# epi.ssequb: Sample size for a parallel equivalence trial, binary outcome In epiR: Tools for the Analysis of Epidemiological Data

## Description

Sample size for a parallel equivalence trial, binary outcome.

## Usage

 `1` ```epi.ssequb(treat, control, delta, n, r = 1, power, nfractional = FALSE, alpha) ```

## Arguments

 `treat` the expected proportion of successes in the treatment group. `control` the expected proportion of successes in the control group. `delta` the equivalence limit, expressed as the absolute change in the outcome of interest that represents a clinically meaningful difference. For an equivalence trial the value entered for `delta` must be greater than zero. `n` scalar, the total number of study subjects in the trial. `r` scalar, the number in the treatment group divided by the number in the control group. `power` scalar, the required study power. `nfractional` logical, return fractional sample size. `alpha` scalar, defining the desired alpha level.

## Value

A list containing the following:

 `n.total` the total number of study subjects required. `n.treat` the required number of study subject in the treatment group. `n.control` the required number of study subject in the control group. `delta` the equivalence limit, as entered by the user. `power` the specified or calculated study power.

## Note

A summary of the key features of superiority, equivalence and non-superiority trial comparisons is shown in the following table (adapted from Campbell et al., 2018 [page 170] and Wang et al., 2017):

 --------------- ------------------------- ------------------------ ---------------------- ---------------------- Test for Null hypothesis Alt hypothesis Type I error Type II error --------------- ------------------------- ------------------------ ---------------------- ---------------------- Superiority H0: Ps - Pn == 0 H1: Ps - Pn != 0 2 sided, 0.050 1 sided, 0.10 or 0.20 Equivalence H0: |Ps - Pn| >= delta H1: |Ps - Pn| < delta 2 sided, 0.050 2 sided, 0.10 or 0.20 Non-inferiority H0: Ps - Pn >= delta H1: Ps - Pn < delta 1 sided, 0.050 1 sided, 0.10 or 0.20 --------------- ------------------------- ------------------------ ---------------------- ----------------------

With a superiority trial the aim is to estimate Ps - Pn with a view to claiming a difference between groups.

With an equivalence trial the aim is not to estimate Ps - Pn but to judge if it is within the margins defined by `delta`.

With a non-inferiority trial the aim is not to estimate Ps - Pn but to judge if it is within the margins defined by `delta`.

Consider a clinical trial comparing two groups, a standard treatment (s) and a new treatment (n). A proportion of subjects in the standard treatment group experience the outcome of interest P_{s} and a proportion of subjects in the new treatment group experience the outcome of interest P_{n}. We specify the absolute value of the maximum acceptable difference between P_{n} and P_{s} as δ.

For an equivalence trial the null hypothesis is:

H_{0}: |P_{s} - P_{n}| ≥q δ

The alternative hypothesis is:

H_{1}: |P_{s} - P_{n}| < δ

An equivalence trial is used if want to prove that two treatments produce the same clinical outcomes. The value of the maximum acceptable difference δ is chosen so that a patient will not detect any change in effect when replacing the standard treatment with the new treatment. For a superiority trial the value entered for `delta` must be greater than or equal to zero.

Note that when:

sign(P_n - P_s - δ) \neq sign(z_{1-α} + z_{1-β})

there is no solution for study power. For typical values of α and β this would occur if P_{n} - P_{s} - δ < 0. That is, when the targeted alternative is within the null hypothesis. The function issues a warning if these conditions are met.

When calculating the power of a study, the argument `n` refers to the total study size (that is, the number of subjects in the treatment group plus the number in the control group).

## References

Chow S, Shao J, Wang H (2008). Sample Size Calculations in Clinical Research. Chapman & Hall/CRC Biostatistics Series, pp. 91.

Ewald B (2013). Making sense of equivalence and non-inferiority trials. Australian Prescriber 36: 170 - 173.

Julious SA (2004). Sample sizes for clinical trials with normal data. Statistics in Medicine 23: 1921 - 1986.

Julious SA (2009). Estimating Samples Sizes in Clinical Trials. CRC, New York.

Machin D, Campbell MJ, Tan SB, Tan SH (2009). Sample Size Tables for Clinical Studies. Wiley Blackwell, New York.

Wang B, Wang H, Tu X, Feng C (2017). Comparisons of superiority, non-inferiority, and equivalence trials. Shanghai Archives of Psychiatry 29, 385 - 388. DOI: 10.11919/j.issn.1002-0829.217163.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## EXAMPLE 1 (from Machin, Campbell, Tan and Tan 2009 p. 113): ## Bennett, Dismukes, Duma et al. (1979) designed a clinical trial to test ## whether combination chemotherapy for a shorter period would be at least ## as good as conventional therapy for patients with cryptococcal meningitis. ## They recruited 39 patients to each treatment arm and wished to conclude ## that a difference of less than 20% in response rate between the treatments ## would indicate equivalence. Assuming a one-sided test size of 10%, a ## power of 80% and an overall response rate of 50%, what would be a ## realistic sample size if the trial were to be repeated? epi.ssequb(treat = 0.50, control = 0.50, delta = 0.20, n = NA, r = 1, power = 0.80, nfractional = FALSE, alpha = 0.10) ## A total of 166 subjects need to be enrolled in the trial, 83 in the ## treatment group and 83 in the control group. ```

epiR documentation built on Oct. 11, 2021, 9:08 a.m.