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Complex Innovative Design
Published in Wei Zhang, Fangrong Yan, Feng Chen, Shein-Chung Chow, Advanced Statistics in Regulatory Critical Clinical Initiatives, 2022
The joint distribution is modeled as a mixture of the conditional distribution of weighted by the marginal distribution of . Here we assume that Z always is observed before Y.
Hierarchical Models and Longitudinal Data
Published in Gary L. Rosner, Purushottam W. Laud, Wesley O. Johnson, Bayesian Thinking in Biostatistics, 2021
Gary L. Rosner, Purushottam W. Laud, Wesley O. Johnson
We now obtain the full conditional distributions corresponding to model (14.9) to illustrate the calculation for a common situation. Knowing how to determine the full conditional distributions here will make it easier in other situations. This section is important for anyone who would like to or might need to write their own program instead of one of the software packages available for Bayesian inference, such as BUGS, JAGS, or Stan (see Appendix C). The illustration of Gibbs sampling below corresponds to the type of models we considered for the analysis of the cow abortion data and the toenail data. The most commonly used prior model is a normal prior for β and a gamma prior for the precision τ. Some full conditionals are not recognizable no matter what prior or model one specifies.
Bayesian Disease Mapping Models
Published in Andrew B. Lawson, Using R for Bayesian Spatial and Spatio-Temporal Health Modeling, 2021
An advantage of the intrinsic Gaussian formulation is that the conditional moments are defined as simple functions of the neighboring values and number of neighbors (). and the conditional distribution is defined as:
Sensitivity analysis of unmeasured confounding in causal inference based on exponential tilting and super learner
Published in Journal of Applied Statistics, 2023
We have proposed a new sensitivity analysis method for causal inference to adjust for unmeasured confounding in the estimation of the mean outcome by combining the ideas of the doubly robust estimator, the exponential tilting method, and the super learner algorithm. In causal inference, when unmeasured confounders exist, the conditional distribution of the observed outcome is different from that of the unobserved outcome given the covariates. We use the exponential tilting assumption to link these two conditional distributions together directly with a univariate sensitivity parameter. This sensitivity parameter addresses the departure from the assumption of no unmeasured confounder. Compared to most of the existing sensitivity analysis in the literature, our method does not require modeling assumptions for the unmeasured confounders as latent variables and hence the unmeasured confounder could be continuous, binary, or categorical and could be univariate or multivariate. In addition, the sensitivity parameter can be interpreted as a log-odds ratio for a binary outcome, which makes the choice of its range relatively easy for practitioners. To reduce the bias of traditional parametric methods, we propose a nonparametric doubly robust estimator by incorporating super learner algorithms. The simulation studies demonstrate the effectiveness of the proposed method and its superiority to some other existing methods.
Likelihood ratio test for genetic association study with case–control data under Probit model
Published in Journal of Applied Statistics, 2022
Zhen Sheng, Yukun Liu, Pengfei Li, Jing Qin
In epidemiology, clinical trials, and genetic association studies, retrospective (or case–control) and prospective studies are two popular approaches to explore whether certain factors are associated with a disease. In prospective studies, researchers first recruit a fixed number of individuals for a certain disease before recording all individuals' information after a period, including both the covariates and disease status. Let X denote a vector of clinical covariates, and the disease status for generic individuals is D = 0 for a non-disease and 1 for a disease. Prospective data are independent and identically distributed (iid) from the joint distribution of D are iid from the conditional distribution of X given D, while those with different disease statuses are no longer identically distributed. Prospective and retrospective data have different joint distributions; therefore, they should be dealt with using different inference methods. An advantage of retrospective over prospective studies is that they can save money, time, or/and effort, especially for rare diseases such as cancer with a prevalence of 0.01%. The price is that the disease prevalence or mortality rate cannot be consistently estimated from retrospective data, which is generally not the case for prospective data.
Statistical inference for distributions with one Poisson conditional
Published in Journal of Applied Statistics, 2021
Barry C. Arnold, B. G. Manjunath
By considering bivariate models in which one marginal distribution is assumed to be of the Poisson form while the conditional distributions of the second variable, given the first, are also assumed to be of the Poisson form, we have developed flexible models called bivariate pseudo-Poisson distributions. Distributional and inferential issues have been investigated for these models. The models discussed in this paper may be considered as viable alternatives to the various bivariate Poisson models that have been introduced in the literature. The simplicity of the structure of the pseudo models allows simple simulation and straightforward parameter estimation and model fitting. They are not a panacea but we would argue that they, and their extensions to higher dimensions and permuted variants of them, deserve a place in the modelers toolkit.