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| 1 | +--- |
| 2 | +title: "Bioequivalence Tests for Parallel Trial Designs: 2 Arms, 1 Endpoint" |
| 3 | +author: "Thomas Debray" |
| 4 | +date: "`r format(Sys.time(), '%B %d, %Y')`" |
| 5 | +output: |
| 6 | + html_document: |
| 7 | + fig_caption: yes |
| 8 | + fig_width: 9 |
| 9 | + fig_height: 6 |
| 10 | +vignette: > |
| 11 | + %\VignetteIndexEntry{Bioequivalence Tests for Parallel Trial Designs: 2 Arms, 1 Endpoint} |
| 12 | + %\VignetteEngine{knitr::rmarkdown} |
| 13 | + %\VignetteEncoding{UTF-8} |
| 14 | +bibliography: 'references.bib' |
| 15 | +link-citations: yes |
| 16 | +--- |
| 17 | + |
| 18 | +```{r setup, include=FALSE, message = FALSE, warning = FALSE} |
| 19 | +knitr::opts_chunk$set(echo = TRUE) |
| 20 | +knitr::opts_chunk$set(comment = "#>", collapse = TRUE) |
| 21 | +options(rmarkdown.html_vignette.check_title = FALSE) #title of doc does not match vignette title |
| 22 | +doc.cache <- T #for cran; change to F |
| 23 | +``` |
| 24 | + |
| 25 | +# Introduction |
| 26 | + |
| 27 | + |
| 28 | +## Difference of Means Test |
| 29 | +This example, adapted from Example 1 in the PASS manual chapter titled *"Biosimilarity Tests for the Difference Between Means Using a Parallel Two-Group Design"*, illustrates the process of planning a clinical trial to assess biosimilarity. Specifically, the trial aims to compare blood pressure outcomes between two groups. |
| 30 | + |
| 31 | +### Scenario |
| 32 | +Drug B is a well-established biologic drug used to control blood pressure. Its exclusive marketing license has expired, creating an opportunity for other companies to develop biosimilars. Drug A is a new competing drug being developed as a potential biosimilar to Drug B. The goal is to determine whether Drug A meets FDA biosimilarity requirements in terms of safety, purity, and therapeutic response when compared to Drug B. |
| 33 | + |
| 34 | +### Trial Design |
| 35 | +The study follows a parallel-group design with the following key assumptions: |
| 36 | + |
| 37 | +* Reference Group (Drug B): The average blood pressure is 96 mmHg, with a within-group standard deviation of 18 mmHg. |
| 38 | +* Mean Difference: As per FDA guidelines, the assumed difference between the two groups is set to $\delta = \sigma/8 = 2.25$ mmHg. |
| 39 | +* Biosimilarity Limits: These are defined as ±1.5σ = ±27 mmHg, ensuring compliance with regulatory requirements. |
| 40 | +* Type-I Error Rate: A one-sided α=0.025 is specified. |
| 41 | +* Desired Power: The target power for the study is 90% |
| 42 | + |
| 43 | +To implement these parameters in R, the following code snippet can be used: |
| 44 | + |
| 45 | +```r |
| 46 | +# Reference group mean blood pressure (Drug B) |
| 47 | +mu_r <- setNames(96, "BP") |
| 48 | + |
| 49 | +# Treatment group mean blood pressure (Drug A) |
| 50 | +mu_t <- setNames(96 + 2.25, "BP") |
| 51 | + |
| 52 | +# Common within-group standard deviation |
| 53 | +sigma <- setNames(18, "BP") |
| 54 | + |
| 55 | +# Lower and upper biosimilarity limits |
| 56 | +lequi_lower <- setNames(-27, "BP") |
| 57 | +lequi_upper <- setNames(27, "BP") |
| 58 | +``` |
| 59 | + |
| 60 | +### Objective |
| 61 | +To explore the power of the test across a range of group sample sizes, the researchers plan to calculate the power for group sizes varying from 6 to 20. These calculations will use the noncentral t-distribution to evaluate the ability of the study design to detect the specified difference and meet biosimilarity criteria. |
| 62 | + |
| 63 | + |
| 64 | +```r |
| 65 | +sampleSize(power = 0.86, alpha = 0.025, |
| 66 | + mu_list = list("R" = mu_r, "T" = mu_t), |
| 67 | + sigma_list = list("R" = sigma, "T" = sigma), |
| 68 | + list_comparator = list("T_vs_R" = c("R", "T")), |
| 69 | + list_lequi.tol = list("T_vs_R" = lequi_lower), |
| 70 | + list_uequi.tol = list("T_vs_R" = lequi_upper), |
| 71 | + dtype = "parallel", ctype = "DOM", lognorm = FALSE, |
| 72 | + adjust = "no", ncores = 1, nsim = 1000, seed = 1234) |
| 73 | +``` |
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