Optimal group testing designs for estimating prevalence with uncertain testing errors

We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait by using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal strategy is to have three group sizes with unequal frequencies. On the basis of a chlamydia study in the U.S.A., we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator. We demonstrate that the locally D- and Ds-optimal designs proposed have high efficiencies even when the prespecified values of the parameters are moderately misspecified

DESIGN PROBLEMS IN MODEL ROBUST REGRESSION AND EXACT D-OPTIMALITY

This thesis deals with two different yet related areas of optimal experimental design. In the first part we seek designs which are optimal in some sense for extrapolation and estimation of the ith derivative at 0 when the true regression function is in a certain class of regression functions. More precisely, the class is defined to be the collection of regression functions such that its (h + 1)th derivative is bounded. The class can be viewed as representing possible departures from an ideal simple model and thus describes a model robust setting. The estimates are restricted to be linear and the designs are restricted to be with minimal number of points. The design and estimate sought is minimax for mean square error. The optimal designs for the cases X = {0,(INFIN)) and X = {-1,1}, where X is the place observations can be taken, are obtained. In the second part, we are interested in finding the exact D-optimal design for estimating the coefficients of the polynomial regression of degree n on {a, b}, using the least square estimator. Salaevskii(1966) conjectures that an exact D-optimal design (xi)* distributes observations as evenly as possible among the n + 1 support points of the D-optimal approximate design. A new and simplified proof of Salaevskii\u27s result that the conjecture holds for sufficiently large N is obtained. Also for polynomial regression of degree (LESSTHEQ) 9, Salaevskii\u27s conjecture is proved except for a few cases

Optimal group testing designs for estimating prevalence with uncertain testing errors

We construct optimal designs for group testing experiments where the goal is to estimate the prevalence of a trait using a test with uncertain sensitivity and specificity. Using optimal design theory for approximate designs, we show that the most efficient design for simultaneously estimating the prevalence, sensitivity, and specificity requires three different group sizes with equal frequencies. However, if estimating prevalence as accurately as possible is the only focus, the optimal strategy is to have three group sizes with unequal frequencies. Based on a Chlamydia study in the United States, we compare performances of competing designs and provide insights into how the unknown sensitivity and specificity of the test affect the performance of the prevalence estimator. We demonstrate that the proposed locally D- and Ds-optimal designs have high efficiencies even when the prespecified values of the parameters are moderately misspecified. Extensions on budget-constrained optimal group testing designs will also be discussed, where both subjects and tests incur costs, and assays have uncertain sensitivity and specificity that may be linked to the group sizes.Non UBCUnreviewedAuthor affiliation: National Sun Yat-sen UniversityFacult

On exact D-optimal designs with 2 two-level factors and n autocorrelated observations

D-optimal design, AR(1) process, Markov process, autocorrelated observations, two-level factor,

Optimal designs for estimating the control values in multi-univariate regression models

This paper considers a linear regression model with a one-dimensional control variable x and an m-dimensional response vector . The components of are correlated with a known covariance matrix. Based on the assumed regression model, it is of interest to obtain a suitable estimation of the corresponding control value for a given target vector on the expected responses. Due to the fact that there is more than one target value to be achieved in the multiresponse case, the m expected responses may meet their target values at different respective control values. Consideration on the performance of an estimator for the control value includes the difference of the expected response E(yi) from its corresponding target value Ti for each component and the optimal value of control point, say x0, is defined to be the one which minimizes the weighted sum of squares of those standardized differences within the range of x. The objective of this study is to find a locally optimal design for estimating x0, which minimizes the mean squared error of the estimator of x0. It is shown that the optimality criterion is equivalent to a c-criterion under certain conditions and explicit solutions with dual response under linear and quadratic polynomial regressions are obtained.Calibration c-criterion Classical estimator Control value Equivalence theorem Locally optimal design Scalar optimal design

Minimax and maximin efficient designs for estimating the location-shift parameter of parallel models with dual responses

Minimax designs and maximin efficient designs for estimating the location-shift parameter of a parallel linear model with correlated dual responses over a symmetric compact design region are derived. A comparison of the behavior of efficiencies between the minimax and maximin efficient designs relative to locally optimal designs is also provided. Both minimax or maximin efficient designs have advantage in terms of estimating efficiencies in different situations.Bioassay Efficiency Equivalence theorem Locally optimal design Location shift parameter Maximin efficient design Minimax design Relative potency

Testing for variance changes in autoregressive models with unknown order

The problem of change point in autoregressive process is studied in this article. We propose a Bayesian information criterion-iterated cumulative sums of squares algorithm to detect the variance changes in an autoregressive series with unknown order. Simulation results and two examples are presented, where it is shown to have good performances when the sample size is relatively small.

Limiting spectral distribution of large-dimensional sample covariance matrices generated by VARMA

The existence of a limiting spectral distribution (LSD) for a large-dimensional sample covariance matrix generated by the vector autoregressive moving average (VARMA) model is established. In particular, we obtain explicit forms of the LSDs for random matrices generated by a first-order vector autoregressive (VAR(1)) model and a first-order vector moving average (VMA(1)) model, as well as random coefficients for VAR(1) and VMA(1). The parameters for these explicit forms are also estimated. Finally, simulations demonstrate that the results are effective.Large-dimensional random matrices Limiting spectral distribution Vector autoregression