Calculate the optimal sample size allocation that 
    produces the highest statistical power for experimental 
    studies under a budget constraint, and
    perform power analyses with and without accommodating 
    cost structures of sampling. The designs cover single-level 
    and multilevel experiments detecting main, mediation, 
    and moderation effects (and some combinations). 
    The references for the proposed methods include: 
    (1) Shen, Z., & Kelcey, B. (2020). 
    Optimal sample allocation under unequal costs in 
    cluster-randomized trials.
    Journal of Educational and Behavioral Statistics, 45(4): 446-474.
        <doi:10.3102/1076998620912418>.
    (2) Shen, Z., & Kelcey, B. (2022b). Optimal sample allocation for
    three-level multisite cluster-randomized trials. 
    Journal of Research on Educational Effectiveness, 15 (1), 130-150.
    <doi:10.1080/19345747.2021.1953200>.
    (3) Shen, Z., & Kelcey, B. (2022a). Optimal sample allocation in
    multisite randomized trials. The Journal of Experimental Education.
    <doi:10.1080/00220973.2020.1830361>.
    (4) Champely, S. (2020). pwr: Basic functions for power analysis 
    (Version 1.3-0) [Software]. Available from 
    <https://CRAN.R-project.org/package=pwr>.

The oblique decision tree (ODT) uses linear combinations of
    predictors as partitioning variables in a decision tree. Oblique
    Decision Random Forest (ODRF) is an ensemble of multiple ODTs
    generated by feature bagging. Both can be used for classification and
    regression as supplements to the classical CART of Breiman (1984)
    <DOI:10.1201/9781315139470> and Random Forest of Breiman (2001)
    <DOI:10.1023/A:1010933404324> respectively.

Outcome-dependent sampling (ODS) schemes are cost-effective ways to enhance study efficiency. 
    In ODS designs, one observes the exposure/covariates with a probability that depends on the outcome 
    variable. Popular ODS designs include case-control for binary outcome, case-cohort for time-to-event 
    outcome, and continuous outcome ODS design (Zhou et al. 2002) <doi: 10.1111/j.0006-341X.2002.00413.x>. 
    Because ODS data has biased sampling nature, standard statistical analysis such as linear regression 
    will lead to biases estimates of the population parameters. This package implements four statistical 
    methods related to ODS designs: (1) An empirical likelihood method analyzing the primary continuous 
    outcome with respect to exposure variables in continuous ODS design (Zhou et al., 2002). (2) A partial 
    linear model analyzing the primary outcome in continuous ODS design (Zhou, Qin and Longnecker, 2011) 
    <doi: 10.1111/j.1541-0420.2010.01500.x>. (3) Analyze a secondary outcome in continuous ODS design 
    (Pan et al. 2018) <doi: 10.1002/sim.7672>. (4) An estimated likelihood method analyzing a secondary 
    outcome in case-cohort data (Pan et al. 2017) <doi: 10.1111/biom.12838>.