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vignettes/sampleSize_Mielke.Rmd

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---
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title: "Sample Size for Multiple Hypothesis Testing in Biosimilar Development"
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author: "Thomas Debray"
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output: rmarkdown::html_vignette
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date: "`r format(Sys.time(), '%B %d, %Y')`"
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output:
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html_document:
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fig_caption: yes
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fig_width: 9
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fig_height: 6
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vignette: >
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%\VignetteIndexEntry{Sample Size for Multiple Hypothesis Testing in Biosimilar Development}
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%\VignetteEngine{knitr::rmarkdown}
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link-citations: yes
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---
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```{r, include = FALSE}
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knitr::opts_chunk$set(
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collapse = TRUE,
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comment = "#>"
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)
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require(kableExtra)
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```{r setup, include=FALSE}
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knitr::opts_chunk$set(echo = TRUE)
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knitr::opts_chunk$set(comment = "#>", collapse = TRUE)
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options(rmarkdown.html_vignette.check_title = FALSE) #title of doc does not match vignette title
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doc.cache <- T #for cran; change to F
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```
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We here reproduce the examples of @mielke_sample_2018. In these examples, the minimal sample size is estimated to give at least 80\% power for the rejection of $k$ out of $m$ tests at a one-sided significance level of $\alpha = 0.05$ in a parallel groups design. It is assumed that the sample size, the true difference between T and R and the standard deviation of the tests is equal in each test.
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We here reproduce the examples of @mielke_sample_2018. As a first step, we load the R package.
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```{r, echo = T, message=F}
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library(SimTOST)
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```
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# Multiple Independent Co-Primary Endpoints
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The first example assumes a ratio of 1.05 between the effect sizes of the test and reference products. @mielke_sample_2018 conducts a difference-of-means test on the log scale, with $\delta = \log(1.05)$. It is assumed that the standard deviation of the log-transformed response variable is $\sigma = 0.3$, and that all tests are independent ($\rho = 0$). Below, we estimate the sample size to demonstrate that the test and reference product are equivalent with respect to all $m=5$ endpoints.

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