Joint Generation of Mixed Data of Different Variable Types in Pharmaceutical Sciences
Abstract
This manuscript focuses on developing a unified framework for simultaneously generating datasets that encompass four major types of variables (binary, ordinal, count, and continuous) under specified marginal distributions and an appropriate dependence structure for simulation studies. Simulation-based approaches are widely employed in pharmaceutical research and practice. A key element of any simulation study is the characterization of model components and parameters that jointly describe a scientific phenomenon. When such characterization cannot be fully achieved through deterministic methods, investigators frequently turn to random number generation (RNG) to produce simulation-driven solutions that capture the inherent randomness of the process. Although numerous RNG techniques have been proposed in the literature, a significant shortcoming is that most were not designed to accommodate all the aforementioned variable types at once. Consequently, these methods often yield only partial solutions, since real-world datasets typically consist of diverse variable forms. The present work contributes a substantial enhancement to the current methodologies by providing a systematic framework and an in-depth exploration of mixed data generation. We introduce an algorithm tailored to generate data with mixed marginals, describe its operational, computational, and practical aspects, and discuss potential extensions to encompass more complex distributional scenarios involving richer marginal features and dependence structures.
Keywords
Biserial correlation, Phi coefficient, Simulation, Random number generation, Mixed data
References
- 1. Amatya A, Demirtas,H. Concurrent generation of multivariate mixed data with variables of dissimilar types. Journal of Statistical Computation and Simulation, 2016; 86(18):3595–3607. doi: 10.1080/00949655.2016.1177530
- 2. Demirtas H, Allozi R, Hu Y, Inan G, Ozbek L. Joint generation of binary, ordinal, count, and normal data with specified marginal and association structures in Monte-Carlo simulations. In ICSA Book Series in Statistics, John Dean Chen and Ding-Geng (Din) Chen (Eds): Monte-Carlo Simulation-Based Statistical Modeling. Singapore: Springer, 2017: 3-15.
- 3. Demirtas H.The design of simulation studies in medical statistics. Statistics in Medicine, 2007b; 26:3818–3821.
- 4. Demirtas H. Simulation-driven inferences for multiply imputed longitudinal datasets. Statistica Neerlandica, 2004a; 58(4):466–482. https://doi.org/10.1111/j.1467-9574.2004.00271.x
- 5. Demirtas H. A multiple imputation framework for massive multivariate data of different variable types: A Monte-Carlo technique. In ICSA Book Series in Statistics, John Dean Chen and Ding-Geng (Din) Chen (Eds): Monte-Carlo Simulation- Based Statistical Modeling. Singapore: Springer, 2017c: 143-162.
- 6. Demirtas H. A method for multivariate ordinal data generation given marginal distributions and correlations. Journal of Statistical Computation and Simulation, 2006; 76(11):1017–1025. DOI:10.1080/10629360600569246
- 7. Demirtas H, Doganay B. Simultaneous generation of binary and normal data with specified marginal and association structures. Journal of Biopharmaceutical Statistics, 2012; 22(2):223–236. DOI:10.1080/10543406.2010.521874
- 8. Demirtas H, Yavuz Y. Concurrent generation of ordinal and normal data. Journal of Biopharmaceutical Statistics, 2015;25(4):635–650. DOI: 10.1080/10543406.2014.920868
- 9. Amatya A, Demirtas H. Simultaneous generation of multivariate mixed data with Poisson and normal marginals. Journal of Statistical Computation and Simulation, 2015a;85(15):3129–3139. https://doi.org/10.1080/00949655.2014.953534
- 10. Emrich JL, Piedmonte M.R. A method for generating high-dimensional multivariate binary variates. The American Statistician, 1991;45(4):302–-304.