Dynamic logistic state space prediction model for clinical decision making

Prediction modeling for clinical decision making is of great importance and needed to be updated frequently with the changes of patient population and clinical practice. Existing methods are either done in an ad hoc fashion, such as model recalibration or focus on studying the relationship between predictors and outcome and less so for the purpose of prediction. In this article, we propose a dynamic logistic state space model to continuously update the parameters whenever new information becomes available. The proposed model allows for both time-varying and time-invariant coefficients. The varying coefficients are modeled using smoothing splines to account for their smooth trends over time. The smoothing parameters are objectively chosen by maximum likelihood. The model is updated using batch data accumulated at prespecified time intervals, which allows for better approximation of the underlying binomial density function. In the simulation, we show that the new model has significantly higher prediction accuracy compared to existing methods. We apply the method to predict 1 year survival after lung transplantation using the United Network for Organ Sharing data.     

Shape-space smoothing splines for planar landmark data

A method is developed for fitting smooth curves through a seriesof shapes of landmarks in two dimensions using unrolling andunwrapping procedures in Riemannian manifolds. An explicit methodof calculation is given which is analogous to that of Jupp &Kent (1987) for spherical data. The resulting splines are calledshape-space smoothing splines. The method resembles that offitting smoothing splines in real spaces in that, if the smoothingparameter is zero, the resulting curve interpolates the datapoints, and if it is infinitely large the curve is a geodesicline. The fitted path to the data is defined such that its unrolledversion at the tangent space of the starting point is a cubicspline fitted to the unwrapped data with respect to that path.Computation of the fitted path consists of an iterative procedurewhich converges quickly, and the resulting path is given ina discretised form in terms of a piecewise geodesic path. Theprocedure is applied to the analysis of some human movementdata, and a test for the appropriateness of a mean geodesiccurve is given.     

Estimates of the genetic parameters of turkey body weight using random regression analysis

Random regression (RR) analysis has been recommended to estimate the genetic parameters of longitudinal data. The objective of this study was to evaluate the growth of turkeys using RR models. Data were collected from 957 turkeys and included 15,478 individual body weight recorded during the first week of life and between weeks 2 and 32 by 2-week intervals. To take into account the repeated measurements of weight for each animal, a specific overall growth curve was modelled using a cubic smoothing spline. Animal deviation to this curve was also modelled using an RR function. All data were analysed with the ASReml package. The results showed an increase in heritability estimates over the trajectory and peaked at 0.60 around 20 to 32 weeks of age. Genetic correlations showed that turkeys could be selected at earlier time points, at 12 weeks of age, in order to increase the growth rate. In general, genetic correlation estimates were higher among adjacent ages, decreasing markedly with the increase of distance between ages. Negative genetic correlations were observed between ages.     

采用三次样条拟合胎儿体格发育指标百分位数参考值

目的:生长发育评价标准的最佳形式是年龄别百分位数,然而,目前我国缺乏胎儿的孕周别体格发育指标百分位数评价标准,影响了胎儿宫内生长发育水平的准确评价,本研究拟建立陕西省正常单胎妊娠孕妇胎儿体格发育指标百分位数参考标准。方法:以陕西省西安、汉中、延安5所大型综合医院超声科或妇产科超声室为数据采集点,选择2010-01-01到2010-12-31间进行常规孕期检查的正常单胎妊娠胎儿的超声测量数据,随机抽取一次测量结果,共收集到6832个单胎正常妊娠胎儿的超声测量数据。采用三次样条法对陕西省孕16-41周正常单胎妊娠胎儿的双顶径、腹围、股骨长百分位数进行拟合。结果:三次样条拟合胎儿的双顶径、腹围、股骨长百分位数,各百分位数的决定系数均在0.95以上,均方差均在各指标重复测量的容许误差内,拟合结果满意。计算出了胎儿的孕周别双顶径、腹围、股骨长的P3、P10、P25、P50、P75、P90、P97百分位数。结论:三次样条兼顾了曲线拟合中的拟合优度和光滑度,能更好的实现曲线拟合的目的。所建立的孕周别胎儿体格发育指标百分位数符合胎儿宫内生长发育规律,为胎儿宫内生长发育的准确评价提供了科学、准确的评价工具,可用于产科临床和研究工作中。     

Critical note on the application of the “two-third” spline

The “two-third spline” (2/3S) is a frequently applied method to detrend tree-ring series. It fits a spline with a 50% frequency cutoff at a frequency equal to two-thirds of each sample length in a dataset. It was introduced to ensure a minimum loss of low-frequency variance, which is resolvable during the detrending of ring-width series.In this paper I show potential problems that arise when rusing this method. The 2/3S runs counter the strengths of using a digital filter to detrend – i.e. one is giving up full control over the frequency-removing characteristics of the growth curve and each individual time series retains a different amount of low frequency. Thus, the 2/3S is less suitable for reconstructing climate or to compare environmental impacts on tree growth between groups – both of which comprise the majority of dendrochronological analyses – as it will likely introduce a temporal frequency bias. Within a long chronology it will result in decreasing power to resolve low frequencies towards present in a living-only trees setting, especially when the youngest segment lengths are 100 years and shorter, and more generally during the period where the chronology is constructed from samples with shorter segment lengths compared to the period with longer segment lengths. The frequency bias will also significantly impact regression slopes and correlation coefficients, possibly distorting analyses investigating multiple groups with different mean segment lengths. Highlighting these potential biases, I recommend the community to not use this method on an individual basis but rather to use a fixed spline stiffness for all samples based on the n% criterion (n = 67) of e.g. the mean segment length of the entire dataset.     

The effect of end-point adjustments on smoothing splines used for tree-ring standardization

The cubic smoothing spline has been a popular method for detrending tree-ring data since the 1980s. The common implementation of this procedure (e.g., ARSTAN, dplR) uses a unique method for determining the smoothing parameter that is widely known as the %n criterion. However, this smoothing parameter selection method carries the assumption that end point effects are ignorable. In this paper, we complete the mathematical derivation and show how the original method differs from the complete version, both in the interpretation of the smoothing parameter and in the spline fit. Frequency response curves (FRC) demonstrate how the smoothing parameter is affected by the original assumption. For example, the FRC results indicate that a tree core of 250-year length has a 14% difference in the cut-off frequency when looking at the 67%n criterion. The FRC analysis shows that the existing approach produces a more flexible fit than anticipated, i.e., it is removing more variance than previously thought. For example, a 67%n spline under the existing approach corresponds to a 53%n spline fit. By using both simulated tree-core sequences and a dataset from a Midwest forest, we discuss which conditions result in greater differences between the spline fits and which conditions will have small differences. Tree-core sequences that have more curvature, such as a large-amplitude growth release, will lead to greater differences. Finally, we provide approximations to the end-point effect procedure. For example, using an 83%n criterion under the original approach produces a spline fit approximating the 67%n fit under the complete approach. These approximations could be easily implemented within existing programs like ARSTAN.     

Semiparametric regression for periodic longitudinal hormone data from multiple menstrual cycles

We consider semiparametric regression for periodic longitudinal data. Parametric fixed effects are used to model the covariate effects and a periodic nonparametric smooth function is used to model the time effect. The within-subject correlation is modeled using subject-specific random effects and a random stochastic process with a periodic variance function. We use maximum penalized likelihood to estimate the regression coefficients and the periodic nonparametric time function, whose estimator is shown to be a periodic cubic smoothing spline. We use restricted maximum likelihood to simultaneously estimate the smoothing parameter and the variance components. We show that all model parameters can be easily obtained by fitting a linear mixed model. A common problem in the analysis of longitudinal data is to compare the time profiles of two groups, e.g., between treatment and placebo. We develop a scaled chi-squared test for the equality of two nonparametric time functions. The proposed model and the test are illustrated by analyzing hormone data collected during two consecutive menstrual cycles and their performance is evaluated through simulations.     

Two-stage functional mixed models for evaluating the effect of longitudinal covariate profiles on a scalar outcome

The Daily Hormone Study, a substudy of the Study of Women's Health Across the Nation (SWAN) consisting of more than 600 pre- and perimenopausal women, includes a scalar measure of total hip bone mineral density (BMD) together with repeated measures of creatinine-adjusted follicle stimulating hormone (FSH) assayed from daily urine samples collected over one menstrual cycle. It is of scientific interest to investigate the effect of the FSH time profile during a menstrual cycle on total hip BMD, adjusting for age and body mass index. The statistical analysis is challenged by several features of the data: (1) the covariate FSH is measured longitudinally and its effect on the scalar outcome BMD may be complex; (2) due to varying menstrual cycle lengths, subjects have unbalanced longitudinal measures of FSH; and (3) the longitudinal measures of FSH are subject to considerable among- and within-subject variations and measurement errors. We propose a measurement error partial functional linear model, where repeated measures of FSH are modeled using a functional mixed effects model and the effect of the FSH time profile on BMD is modeled using a partial functional linear model by treating the unobserved true subject-specific FSH time profile as a functional covariate. We develop a two-stage nonparametric regression calibration method using period smoothing splines. Using the connection between smoothing splines and mixed models, we show that a key feature of our approach is that estimation at both stages can be conveniently cast into a unified mixed model framework. A simple testing procedure for constant functional covariate effect is also proposed. The proposed methods are evaluated using simulation studies and applied to the SWAN data.     

Estimating the accuracy of polymerase chain reaction-based tests using endpoint dilution

Polymerase chain reaction (PCR)-based tests for various microorganisms or target DNA sequences are generally acknowledged to be highly "sensitive," yet the concept of sensitivity is ill-defined in the literature on these tests. We propose that sensitivity should be expressed as a function of the number of target DNA molecules in the sample (or specificity, when the target number is 0). However, estimating this "sensitivity curve" is problematic, since it is difficult to construct samples with a fixed number of targets. Nonetheless, using serially diluted replicate aliquots of a known concentration of the target DNA sequence, we show that it is possible to disentangle random variations in the number of target DNA molecules from the underlying test sensitivity. We develop parametric, nonparametric, and semiparametric (spline-based) models for the sensitivity curve. The methods are compared on a new test for M. genitalium.     

The effects of fragmentation and disturbance of rainforest on ground-dwelling small mammals on the Robertson Plateau, New South Wales, Australia

We surveyed ground-dwelling small mammals in twenty-four rainforest remnants which were virtual islands surrounded by farmland on a plateau on the east coast of Australia. We investigated the effect of island size, level of disturbance, isolation and microhabitat on the abundance and species richness of the mammals. The remnants ranged from 0.3 to 29 ha, resulting from fragmentation during 175 years of European occupation. Two rodent species (Rattus fuscipes[Waterhouse, 1839] and R. rattus[Linnaeus, 1758] ) and one marsupial insectivore (Antechinus stuartii Macleay, 1841) were trapped in these remnants, with an additional species (A. swainsonii[Waterhouse, 1840] ) several kilometres away in rainforest on the escarpment of the plateau. Small-mammal species richness was low, but the native species (R. fuscipes and A. stuartii) were abundant. Three-way analyses of variance demonstrated that species richness and abundance decreased significantly with decreasing remnant size and increasing disturbance, but showed no distance effect. The abundance and richness of native species responded even more significantly. The interaction between the first two effects is important. Small remnants are affected most detrimentally by increasing disturbance, large remnants are less affected, and medium sized remnants show intermediate effects. The introduced R. rattus which was least abundant in large remnants, but more abundant in distant than near remnants, was also more abundant in those with major disturbance. The single most important variable in step-wise, multiple linear regression analyses was the logarithm of remnant area not influenced by edge effects, explaining 39% of the variance in species richness, 57% for native species richness and 46% for A. stuartii abundance. Disturbance related variables additionally contributed from 12 to 30% of the variance in dependent variables, while habitat variables explained between 22 and 48% of the variance, and accounted for two thirds of the explainable variance in R. fuscipes abundance. The implications of our results for wildlife conservation on the plateau are discussed.     

On partial local smoothing rules for curve estimation

We compare the performances of local and global rules for smoothingparameter choice, in terms of asymptotic mean squared errorsof the resulting estimators. In some instances there is surprisinglylittle to choose between local and global approaches; our analysisidentifies contexts where the differences are small or large.This work motivates development of smoothing rules that forma ‘half-way house’ between local and global smoothing.There, interpolation provides a basis for partial local smoothing.A key result shows that interpolation on even a coarse gridcan produce a very good approximation to full local smoothing.Our theoretical and numerical results lead us to suggest linearinterpolation of a bandwidth obtained by integral approximationson discrete intervals.     

How Well do Foragers Protect Food Consumption? Panel Evidence from a Native Amazonian Society in Bolivia

The ability of rural people to protect their food consumption matters because it captures their economic vulnerability. How well do foragers protect consumption from adverse income shocks and does protection work equally well for all people in the household? We answer the queries with data from 156 adults and 169 children collected over five consecutive quarters from the Tsimane’, a native Amazonian society of foragers and farmers in Bolivia. We estimate whether quarterly changes in the logarithm of consumption bear an association with quarterly changes in the logarithm of cash income while controlling for many confounders, including covariant shocks. We use anthropometric indices of short-run nutritional status to proxy for food consumption and use instrumental variables to abate biases from the endogeneity of income. We found that child consumption was fully protected from income growth, but adult consumption was not as well protected. Estimates of income elasticities of consumption fell toward the lower range of estimates from previous studies of farming and industrial societies. We present several hypotheses to explain how the Tsimane’ smooth consumption.     

Comparing three methods for variance estimation with duplicated high density oligonucleotide arrays

Microarray experiments are being increasingly used in molecular biology. A common task is to detect genes with differential expression across two experimental conditions, such as two different tissues or the same tissue at two time points of biological development. To take proper account of statistical variability, some statistical approaches based on the t-statistic have been proposed. In constructing the t-statistic, one needs to estimate the variance of gene expression levels. With a small number of replicated array experiments, the variance estimation can be challenging. For instance, although the sample variance is unbiased, it may have large variability, leading to a large mean squared error. For duplicated array experiments, a new approach based on simple averaging has recently been proposed in the literature. Here we consider two more general approaches based on nonparametric smoothing. Our goal is to assess the performance of each method empirically. The three methods are applied to a colon cancer data set containing 2,000 genes. Using two arrays, we compare the variance estimates obtained from the three methods. We also consider their impact on the t-statistics. Our results indicate that the three methods give variance estimates close to each other. Due to its simplicity and generality, we recommend the use of the smoothed sample variance for data with a small number of replicates. Electronic Publication     

Nonparametric inference for local extrema with application to oligonucleotide microarray data in yeast genome

Identifying local extrema of expression profiles is one primary objective in some cDNA microarray experiments. To study the replication dynamics of the yeast genome, for example, local peaks of hybridization intensity profiles correspond to putative replication origins. We propose a nonparametric kernel smoothing (NKS) technique to detect local hybridization intensity extrema across chromosomes. The novelty of our approach is that we base our inference procedures on equilibrium points, namely those locations at which the first derivative of the intensity curve is zero. The proposed smoothing technique provides both point and interval estimation for the location of local extrema. Also, this technique can be used to test for the hypothesis of either one or multiple suspected locations being the true equilibrium points. We illustrate the proposed method on a microarray data set from an experiment designed to study the replication origins in the yeast genome, in that the locations of autonomous replication sequence (ARS) elements are identified through the equilibrium points of the smoothed intensity profile curve. Our method found a few ARS elements that were not detected by the current smoothing methods such as the Fourier convolution smoothing.     

Functional mixed-effects model for periodic data

Periodic data are frequently collected in biomedical experiments. We consider the underlying periodic curves giving rise to these data, and account for the periodicity in their functional model to improve estimation and inference. We propose to incorporate the periodic constraint in the functional mixed-effects model setting. Both the fixed functional effects and random functional effects are modeled in the same periodic functional space, hence the population-average estimates and subject-specific predictions are all periodic. An efficient algorithm is given to estimate the proposed model by an O(N) modified Kalman filtering and smoothing algorithm. The proposed method is evaluated in different scenarios through simulations. Treatments to none-full period data and missing observations along the period are also given. Analysis of a cortisol data set obtained from a study on fibromyalgia is conducted as illustration.