). The combined prediction analysis using both 5-HTT and 5-HT1A was able to predict remission with 84.6% accuracy (87.5% specificity, 60% sensitivity). Additional analyses BPD and controls pre- or post-treatment, and the change in binding were not significant and unrelated to treatment response (p > 0.05). CONCLUSIONS: Our findings suggest that while lithium may not act directly via 5-HTT or 5-HT1A to ameliorate depressive symptoms, pre-treatment binding may be a potential biomarker for successful treatment of BPD with lithium. CLINICAL TRIAL REGISTRATION: PET and MRI Brain Imaging of Bipolar Disorder Identifier: NCT01880957; URL: https://clinicaltrials.gov/ct2/show/NCT01880957.

Simultaneous confidence corridors for mean functions in functional data analysis of imaging data.

Motivated by recent work involving the analysis of biomedical imaging data, we present a novel procedure for constructing simultaneous confidence corridors for the mean of imaging data. We propose to use flexible bivariate splines over triangulations to handle an irregular domain of the images that is common in brain imaging studies and in other biomedical imaging applications. The proposed spline estimators of the mean functions are shown to be consistent and asymptotically normal under some regularity conditions. We also provide a computationally efficient estimator of the covariance function and derive its uniform consistency. The procedure is also extended to the two-sample case in which we focus on comparing the mean functions from two populations of imaging data. Through Monte Carlo simulation studies, we examine the finite sample performance of the proposed method. Finally, the proposed method is applied to analyze brain positron emission tomography data in two different studies. One data set used in preparation of this article was obtained from the Alzheimer's Disease Neuroimaging Initiative (ADNI) database.

A Bayesian approach to joint modeling of matrix-valued imaging data and treatment outcome with applications to depression studies.

In this paper, we propose a unified Bayesian joint modeling framework for studying association between a binary treatment outcome and a baseline matrix-valued predictor. Specifically, a joint modeling approach relating an outcome to a matrix-valued predictor through a probabilistic formulation of multilinear principal component analysis is developed. This framework establishes a theoretical relationship between the outcome and the matrix-valued predictor, although the predictor is not explicitly expressed in the model. Simulation studies are provided showing that the proposed method is superior or competitive to other methods, such as a two-stage approach and a classical principal component regression in terms of both prediction accuracy and estimation of association; its advantage is most notable when the sample size is small and the dimensionality in the imaging covariate is large. Finally, our proposed joint modeling approach is shown to be a very promising tool in an application exploring the association between baseline electroencephalography data and a favorable response to treatment in a depression treatment study by achieving a substantial improvement in prediction accuracy in comparison to competing methods.

Physiological effects of starter-induced ruminal acidosis in calves before, during, and after weaning.

The objectives were to nutritionally induce or blunt ruminal acidosis in young calves and to compare indicators of rumen and systemic health. Ten bull calves (n = 5/diet) were ruminally cannulated at 3 wk of age and received milk replacer and 1 of 2 calf starter diets that were designed to cause (AC; pelleted, 42.7% starch, 15.1% neutral detergent fiber, 57.8% nonfiber carbohydrates) or blunt (BL; texturized, 35.3% starch, 25.3% neutral detergent fiber, 48.1% nonfiber carbohydrates) ruminal acidosis. Mean birth weight was 38.7 ± 1.3 kg. Body weight and calf starter intake were measured weekly. Rumen contents were sampled at -8, -4, 0, 2, 4, 8, 12, and 24 h relative to starter feeding during wk 6, 8, 10, 12, 14, and 16 of age. Blood was collected from the jugular vein during the same weeks for complete blood cell count, blood pH, and partial pressures of oxygen and carbon dioxide. Rate of starter consumption was assessed during wk 16. Marker systems were used to estimate liquid passage and volatile fatty acid absorption rates. Calves were slaughtered at 17 wk, and rumen tissue was collected and assessed for papillae length, width, and degree of tissue degradation. Mean ruminal pH ± standard error was 5.37 ± 0.24 and 5.63 ± 0.24 for AC and BL calves, respectively. Lowest pH values were observed the week after weaning. Total ruminal volatile fatty acid concentrations were 131.5 and 124.8 ± 2.4 mM in AC and BL calves, respectively, and increased with age and time after feeding. Dry matter intake was lower in AC calves at wk 4 and remained lower through wk 16. Rate of starter consumption was also lower in AC calves at wk 16. Body weight also was also lower for AC calves from wk 5 through 16. Blood hemoglobin and hematocrit were lower in AC calves, but other blood characteristics were not different. Rumen volume increased with age and tended to be greater in BL calves. Passage rate and papillae length and width were not different between diets, but AC calves experienced a greater degree of tissue degradation. Ruminal acidosis symptoms in calves appear similar to those in adult cattle, and the etiology of the disease seems to follow similar mechanisms. It is clear from this study that symptoms can be moderated by diet, but further research is needed to determine whether symptoms can be nutritionally prevented or whether calves that experience ruminal acidosis are more susceptible to the disease as adults.

A single-index model with multiple-links.

In a regression model for treatment outcome in a randomized clinical trial, a treatment effect modifier is a covariate that has an interaction with the treatment variable, implying that the treatment efficacies vary across values of such a covariate. In this paper, we present a method for determining a composite variable from a set of baseline covariates, that can have a nonlinear association with the treatment outcome, and acts as a composite treatment effect modifier. We introduce a parsimonious generalization of the single-index models that targets the effect of the interaction between the treatment conditions and the vector of covariates on the outcome, a single-index model with multiple-links (SIMML) that estimates a single linear combination of the covariates (i.e., a single-index), with treatment-specific nonparametric link functions. The approach emphasizes a focus on the treatment-by-covariates interaction effects on the treatment outcome that are relevant for making optimal treatment decisions. Asymptotic results for estimator are obtained under possible model misspecification. A treatment decision rule based on the derived single-index is defined, and it is compared to other methods for estimating optimal treatment decision rules. An application to a clinical trial for the treatment of depression is presented.

Accuracy and reliability of [11C]PBR28 specific binding estimated without the use of a reference region.

[11C]PBR28 is a positron emission tomography radioligand used to examine the expression of the 18 kDa translocator protein (TSPO). TSPO is located in glial cells and can function as a marker for immune activation. Since TSPO is expressed throughout the brain, no true reference region exists. For this reason, an arterial input function is required for accurate quantification of [11C]PBR28 binding and the most common outcome measure is the total distribution volume (VT). Notably, VT reflects both specific binding and non-displaceable binding. Therefore, estimates of specific binding, such as binding potential (e.g. BPND) and specific distribution volume (VS) should theoretically be more sensitive to underlying differences in TSPO expression. It is unknown, however, if unbiased and accurate estimates of these outcome measures are obtainable for [11C]PBR28. The Simultaneous Estimation (SIME) method uses time-activity-curves from multiple brain regions with the aim to obtain a brain-wide estimate of the non-displaceable distribution volume (VND), which can subsequently be used to improve the estimation of BPND and VS. In this study we evaluated the accuracy of SIME-derived VND, and the reliability of resulting estimates of specific binding for [11C]PBR28, using a combination of simulation experiments and in vivo studies in healthy humans. The simulation experiments, based on data from 54 unique [11C]PBR28 examinations, showed that VND values estimated using SIME were both precise and accurate. Data from a pharmacological competition challenge (n = 5) showed that SIME provided VND values that were on average 19% lower than those obtained using the Lassen plot, but similar to values obtained using the Likelihood-Estimation of Occupancy technique. Test-retest data (n = 11) showed that SIME-derived VS values exhibited good reliability and precision, while larger variability was observed in SIME-derived BPND values. The results support the use of SIME for quantifying specific binding of [11C]PBR28, and suggest that VS can be used in complement to the conventional outcome measure VT. Additional studies in patient cohorts are warranted.