#Introduction

This document presents a critical review of the study titled “Efficacy of the intertransverse process block: single or multiple injection? A randomized, non-inferiority, blinded, cross-over trial in healthy volunteers”. The study compares the efficacy of single versus multiple injections in achieving sufficient block through a non-inferiority trial design. Here, we will evaluate the sample size calculation, methodology, and statistical validity of the non-inferiority approach, with coding examples in R to demonstrate sample size calculations for similar trials.

Non-Inferiority Trial Design and Sample Size Calculation

Non-inferiority trials aim to determine if a new intervention is not significantly worse than a standard treatment by a predefined margin, called the non-inferiority margin (d). For this trial design, we use the following null and alternative hypotheses:

Sample size in a non-inferiority trial depends on the following key parameters (Julious, 2004):

Step 1: Setting Parameters

In this analysis, we will reproduce a sample size calculation for a continuous outcome non-inferiority trial based on the specifications given in the study.

# Parameters for sample size calculation
alpha <- 0.05                  # Significance level (5%)
power <- 0.80                  # Desired power (80%)
sd_outcome <- 1.42              # Assumed standard deviation from previous ITP literature
non_inferiority_margin <- 1.5  # Non-inferiority margin (clinically acceptable difference)

# Calculate critical values for the normal distribution
z_alpha <- qnorm(1 - alpha)
z_beta <- qnorm(power)

Here, we define the significance level, power, standard deviation (from relevant prior studies or pilot data), and non-inferiority margin (Julious, 2004). The critical values for a normal distribution, z_alpha and z_beta, correspond to the alpha and beta levels, respectively.

Step 2: Calculating Sample Size

The formula for calculating sample size in a continuous outcome non-inferiority trial is given by: Julious SA. Sample sizes for clinical trials with Normal data. Statist. Med. 2004; 23:1921-1986. \[ n = \frac{2 \times \sigma^2 \times (z_{\alpha} + z_{\beta})^2}{d^2} \]

This formula ensures enough participants to detect a non-inferior outcome within the chosen margin with the specified power (Julious et al., 1986).

# Sample size calculation
n <- (2 * sd_outcome^2 * (z_alpha + z_beta)^2) / non_inferiority_margin^2
n <- ceiling(n)  # Rounds up to the next whole number
cat("Required sample size per group:", n, "\n")
## Required sample size per group: 12

The ceiling() function rounds up to ensure whole participants are recruited per group. In this example, a sufficiently powered study would require n participants in each arm.

Step 3: Interpreting Results

The calculated sample size provides the minimum number of participants needed in each group to achieve statistical power and accurately evaluate the non-inferiority hypothesis.

The importance of correctly calculating sample size in non-inferiority trials lies in reducing the likelihood of Type II errors (false negatives), which can lead to erroneous conclusions of non-inferiority when the sample is too small (Piaggio et al., 2006).

Assessing the Methodology of Nielsen et al.

The authors of the study based their sample size calculation on data from previous intertransverse process blocks, rather than using data from the current standard of care (paravertebral block). This approach might affect the study’s validity, as non-inferiority trials should ideally base the margin and parameters on well-established standards to ensure clinical relevance (Piaggio et al., 2012). The sample size, calculated for a significance level of 0.05 and a power of 80%, might not be adequate if the standard deviation for the paravertebral block is different from that of the chosen reference.

Step 4: Reevaluation Based on Standard Treatment Data

To address this, we recalculate the sample size using data from the standard paravertebral block.

Assuming a standard deviation of 1.65 (Uppa paravertebral blocks. DOI: 10.1097/AAP.0000000000000631) and the same non-inferiority margin:

# Updated parameters for recalculation
sd_standard <- 1.65

# Recalculate sample size based on updated parameters
n_updated <- (2 * sd_standard^2 * (z_alpha + z_beta)^2) / non_inferiority_margin^2
n_updated <- ceiling(n_updated)
cat("Updated sample size per group:", n_updated, "\n")
## Updated sample size per group: 15

The recalculated sample size based on updated data demonstrates the difference in sample requirements if parameters are adjusted for the standard treatment, showing the impact of parameter selection on study power and validity.

Conclusion

This analysis underscores the importance of sample size calculations tailored to the treatment standard in non-inferiority trials, particularly when comparing an intervention to a widely accepted standard. Studies that do not consider the standard treatment may lack sufficient power, thus risking false conclusions about efficacy.

In conclusion, non-inferiority studies require rigorous adherence to methodological standards to ensure clinical relevance, especially when the treatment is evaluated against an established intervention (Piaggio et al., 2012; Jones et al., 1996).

References

Julious SA. Sample sizes for clinical trials with Normal data. Stat Med. 2004;23:1921-1986. Jones B, Jarvis P, Lewis JA, Ebbutt AF. Trials to assess equivalence: the importance of rigorous methods. BMJ. 1996;313(7048):36-39. Piaggio G, Elbourne DR, Altman DG, Pocock SJ, Evans SJ. Reporting of noninferiority and equivalence randomized trials: extension of the CONSORT 2010 statement. JAMA. 2012;308(24):2594-2604. Sealed Envelope Ltd. 2012. Power calculator for continuous outcome non-inferiority trial. [Online] Available from: https://www.sealedenvelope.com/power/continuous-noninferior/