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Process Development
Published in Harry Yang, Steven J. Novick, Bayesian Analysis with R for Drug Development, 2019
Minimally informative priors are used for the 40 regression coefficients (10 × 4) and a scaled inverse Wishart prior is used for the variance–covariance matrix (Hofer 2009). The prior for the variance–covariance matrix is assigned based on a method suggested by Gelman and Hill (2007), who show that the simpler inverse Wishart prior often carries information. To begin, the variance–covariance matrix is first expressed as
CMC Requirements for Biological Products
Published in Shein-Chung Chow, Analytical Similarity Assessment in Biosimilar Product Development, 2018
Now, consider the example concerning the liquid chromatography method discussed in LeBlond (2014). The design space is {x: Pr[Y ∊ A|x, data] ≥ 0.9}. To calculate the posterior predictive probability, minimally informative priors b0, b3, and b6 ~ N(0, 0.0001), b1 and b2 ~ N(0, 0.001), and b4, b5, and b7 ~ N(0, 0.01) are used for the eight regression coefficients in model (1), based on examining the results of a frequentist analysis of the data, and a scalar inverse Wishart prior is used for the variance-covariance matrix. The variance-covariance matrix can be expressed as
Multiple Imputation for Sampled Cohort Data
Published in Ørnulf Borgan, Norman E. Breslow, Nilanjan Chatterjee, Mitchell H. Gail, Alastair Scott, Christopher J. Wild, Handbook of Statistical Methods for Case-Control Studies, 2018
to obtain estimates and corresponding variance-covariance matrix . Next, K independent draws of the parameters, denoted (), are taken from a multivariate normal distribution with mean vector and variance-covariance matrix . The kth set of imputations of X is obtained by drawing from a Bernoulli distribution with probability
Sociopolitical control as a mediator between ethnic identity and social support on 30-day drug use among black girls
Published in Journal of Ethnicity in Substance Abuse, 2023
Ijeoma Opara, Ashley V. Hill, Amanda Calhoun, Marline Francois, Courtnae Alves, Pauline Garcia-Reid, Robert J. Reid
We performed structural equation modeling (SEM) procedures with AMOS 16.0 (Arbuckle, 2007) to test a path model that included only observed variables. Maximum likelihood estimation was used to analyze the variance– covariance matrix. We interpreted several fit indices that are widely accepted and considered to be robust measures of fit. These included the discrepancy Chi-square (V2), the discrepancy-to-df ratio, the Comparative Fit Index, the Tucker-Lewis Index, and the Root Mean Square of Error Approximation. Non-significant V2 values and discrepancy-to-df ratios less than 2.0 indicate acceptable fit. Higher values (i.e., greater than .90) on the Comparative Fit Index and Tucker-Lewis Index and smaller Root Mean Square Error of Approximation values are desirable. Demographic variables were all examined in preliminary analyses; however, only gender and age contributed to the predictive model and were included in the main analysis.
Alcohol Use Cravings as a Mediator Between Associated Risk Factors on Increased Alcohol Use among Youth Adults in New York During the COVID-19 Pandemic
Published in Alcoholism Treatment Quarterly, 2021
Ijeoma Opara, Sana Malik, David T. Lardier, Joyonna Gamble-George, Ryan J. Kelly, Chukwuemeka N. Okafor, R. Neil Greene, Deanna Parisi
Chi-square tests were conducted between sociodemographic characteristics and the outcome variable, increased alcohol use due to the New York COVID-19 stay-at-home orders. In addition, we used chi-square tests to determine significant differences between clinically relevant predictors including depression severity and COVID-19 diagnosis on increased alcohol use. Independent sample t-tests were conducted between the outcome of interest and clinically relevant predictors including raw alcohol-use-cravings scores and raw sleep-disturbances scores. Last, structural equation modeling (SEM) techniques in STATA were conducted to examine a mediation path model between depression severity, COVID-19 diagnosis, sleep severity, and increased alcohol use due to the New York COVID-19 stay-at-home. Maximum likelihood (ML) estimations were used to examine the variance-covariance matrix. Mediation was tested using bias-corrected bootstrap confidence intervals, which provide more-accurate intervals (Mallinckrodt et al., 2006). Bias-corrected bootstrap confidence intervals also improve the power of the test of the indirect effect (Shrout & Bolger, 2002). A significant indirect effect is present when confidence intervals do not include zero (Hayes, 2009). Sociodemographic variables with a p ≤ .20 were chosen as covariates (Bursac, Gauss, Williams, & Hosmer, 2008) and retained based on meaningful contribution and statistical significance to the final analytical model (Aneshensel, 2013).
Likelihood-based quantile autoregressive distributed lag models and its applications
Published in Journal of Applied Statistics, 2020
Yuzhu Tian, Liyong Wang, Manlai Tang, Yanchao Zang, Maozai Tian
For σ, let 17) as the σ as follows: 13), (17), (21), we repeat E-step and M-step to update 22] provided a calculation formula to derive the confidence intervals of parameters for EM algorithm. However, it is essential to estimate complex variance–covariance matrix. As a kind of widespread random simulation algorithm, Bootstrap resampling method provide an efficient and simple alternative to construct confidence intervals of unknown parameters. A large number of empirical studies demonstrated that Bootstrap method generally outperform the direct confidence intervals based on asymptotic variance, especially for small sample cases. A detailed introduction about Bootstrap method can refer to Efron and Tibshirani [6] and Davison and Hinkley [3], etc.