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.     

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.     

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.     

Extensions of the Penalized Spline of Propensity Prediction Method of Imputation

Summary .  Little and An (2004,  Statistica Sinica   14, 949–968) proposed a penalized spline of propensity prediction (PSPP) method of imputation of missing values that yields robust model-based inference under the missing at random assumption. The propensity score for a missing variable is estimated and a regression model is fitted that includes the spline of the estimated logit propensity score as a covariate. The predicted unconditional mean of the missing variable has a double robustness (DR) property under misspecification of the imputation model. We show that a simplified version of PSPP, which does not center other regressors prior to including them in the prediction model, also has the DR property. We also propose two extensions of PSPP, namely, stratified PSPP and bivariate PSPP, that extend the DR property to inferences about conditional means. These extended PSPP methods are compared with the PSPP method and simple alternatives in a simulation study and applied to an online weight loss study conducted by Kaiser Permanente.     

Time-varying-response smoothing

Cubic smoothing splines with a fixed-period response are used widely in producing “expected” growth curves for ring-width and density data in dendroclimatology. A simple modification to the procedure which generates these splines enables the use of a smoothing spline with a user-specified, time-varying flexibility and hence time-varying-response characteristics. The revised procedure is presented here, along with different examples of its application in the context of Regional Curve Standardisation (RCS). The ability to generate a smoothing spline with time-dependent flexibility may have wider application in tree-ring studies.     

Endocranial volume of Australopithecus africanus: new CT-based estimates and the effects of missing data and small sample size

Estimation of endocranial volume in Australopithecus africanus is important in interpreting early hominin brain evolution. However, the number of individuals available for investigation is limited and most of these fossils are, to some degree, incomplete and/or distorted. Uncertainties of the required reconstruction (‘missing data uncertainty’) and the small sample size (‘small sample uncertainty’) both potentially bias estimates of the average and within-group variation of endocranial volume in A. africanus.We used CT scans, electronic preparation (segmentation), mirror-imaging and semilandmark-based geometric morphometrics to generate and reconstruct complete endocasts for Sts 5, Sts 60, Sts 71, StW 505, MLD 37/38, and Taung, and measured their endocranial volumes (EV). To get a sense of the reliability of these new EV estimates, we then used simulations based on samples of chimpanzees and humans to: (a) test the accuracy of our approach, (b) assess missing data uncertainty, and (c) appraise small sample uncertainty.Incorporating missing data uncertainty of the five adult individuals, A. africanus was found to have an average adult endocranial volume of 454-461 ml with a standard deviation of 66-75 ml. EV estimates for the juvenile Taung individual range from 402 to 407 ml. Our simulations show that missing data uncertainty is small given the missing portions of the investigated fossils, but that small sample sizes are problematic for estimating species average EV. It is important to take these uncertainties into account when different fossil groups are being compared.     

Zum Konkurrenzverhalten von Mischverunkrautungen bei Wintergerste in Abhängigkeit von ökologischen Bedingungen

Mechanisms of insecticide and acaricide resistance are, as a rule, inherited as single autosomal genes. Pesticide‐treated pest populations with established resistance mechanisms mostly consist of both susceptible and resistant individuals. For practical purposes determination of the level of resistance (percent of resistant individuals) is more informative than the resistance degree. A method of spline regression analysis is presented allowing the evaluation of the status of resistance by calculating bioassay data.     

Model selection for Cox models with time-varying coefficients

Summary Cox models with time-varying coefficients offer great flexibility in capturing the temporal dynamics of covariate effects on right-censored failure times. Because not all covariate coefficients are time varying, model selection for such models presents an additional challenge, which is to distinguish covariates with time-varying coefficient from those with time-independent coefficient. We propose an adaptive group lasso method that not only selects important variables but also selects between time-independent and time-varying specifications of their presence in the model. Each covariate effect is partitioned into a time-independent part and a time-varying part, the latter of which is characterized by a group of coefficients of basis splines without intercept. Model selection and estimation are carried out through a fast, iterative group shooting algorithm. Our approach is shown to have good properties in a simulation study that mimics realistic situations with up to 20 variables. A real example illustrates the utility of the method.     

Quadratic inference functions for varying-coefficient models with longitudinal data

Nonparametric smoothing methods are used to model longitudinal data, but the challenge remains to incorporate correlation into nonparametric estimation procedures. In this article, we propose an efficient estimation procedure for varying-coefficient models for longitudinal data. The proposed procedure can easily take into account correlation within subjects and deal directly with both continuous and discrete response longitudinal data under the framework of generalized linear models. The proposed approach yields a more efficient estimator than the generalized estimation equation approach when the working correlation is misspecified. For varying-coefficient models, it is often of interest to test whether coefficient functions are time varying or time invariant. We propose a unified and efficient nonparametric hypothesis testing procedure, and further demonstrate that the resulting test statistics have an asymptotic chi-squared distribution. In addition, the goodness-of-fit test is applied to test whether the model assumption is satisfied. The corresponding test is also useful for choosing basis functions and the number of knots for regression spline models in conjunction with the model selection criterion. We evaluate the finite sample performance of the proposed procedures with Monte Carlo simulation studies. The proposed methodology is illustrated by the analysis of an acquired immune deficiency syndrome (AIDS) data set.     

High Prepregnancy BMI Increases the Risk of Postpartum Anemia

Objective: To assess the independent effect of prepregnancy BMI on the risk of postpartum anemia. Research Methods and Procedures: Pregnant women from North Carolina who enrolled in the Iron Supplementation Study at their first prenatal visit at <20 weeks gestation and who delivered a live infant were followed to the postpartum visit (n = 439). BMI had a curvilinear relation in the logit of postpartum anemia; therefore, a restricted quadratic spline with three knots at the inflection points was used to specify BMI. Multiple log binomial regression was used to quantify the relation between prepregnancy BMI and postpartum anemia after adjusting for maternal ethnicity/race, education, smoking, initial hemoglobin concentration, and prenatal iron supplementation. Results: Prevalence of postpartum anemia was 19.1%. After adjusting for confounders, we found that risk of postpartum anemia was similar for women with BMI values from 17 to 24 compared with women with a BMI of 20. Adjusted relative risk increased as BMI increased from 24 to 38. Women with a BMI of 28 had ～1.8 times the postpartum anemia risk of a woman with a BMI of 20 (95% confidence interval 1.3, 2.5), and obese women with a BMI of 36 had ～2.8 times the risk (95% confidence interval 1.7, 4.7). Discussion: These data suggest that high prepregnancy BMI substantially increases the risk of postpartum anemia. Postpartum anemia screening and iron supplementation of overweight and obese women may be warranted.     

Quantitative assessment of the accuracy for three interpolation techniques in kinematic analysis of human movement

Marker obstruction during human movement analyses requires interpolation to reconstruct missing kinematic data. This investigation quantifies errors associated with three interpolation techniques and varying interpolated durations. Right ulnar styloid kinematics from 13 participants performing manual wheelchair ramp ascent were reconstructed using linear, cubic spline and local coordinate system (LCS) interpolation from 11–90% of one propulsive cycle. Elbow angles (flexion/extension and pronation/supination) were calculated using real and reconstructed kinematics. Reconstructed kinematics produced maximum elbow flexion/extension errors of 37.1 (linear), 23.4 (spline) and 9.3 (LCS) degrees. Reconstruction errors are unavoidable [minimum errors of 6.7 mm (LCS); 0.29 mm (spline); 0.42 mm (linear)], emphasising careful motion capture system setup must be performed to minimise data interpolation. For the observed movement, LCS-based interpolation (average error of 14.3 mm; correlation of 0.976 for elbow flexion/extension) was most suitable for reconstructing durations longer than 200 ms. Spline interpolation was superior for shorter durations.     

使用线性微分方程构建初步的乳腺癌转移相关基因网络模型

随着基因芯片的技术的推广,越来越多的表达数据需要被处理和分析．利用这些表达数据提取基因调控矩阵从而构建基因网络是一个重要的问题．通过线性微分方程模型可以初步构建基因网络,了解网络结构,提取最显著的信息．然而由于分子生物学的条件限制或者数据来源的限制,导致实验数据不充分,使方程组无解．本文使用三次样条方法,对26例临床、病理资料完备的具有淋巴结转移的乳腺癌基因表达数据进行插值处理,使表达数据满秩,从而使用最小二乘法解出加权矩阵,构建初步的表达基因调控网络．通过对构建的基因网络的初步分析表明:乳腺癌转移的形成是由多基因异常引起多条传导通路异常,致使细胞恶性转化的结果,这与生物学上公认的看法是相一致的．因此,利用此线性模型方法对基因表达谱进行分析兵有一定可行性,在认识乳腺癌转移机制,乳腺癌诊断和治疗方面具有一定的理论和应用价值．     

Joint model of recurrent events and a terminal event with time‐varying coefficients

Joint modeling of recurrent events and a terminal event has been studied extensively in the past decade. However, most of the previous works assumed constant regression coefficients. This paper proposes a joint model with time‐varying coefficients in both event components. The proposed model not only accommodates the correlation between the two type of events, but also characterizes the potential time‐varying covariate effects. It is especially useful for evaluating long‐term risk factors' effect that could vary with time. A Gaussian frailty is used to model the correlation between event times. The nonparametric time‐varying coefficients are modeled using cubic splines with penalty terms. A simulation study shows that the proposed estimators perform well. The model is used to analyze the readmission rate and mortality jointly for stroke patients admitted to Veterans Administration (VA) Hospitals.     

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.     

Geometric morphometrics in entomology: Basics and applications

The recent expansion of a variety of morphometric tools has brought about a revolution in the comparison of morphology in the context of the size and shape in various fields including entomology. First, an overview of the theoretical issues of geometric morphometrics is presented with a caution about the usage of traditional morphometric measurements. Second, focus is then placed on two broad approaches as tools for geometric morphometrics; that is, the landmark‐based and the outline‐based approaches. A brief outline of the two methodologies is provided with some important cautions. The increasing trend of entomological studies in using the procedures of geometric morphometrics is then summarized. Finally, information is provided on useful toolkits such as computer software as well as codes and packages of the R statistical software that could be used in geometric morphometrics.     

A geometric morphometric analysis of the shape of the first upper molar in mice of the genus Mus (Muridae, Rodentia)

Phenotypic variation in the shape of the first upper molar among 595 mice, representing nine extant and three extinct taxa of the genus Mus , was studied with thin-plate spline analysis. The reliability of classification of individual specimens into known groups based on their molars varied from 75 to 100%, depending on group and method used. Including 13 sliding semilandmarks to the analysis improved the detection of different kinds of size and shape variation as well as visualization of shape differences between studied groups. Correlation between phylogenetic and morphometric distances suggested about 80% contribution of phylogenetic inertia to the molar shape variation; moreover, the importance of localized versus global shape changes was similar in the detection of phylogenetic signals. Finally, shape changes along individual evolutionary lineages were revealed, suggesting a few cases of reversals, convergence and/or retention of ancestral shape. The evolution of mouse molars has thus been driven by random effects of drift together with stabilizing selection and convergence.     

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。