Improved nonparametric estimation of the optimal diagnostic cut‐off point associated with the Youden index under different sampling schemes

A diagnostic cut‐off point of a biomarker measurement is needed for classifying a random subject to be either diseased or healthy. However, the cut‐off point is usually unknown and needs to be estimated by some optimization criteria. One important criterion is the Youden index, which has been widely adopted in practice. The Youden index, which is defined as the maximum of (sensitivity + specificity ?1), directly measures the largest total diagnostic accuracy a biomarker can achieve. Therefore, it is desirable to estimate the optimal cut‐off point associated with the Youden index. Sometimes, taking the actual measurements of a biomarker is very difficult and expensive, while ranking them without the actual measurement can be relatively easy. In such cases, ranked set sampling can give more precise estimation than simple random sampling, as ranked set samples are more likely to span the full range of the population. In this study, kernel density estimation is utilized to numerically solve for an estimate of the optimal cut‐off point. The asymptotic distributions of the kernel estimators based on two sampling schemes are derived analytically and we prove that the estimators based on ranked set sampling are relatively more efficient than that of simple random sampling and both estimators are asymptotically unbiased. Furthermore, the asymptotic confidence intervals are derived. Intensive simulations are carried out to compare the proposed method using ranked set sampling with simple random sampling, with the proposed method outperforming simple random sampling in all cases. A real data set is analyzed for illustrating the proposed method.     

An adaptive bivariate kernel smoothing method for determining instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae

1. In insects, instar determination is generally based on the frequency distribution of sclerotised body part measurements. Commonly used univariate methods, such as histograms and univariate kernel smoothing, are not sufficient to reflect the distribution of the measurements, because development of sclerotised body parts is multidimensional. 2. This study used an adaptive bivariate kernel smoothing method, based on 10 pairs of separating variables, to differentiate instars of Austrosimulium tillyardianum (Diptera: Simuliidae) larvae in two‐dimensional space. A variable bandwidth matrix was used and separation lines between instars were defined. Using the Crosby growth ratio, Brooks' rule and the new standard recently proposed, larvae were separated into nine instars. It was found that, using the bivariate kernel smoothing method, the clustering accuracy and determination of separation lines as instar class limits were higher than those associated with the univariate kernel smoothing method. With the exceptions of the paired separating variables, head capsule length and antennal segment 3 length (AS3L), the mean probabilities of correct classifications was > 85%. The pair of separating variables that yielded the greatest classification accuracy comprised mandible length (ML) and AS3L, which had mean probabilities of 0.8984. The clustering accuracy was higher for early‐ and late‐instar larvae, but lower for instars 6 and 7. The adaptive bivariate kernel smoothing method was better than univariate methods for instar determination, especially in the detection of divisions between instars and identification of a larval instar.     

Classification of Trends Via the Linear State Space Model

A method is presented for classification of trend curves based on the linear state space model. In this approach information about the smoothness of the trend curves is incorporated into the classification model by a nonstationary stochastic trend model and can thereby be used to obtain a better classification. In the case of small data sets the performance of the classification is significantly improved in comparison with the usual cluster analysis. Maximum likelihood estimation can be used to calculate the parameters of this model and to determine the classification. The classification algorithm is described in detail and the results are compared to those of the usual cluster analysis by simulation studies and by an application to tree ring data.     

Variable selection for the single-index model

We consider variable selection in the single-index model. Weprove that the popular leave-m-out crossvalidation method hasdifferent behaviour in the single-index model from that in linearregression models or nonparametric regression models. A newconsistent variable selection method, called separated crossvalidation,is proposed. Further analysis suggests that the method has betterfinite-sample performance and is computationally easier thanleave-m-out crossvalidation. Separated crossvalidation, appliedto the Swiss banknotes data and the ozone concentration data,leads to single-index models with selected variables that havebetter prediction capability than models based on all the covariates.     

Multidimensional adaptive P-splines with application to neurons' activity studies

The receptive field (RF) of a visual neuron is the region of the space that elicits neuronal responses. It can be mapped using different techniques that allow inferring its spatial and temporal properties. Raw RF maps (RFmaps) are usually noisy, making it difficult to obtain and study important features of the RF. A possible solution is to smooth them using P-splines. Yet, raw RFmaps are characterized by sharp transitions in both space and time. Their analysis thus asks for spatiotemporal adaptive P-spline models, where smoothness can be locally adapted to the data. However, the literature lacks proposals for adaptive P-splines in more than two dimensions. Furthermore, the extra flexibility afforded by adaptive P-spline models is obtained at the cost of a high computational burden, especially in a multidimensional setting. To fill these gaps, this work presents a novel anisotropic locally adaptive P-spline model in two (e.g., space) and three (space and time) dimensions. Estimation is based on the recently proposed SOP (Separation of Overlapping Precision matrices) method, which provides the speed we look for. Besides the spatiotemporal analysis of the neuronal activity data that motivated this work, the practical performance of the proposal is evaluated through simulations, and comparisons with alternative methods are reported.