## Lu, et al. (2008)

Lu, et al. (2008) proposed a sample size estimation method for a mixed model of repeated measures (MMRM), assuming a monotone missingness and the missing data are missing at random.
They considered the Wald test for testing the mean difference of the final time point.
This web application is an implementation of the method of Lu, et al. (Section 3.1).
For more details refer to the Reference 1.

Correlation matrix: as shown in the example below, please define the matrix elements rowwise; white spaces are used to separate elements within a row, and line breaks are used to separate the rows.

Retention: $p_a = (n_{a1}/n_{a1}, n_{a2}/n_{a1}, \ldots, n_{aJ}/n_{a1})$, denote the retention rate vector, in which elements are the non-dropout rates at each time point.
As shown in the example below, input values are separated by white space.

Allcation ratio: When $\lambda \gt 1$, sample size of group A is larger than of group B ($n_a = \lambda n_b$).
For instance, when $\lambda = 2$, $n_a = 2 n_b$.

Mean difference ($\delta$): The mean difference at the last time point.

## Application

## Reference

- Lu K, Luo X, Chen PY. Sample size estimation for repeated measures analysis in randomized clinical trials with missing data. International Journal of Biostatistics 2008; 4(1): Article 9. [Web]

## Version history

- 2014/12/25 Added: a SAS/IML program
- 2014/12/18 Added: English translation
- 2014/12/17 Added: R script output for z-test
- 2014/12/12 Added: t-test
- 2014/12/11 Added: test release

## To cite this page

- Nagashima K. A sample size determination tool for mixed models for repeated measures [Internet]. 2014 Dec 11 [cited 20XX YYY ZZ]; Available from: https://nshi.jp/en/js/mmrm/.