The statistics for testing for monotonic trend
To test for monotonic trend, the following five statistics are implemented in the package:
1. The likelihood ratio test (Barlow et al. 1972, and Robertson et al. 1988)
2. Williams (Williams, 1971 and 1972)
3. Marcus (Marcus, 1976)
4. The M statistic (Hu et al., 2005)
5. The modified M statistic (Lin et al., 2007)
The formulas for the statistics are presented below:

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where
References:

- Barlow, R., Bartholomew, D., Bremner, M. and Brunk, H. (1972) Statistical Inference Under Order Restriction. New York: Wiley.
- Hu, J., Kapoor, M., Zhang, W., Hamilton, S. and Coombes, K. (2005) Analysis of dose response effects on gene expression data with comparison of two microarray platforms. Bioinformatics, 21(17), 3524–3529.
- Marcus, R. (1976) The powers of some tests of the quality of normal means against an ordered alternative. Biometrika, 63,177–83.
- Lin, D., Shkedy, Z., Yekutieli, D., Burzykowski, T., G¨ohlmann, H., De Bondt, A., Perera, T., Geerts, T. and Bijnens, L. (2007) Testing for trends in dose-response microarray experiments: A comparison of several testing procedures, multiplicity and resamplingbased inference. Statistical Applications in Genetics and Molecular Biology, 6(1), Article 26.
- Setia Pramana, Dan Lin, Philippe Haldermans, Ziv Shkedy, Tobias Verbeke, Hinrich Göhlmann, An De Bondt, Willem Talloen, and Luc Bijnens. 2010, Analysis of Dose-response Studies in Microarray Experiments using The R IsoGene Package, R Journal, 2/1.

- Setia Pramana, Philippe Haldermans , and TobiasVerbeke. (2012) A User Friendly Interface for Analyzing Dose-response Studies in Microarray Experiments: The IsoGeneGUI package. A Book Chapter in Lin, D., Shkedy, Z., Amaratunga,D., Yekutieli, D and Bijnens, L. (Editors), "Modeling of Dose-response Microarray Data in Early Drug Development Experiments Using R", Springer.
- Robertson, T., Wright, F. and Dykstra, R. (1988) Order Restricted Statistical Inference. Wiley.
- Williams, D. (1971) A test for differences between treatment means when several dose levels are compared with a zero dose control. Biometrics, 27, 103–117.
- Williams, D. (1972) The comparison of several dose levels with a zero dose control. Biometrics, 28, 519–531.