Methods for functional regression and nonlinear mixed-effects models with applications to PET data

The overall theme of this thesis focuses on methods for functional regression and nonlinear mixed-effects models with applications to PET data. The first part considers the problem of variable selection in regression models with functional responses and scalar predictors. We pose the function-on-scalar model as a multivariate regression problem and use group-MCP for variable selection. We account for residual covariance by "pre-whitening" using an estimate of the covariance matrix, and establish theoretical properties for the resulting estimator. We further develop an iterative algorithm that alternately updates the spline coefficients and covariance. Our method is illustrated by the application to two-dimensional planar reaching motions in a study of the effects of stroke severity on motor control. The second part introduces a functional data analytic approach for the estimation of the IRF, which is necessary for describing the binding behavior of the radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject's IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which shrinkage and roughness penalties are incorporated to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and non-negativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data. The third part discusses a nonlinear mixed-effects modeling approach for PET data analysis under the assumption of a compartment model. The traditional NLS estimators of the population parameters are applied in a two-stage analysis, which brings instability issue and neglects the variation in rate parameters. In contrast, we propose to estimate the rate parameters by fitting nonlinear mixed-effects (NLME) models, in which all the subjects are modeled simultaneously by allowing rate parameters to have random effects and population parameters can be estimated directly from the joint model. Simulations are conducted to compare the power of detecting group effect in both rate parameters and summarized measures of tests based on both NLS and NLME models. We apply our NLME approach to clinical PET data to illustrate the model building procedure

Effects of serelaxin in acute heart failure patients with renal impairment:results from RELAX-AHF

Serelaxin showed beneficial effects on clinical outcome and trajectories of renal markers in patients with acute heart failure. We aimed to study the interaction between renal function and the treatment effect of serelaxin.In the current post hoc analysis of the RELAX-AHF trial, we included all patients with available estimated glomerular filtration rate (eGFR) at baseline (n = 1132). Renal impairment was defined as an eGFR &lt;60 ml/min/1.73 m(2) estimated by creatinine.817 (72.2 %) patients had a baseline eGFR &lt;60 ml/min/1.73 m(2). In placebo-treated patients, baseline renal impairment was related to a higher 180 day cardiovascular (HR 3.12, 95 % CI 1.33-7.30) and all-cause mortality (HR 2.81, 95 % CI 1.34-5.89). However, in serelaxin-treated patients, the risk of cardiovascular and all-cause mortality was less pronounced (HR 1.19, 95 % CI 0.54 -2.64; p for interaction = 0.106, and HR 1.15 95 % CI 0.56-2.34 respectively; p for interaction = 0.088). In patients with renal impairment, treatment with serelaxin resulted in a more pronounced all-cause mortality reduction (HR 0.53, 95 % CI 0.34-0.83), compared with patients without renal impairment (HR 1.30, 95 % CI 0.51-3.29).Renal dysfunction was associated with higher cardiovascular and all-cause mortality in placebo-treated patients, but not in serelaxin-treated patients. The observed reduction in (cardiovascular) mortality in RELAX-AHF was more pronounced in patients with renal dysfunction. These observations need to be confirmed in the ongoing RELAX-AHF-2 trial.</p

Assessing population structure and body condition to inform conservation strategies for a small isolated Asian elephant (Elephas maximus) population in southwest China.

The Asian elephant (Elephas maximus) population in Nangunhe National Nature Reserve in China represents a unique evolutionary branch that has been isolated for more than twenty years from neighboring populations in Myanmar. The scarcity of information on population structure, sex ratio, and body condition makes it difficult to develop effective conservation measures for this elephant population. Twelve individuals were identified from 3,860 valid elephant images obtained from February to June 2018 (5,942 sampling effort nights) at 52 camera sites. Three adult females, three adult males, one subadult male, two juvenile females, two juvenile males and one male calf were identified. The ratio of adult females to adult males was 1:1, and the ratio of reproductive ability was 1:0.67, indicating the scarcity of reproductive females as an important limiting factor to population growth. A population density of 5.32 ± 1.56 elephants/100 km2 was estimated using Spatially Explicit Capture Recapture (SECR) models. The health condition of this elephant population was assessed using an 11-point scale of Body Condition Scoring (BCS). The average BCS was 5.75 (n = 12, range 2-9), with adult females scoring lower than adult males. This isolated population is extremely small and has an inverted pyramid age structure and therefore is at a high risk of extinction. We propose three plans to improve the survival of this population: improving the quality and quantity of food resources, removing fencing and establishing corridors between the east and wet parts of Nangunhe reserve

Functional Data Analysis of Dynamic PET Data

<p>One application of positron emission tomography (PET), a nuclear imaging technique, in neuroscience involves in vivo estimation of the density of various proteins (often, neuroreceptors) in the brain. PET scanning begins with the injection of a radiolabeled tracer that binds preferentially to the target protein; tracer molecules are then continuously delivered to the brain via the bloodstream. By detecting the radioactive decay of the tracer over time, dynamic PET data are constructed to reflect the concentration of the target protein in the brain at each time. The fundamental problem in the analysis of dynamic PET data involves estimating the impulse response function (IRF), which is necessary for describing the binding behavior of the injected radiotracer. Virtually all existing methods have three common aspects: summarizing the entire IRF with a single scalar measure; modeling each subject separately; and the imposition of parametric restrictions on the IRF. In contrast, we propose a functional data analytic approach that regards each subject’s IRF as the basic analysis unit, models multiple subjects simultaneously, and estimates the IRF nonparametrically. We pose our model as a linear mixed effect model in which population level fixed effects and subject-specific random effects are expanded using a <i>B</i>-spline basis. Shrinkage and roughness penalties are incorporated in the model to enforce identifiability and smoothness of the estimated curves, respectively, while monotonicity and nonnegativity constraints impose biological information on estimates. We illustrate this approach by applying it to clinical PET data with subjects belonging to three diagnosic groups. We explore differences among groups by means of pointwise confidence intervals of the estimated mean curves based on bootstrap samples. Supplementary materials for this article are available online.</p

Effects of serelaxin in acute heart failure patients with renal impairment: results from RELAX-AHF.

BackgroundSerelaxin showed beneficial effects on clinical outcome and trajectories of renal markers in patients with acute heart failure. We aimed to study the interaction between renal function and the treatment effect of serelaxin.MethodsIn the current post hoc analysis of the RELAX-AHF trial, we included all patients with available estimated glomerular filtration rate (eGFR) at baseline (n&nbsp;=&nbsp;1132). Renal impairment was defined as an eGFR &lt;60&nbsp;ml/min/1.73&nbsp;m(2) estimated by creatinine.Results817 (72.2&nbsp;%) patients had a baseline eGFR&nbsp;&lt;60&nbsp;ml/min/1.73&nbsp;m(2). In placebo-treated patients, baseline renal impairment was related to a higher 180&nbsp;day cardiovascular (HR 3.12, 95&nbsp;% CI 1.33-7.30) and all-cause mortality (HR 2.81, 95&nbsp;% CI 1.34-5.89). However, in serelaxin-treated patients, the risk of cardiovascular and all-cause mortality was less pronounced (HR 1.19, 95&nbsp;% CI 0.54 -2.64; p for interaction&nbsp;=&nbsp;0.106, and HR 1.15 95&nbsp;% CI 0.56-2.34 respectively; p for interaction&nbsp;=&nbsp;0.088). In patients with renal impairment, treatment with serelaxin resulted in a more pronounced all-cause mortality reduction (HR 0.53, 95&nbsp;% CI 0.34-0.83), compared with patients without renal impairment (HR 1.30, 95&nbsp;% CI 0.51-3.29).ConclusionRenal dysfunction was associated with higher cardiovascular and all-cause mortality in placebo-treated patients, but not in serelaxin-treated patients. The observed reduction in (cardiovascular) mortality in RELAX-AHF was more pronounced in patients with renal dysfunction. These observations need to be confirmed in the ongoing RELAX-AHF-2 trial