Kernel Estimation of Rate Function for Recurrent Event Data

Recurrent event data are largely characterized by the rate function but smoothing techniques for estimating the rate function have never been rigorously developed or studied in statistical literature. This paper considers the moment and least squares methods for estimating the rate function from recurrent event data. With an independent censoring assumption on the recurrent event process, we study statistical properties of the proposed estimators and propose bootstrap procedures for the bandwidth selection and for the approximation of confidence intervals in the estimation of the occurrence rate function. It is identified that the moment method without resmoothing via a smaller bandwidth will produce curve with nicks occurring at the censoring times, whereas there is no such problem with the least squares method. Furthermore, the asymptotic variance of the least squares estimator is shown to be smaller under regularity conditions. However, in the implementation of the bootstrap procedures, the moment method is computationally more efficient than the least squares method because the former approach uses condensed bootstrap data. The performance of the proposed procedures is studied through Monte Carlo simulations and an epidemiological example on intravenous drug users.

Accurate and robust reconstruction of proximal femur from sparse intraoperative data and dense point distribution model for surgical navigation

Constructing a 3D surface model from sparse-point data is a nontrivial task. Here, we report an accurate and robust approach for reconstructing a surface model of the proximal femur from sparse-point data and a dense-point distribution model (DPDM). The problem is formulated as a three-stage optimal estimation process. The first stage, affine registration, is to iteratively estimate a scale and a rigid transformation between the mean surface model of the DPDM and the sparse input points. The estimation results of the first stage are used to establish point correspondences for the second stage, statistical instantiation, which stably instantiates a surface model from the DPDM using a statistical approach. This surface model is then fed to the third stage, kernel-based deformation, which further refines the surface model. Handling outliers is achieved by consistently employing the least trimmed squares (LTS) approach with a roughly estimated outlier rate in all three stages. If an optimal value of the outlier rate is preferred, we propose a hypothesis testing procedure to automatically estimate it. We present here our validations using four experiments, which include 1 leave-one-out experiment, 2 experiment on evaluating the present approach for handling pathology, 3 experiment on evaluating the present approach for handling outliers, and 4 experiment on reconstructing surface models of seven dry cadaver femurs using clinically relevant data without noise and with noise added. Our validation results demonstrate the robust performance of the present approach in handling outliers, pathology, and noise. An average 95-percentile error of 1.7-2.3 mm was found when the present approach was used to reconstruct surface models of the cadaver femurs from sparse-point data with noise added.

Evaluating northern hardwood management using retrospective analysis and diameter distributions

Northern hardwood management was assessed throughout the state of Michigan using data collected on recently harvested stands in 2010 and 2011. Methods of forensic estimation of diameter at breast height were compared and an ideal, localized equation form was selected for use in reconstructing pre-harvest stand structures. Comparisons showed differences in predictive ability among available equation forms which led to substantial financial differences when used to estimate the value of removed timber. Management on all stands was then compared among state, private, and corporate landowners. Comparisons of harvest intensities against a liberal interpretation of a well-established management guideline showed that approximately one third of harvests were conducted in a manner which may imply that the guideline was followed. One third showed higher levels of removals than recommended, and one third of harvests were less intensive than recommended. Multiple management guidelines and postulated objectives were then synthesized into a novel system of harvest taxonomy, against which all harvests were compared. This further comparison showed approximately the same proportions of harvests, while distinguishing sanitation cuts and the future productive potential of harvests cut more intensely than suggested by guidelines. Stand structures are commonly represented using diameter distributions. Parametric and nonparametric techniques for describing diameter distributions were employed on pre-harvest and post-harvest data. A common polynomial regression procedure was found to be highly sensitive to the method of histogram construction which provides the data points for the regression. The discriminative ability of kernel density estimation was substantially different from that of the polynomial regression technique.

Using contingent valuation to estimate willingness to pay for improved water source in rural Uganda

This research was conducted in August of 2011 in the villages of Kigisu and Rubona in rural Uganda while the author was serving as a community health volunteer with the U.S. Peace Corps. The study used the contingent valuation method (CVM) to estimate the populations’ willingness to pay (WTP) for the operation and maintenance of an improved water source. The survey was administered to 122 households out of 400 in the community, gathering demographic information, health and water behaviors, and using an iterative bidding process to estimate WTP. Households indicated a mean WTP of 286 Ugandan Shillings (UGX) per 20 liters for a public tap and 202 UGX per 20 liters from a private tap. The data were also analyzed using an ordered probit model. It was determined that the number of children in the home, and the distance from the existing source were the primary variables influencing households’ WTP.

What do case-control studies estimate? Survey of methods and assumptions in published case-control research

To evaluate strategies used to select cases and controls and how reported odds ratios are interpreted, the authors examined 150 case-control studies published in leading general medicine, epidemiology, and clinical specialist journals from 2001 to 2007. Most of the studies (125/150; 83%) were based on incident cases; among these, the source population was mostly dynamic (102/125; 82%). A minority (23/125; 18%) sampled from a fixed cohort. Among studies with incident cases, 105 (84%) could interpret the odds ratio as a rate ratio. Fifty-seven (46% of 125) required the source population to be stable for such interpretation, while the remaining 48 (38% of 125) did not need any assumptions because of matching on time or concurrent sampling. Another 17 (14% of 125) studies with incident cases could interpret the odds ratio as a risk ratio, with 16 of them requiring the rare disease assumption for this interpretation. The rare disease assumption was discussed in 4 studies but was not relevant to any of them. No investigators mentioned the need for a stable population. The authors conclude that in current case-control research, a stable exposure distribution is much more frequently needed to interpret odds ratios than the rare disease assumption. At present, investigators conducting case-control studies rarely discuss what their odds ratios estimate.

EFFECT OF ELECTRICAL DISCHARGE PATTERN ON SPARK IGNITED FLAME KERNEL DEVELOPMENT

Fuel-lean combustion and exhaust gas recirculation (EGR) in spark ignition engines improve engine efficiency and reduce emission. However, flame initiation becomes more difficult in lean and dilute fuel-air mixture with traditional spark discharge. This research proposal will first provide an intensive review on topics related to spark ignition including properties of electrical discharge, flame kernel behavior and spark ignition modeling and simulation. Focus will be laid on electrical discharge pattern effect as it is showing prospect in extending ignition limits in SI engines. An experimental setup has been built with an optically accessible constant volume combustion vessel. Multiple imaging techniques as well as spectroscopy will be applied. By varying spark discharge patterns, preliminary test results are available on consequent flame kernel development. In addition to experimental investigation of spark plasma and flame kernel development, spark ignition modeling with detailed description of plasma channel is also proposed for this study.