Simple Estimators of the Intensity of Seasonal Occurrence

Background: Edwards's method is a widely used approach for fitting a sine curve to a time-series of monthly frequencies. From this fitted curve, estimates of the seasonal intensity of occurrence (i.e., peak-to-low ratio of the fitted curve) can be generated. Methods: We discuss various approaches to the estimation of seasonal intensity assuming Edwards's periodic model, including maximum likelihood estimation (MLE), least squares, weighted least squares, and a new closed-form estimator based on a second-order moment statistic and non-transformed data. Through an extensive Monte Carlo simulation study, we compare the finite sample performance characteristics of the estimators discussed in this paper. Finally, all estimators and confidence interval procedures discussed are compared in a re-analysis of data on the seasonality of monocytic leukemia. Results: We find that Edwards's estimator is substantially biased, particularly for small numbers of events and very large or small amounts of seasonality. For the common setting of rare events and moderate seasonality, the new estimator proposed in this paper yields less finite sample bias and better mean squared error than either the MLE or weighted least squares. For large studies and strong seasonality, MLE or weighted least squares appears to be the optimal analytic method among those considered. Conclusion: Edwards's estimator of the seasonal relative risk can exhibit substantial finite sample bias. The alternative estimators considered in this paper should be preferred

A Semiparametric Model Selection Criterion with Applications to the Marginal Structural Model

Estimators for the parameter of interest in semiparametric models often depend on a guessed model for the nuisance parameter. The choice of the model for the nuisance parameter can affect both the finite sample bias and efficiency of the resulting estimator of the parameter of interest. In this paper we propose a finite sample criterion based on cross validation that can be used to select a nuisance parameter model from a list of candidate models. We show that expected value of this criterion is minimized by the nuisance parameter model that yields the estimator of the parameter of interest with the smallest mean-squared error relative to the expected value of an initial consistent reference estimator. In a simulation study, we examine the performance of this criterion for selecting a model for a treatment mechanism in a marginal structural model (MSM) of point treatment data. For situations where all possible models cannot be evaluated, we outline a forward/backward model selection algorithm based on the cross validation criterion proposed in this paper and show how it can be used to select models for multiple nuisance parameters. We evaluate the performance of this algorithm in a simulation study of the one-step estimator of the parameter of interest in a MSM where models for both a treatment mechanism and a conditional expectation of the response need to be selected. Finally, we apply the forward model selection algorithm to a MSM analysis of the relationship between boiled water use and gastrointestinal illness in HIV positive men

Identification of causal effects on binary outcomes using structural mean models

Structural mean models (SMMs) were originally formulated to estimate causal effects among those selecting treatment in randomized controlled trials affected by nonignorable noncompliance. It has already been established that SMMs can identify these causal effects in randomized placebo-controlled trials under fairly weak assumptions. SMMs are now being used to analyze other types of study where identification depends on a no effect modification assumption. We highlight how this assumption depends crucially on the unknown causal model that generated the data, and so is difficult to justify. However, we also highlight that, if treatment selection is monotonic, additive and multiplicative SMMs do identify local (or complier) causal effects, but that the double-logistic SMM estimator does not without further assumptions. We clarify the proper interpretation of inferences from SMMs by means of an application and a simulation study. © 2010 The Author

The Madison plasma dynamo experiment: a facility for studying laboratory plasma astrophysics

The Madison plasma dynamo experiment (MPDX) is a novel, versatile, basic plasma research device designed to investigate flow driven magnetohydrodynamic (MHD) instabilities and other high-$\beta$ phenomena with astrophysically relevant parameters. A 3 m diameter vacuum vessel is lined with 36 rings of alternately oriented 4000 G samarium cobalt magnets which create an axisymmetric multicusp that contains $\sim$14 m$^{3}$ of nearly magnetic field free plasma that is well confined and highly ionized $(>50\%)$. At present, 8 lanthanum hexaboride (LaB$_6$) cathodes and 10 molybdenum anodes are inserted into the vessel and biased up to 500 V, drawing 40 A each cathode, ionizing a low pressure Ar or He fill gas and heating it. Up to 100 kW of electron cyclotron heating (ECH) power is planned for additional electron heating. The LaB$_6$ cathodes are positioned in the magnetized edge to drive toroidal rotation through ${\bf J}\times{\bf B}$ torques that propagate into the unmagnetized core plasma. Dynamo studies on MPDX require a high magnetic Reynolds number $Rm > 1000$, and an adjustable fluid Reynolds number $10< Re <1000$, in the regime where the kinetic energy of the flow exceeds the magnetic energy ($M_A^2=($v$/$v$_A)^2 > 1$). Initial results from MPDX are presented along with a 0-dimensional power and particle balance model to predict the viscosity and resistivity to achieve dynamo action.Comment: 14 pages, 13 figure

On a preference‐based instrumental variable approach in reducing unmeasured confounding‐by‐indication

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/110880/1/sim6404.pd

The Wisconsin Plasma Astrophysics Laboratory

The Wisconsin Plasma Astrophysics Laboratory (WiPAL) is a flexible user facility designed to study a range of astrophysically relevant plasma processes as well as novel geometries that mimic astrophysical systems. A multi-cusp magnetic bucket constructed from strong samarium cobalt permanent magnets now confines a 10 m$^3$, fully ionized, magnetic-field free plasma in a spherical geometry. Plasma parameters of $T_{e}\approx5$ to $20$ eV and $n_{e}\approx10^{11}$ to $5\times10^{12}$ cm$^{-3}$ provide an ideal testbed for a range of astrophysical experiments including self-exciting dynamos, collisionless magnetic reconnection, jet stability, stellar winds, and more. This article describes the capabilities of WiPAL along with several experiments, in both operating and planning stages, that illustrate the range of possibilities for future users.Comment: 21 pages, 12 figures, 2 table

Doubly Robust Inference when Combining Probability and Non-probability Samples with High-dimensional Data

Non-probability samples become increasingly popular in survey statistics but may suffer from selection biases that limit the generalizability of results to the target population. We consider integrating a non-probability sample with a probability sample which provides high-dimensional representative covariate information of the target population. We propose a two-step approach for variable selection and finite population inference. In the first step, we use penalized estimating equations with folded-concave penalties to select important variables for the sampling score of selection into the non-probability sample and the outcome model. We show that the penalized estimating equation approach enjoys the selection consistency property for general probability samples. The major technical hurdle is due to the possible dependence of the sample under the finite population framework. To overcome this challenge, we construct martingales which enable us to apply Bernstein concentration inequality for martingales. In the second step, we focus on a doubly robust estimator of the finite population mean and re-estimate the nuisance model parameters by minimizing the asymptotic squared bias of the doubly robust estimator. This estimating strategy mitigates the possible first-step selection error and renders the doubly robust estimator root-n consistent if either the sampling probability or the outcome model is correctly specified