arXiv subjects

Liping Tong

Publications and source records attributed to Liping Tong.

6 recordsLinked to original sources

arXiv2024

CDsampling: An R Package for Constrained D-Optimal Sampling in Paid Research Studies

In the context of paid research studies and clinical trials, budget considerations often require patient sampling from available populations which comes with inherent constraints. We introduce the R package CDsampling, which is the first to our knowledge to integrate optimal design theories within the framework of constrained sampling. This package offers the possibility to find both D-optimal approximate and exact allocations for samplings with or without constraints. Additionally, it provides functions to find constrained uniform sampling as a robust sampling strategy when the model information is limited. To demonstrate its efficacy, we provide simulated examples and a real-data example with datasets embedded in the package and compare them with classical sampling methods. Furthermore, the package revisits the theoretical results of the Fisher information matrix for generalized linear models (including regular linear regression model) and multinomial logistic models, offering functions for its computation.

stat.CO↗

arXiv2024

Constrained D-optimal Design for Paid Research Study

We consider constrained sampling problems in paid research studies or clinical trials. When qualified volunteers are more than the budget allowed, we recommend a D-optimal sampling strategy based on the optimal design theory and develop a constrained lift-one algorithm to find the optimal allocation. Unlike the literature which mainly deals with linear models, our solution solves the constrained sampling problem under fairly general statistical models, including generalized linear models and multinomial logistic models, and with more general constraints. We justify theoretically the optimality of our sampling strategy and show by simulation studies and real-world examples the advantages over simple random sampling and proportionally stratified sampling strategies.

stat.ME↗

arXiv2023

Multinomial Link Models

We propose a new family of regression models for analyzing categorical responses, called multinomial link models. It consists of four classes, namely, mixed-link models that generalize existing multinomial logistic models and their extensions, two-group models that can incorporate the observations with NA or unknown responses, dichotomous conditional link models that handle longitudinal binary responses, and po-npo mixture models that are more flexible than partial proportional odds models. By characterizing the feasible parameter space, deriving necessary and sufficient conditions, and developing validated algorithms to guarantee the finding of feasible maximum likelihood estimates, we solve the infeasibility issue of existing statistical software when estimating parameters for cumulative link models. We also provide explicit formulae and detailed algorithms for computing the Fisher information matrix and selecting the best models among the new family. The applications to real datasets show that the new models can fit the data significantly better, correct misleading conclusions due to missing responses, and make more informative statistical inference.

stat.ME↗

arXiv2017

D-optimal Designs with Ordered Categorical Data

Cumulative link models have been widely used for ordered categorical responses. Uniform allocation of experimental units is commonly used in practice, but often suffers from a lack of efficiency. We consider D-optimal designs with ordered categorical responses and cumulative link models. For a predetermined set of design points, we derive the necessary and sufficient conditions for an allocation to be locally D-optimal and develop efficient algorithms for obtaining approximate and exact designs. We prove that the number of support points in a minimally supported design only depends on the number of predictors, which can be much less than the number of parameters in the model. We show that a D-optimal minimally supported allocation in this case is usually not uniform on its support points. In addition, we provide EW D-optimal designs as a highly efficient surrogate to Bayesian D-optimal designs. Both of them can be much more robust than uniform designs.

math.ST↗

arXiv2013

Analytic Solutions for D-optimal Factorial Designs under Generalized Linear Models

We develop two analytic approaches to solve D-optimal approximate designs under generalized linear models. The first approach provides analytic D-optimal allocations for generalized linear models with two factors, which include as a special case the $2^2$ main-effects model considered by Yang, Mandal and Majumdar (2012). The second approach leads to explicit solutions for a class of generalized linear models with more than two factors. With the aid of the analytic solutions, we provide a necessary and sufficient condition under which a D-optimal design with two quantitative factors could be constructed on the boundary points only. It bridges the gap between D-optimal factorial designs and D-optimal designs with continuous factors.

stat.CO↗

arXiv2009

Efficient Calculation of P-value and Power for Quadratic Form Statistics in Multilocus Association Testing

We address the asymptotic and approximate distributions of a large class of test statistics with quadratic forms used in association studies. The statistics of interest do not necessarily follow a chi-square distribution and take the general form $D=X^T A X$, where $X$ follows the multivariate normal distribution, and $A$ is a general similarity matrix which may or may not be positive semi-definite. We show that $D$ can be written as a linear combination of independent chi-square random variables, whose distribution can be approximated by a chi-square or the difference of two chi-square distributions. In the setting of association testing, our methods are especially useful in two situations. First, for a genome screen, the required significance level is much smaller than 0.05 due to multiple comparisons, and estimation of p-values using permutation procedures is particularly challenging. An efficient and accurate estimation procedure would therefore be useful. Second, in a candidate gene study based on haplotypes when phase is unknown a computationally expensive method-the EM algorithm-is usually required to infer haplotype frequencies. Because the EM algorithm is needed for each permutation, this results in a substantial computational burden, which can be eliminated with our mathematical solution. We assess the practical utility of our method using extensive simulation studies based on two example statistics and apply it to find the sample size needed for a typical candidate gene association study when phase information is not available. Our method can be applied to any quadratic form statistic and therefore should be of general interest.

stat.AP↗