This document provides 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. We will assess 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 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 hypotheses:
Sample size in a non-inferiority trial depends on the following key parameters (Julious, 2004):
To reproduce a sample size calculation for a continuous outcome non-inferiority trial, the following parameters from the study should ideally be based on robust data sources.
In cases where direct measures of the standard deviation (SD) are unavailable, alternative data sources can provide an approximation. In this context, the study could utilize data from Uppal et al., which reported a range of 0 to 1 as the interquartile range (IQR) for block effectiveness. For a normal distribution, the SD can be approximated from the IQR by dividing it by 1.35 (the approximate scaling factor between the IQR and the SD in a normal distribution). Thus, the SD estimate is:
# Estimate standard deviation from the interquartile range (IQR)
iqr <- 1 # IQR value from 0 to 1 based on Uppal et al.
sd_approx <- iqr / 1.35 # Approximate standard deviation
cat("Approximate standard deviation:", sd_approx, "\n")## Approximate standard deviation: 0.7407407# Hozo SP, Djulbegovic B, Hozo I. Estimating the mean and variance from the median, range, and the size of a sample. BMC Med Res Methodol. 2005;5:13.This calculated SD of 0.74 serves as a conservative measure of variability, ensuring that the study has sufficient power while maintaining clinical relevance.
With these parameters, the non-inferiority margin should reflect a clinically meaningful threshold. Given the estimated SD of 0.74, a reasonable non-inferiority margin would be approximately 50% of this value, or 0.37. Using this margin provides sensitivity in detecting meaningful differences and maintains clinical rigor in determining non-inferiority.
# Parameters for sample size calculation
alpha <- 0.05 # Significance level (5%)
power <- 0.90 # Desired power (90%)
sd_outcome <- 0.74 # Estimated SD from IQR of Uppal's data
non_inferiority_margin <- 0.37 # Non-inferiority margin (50% of SD)
# Calculate critical values for the normal distribution
z_alpha <- qnorm(1 - alpha)
z_beta <- qnorm(power)The formula for calculating sample size in a continuous outcome non-inferiority trial is as follows (Julious, 2004):
\[ n = \frac{2 \times \sigma^2 \times (z_{\alpha} + z_{\beta})^2}{d^2} \]
This formula calculates the minimum number of participants needed to detect a non-inferior outcome within the chosen margin with the specified power.
# Sample size calculation
n <- (2 * sd_outcome^2 * (z_alpha + z_beta)^2) / non_inferiority_margin^2
n <- ceiling(n) # Rounds up to ensure whole participant numbers
cat("Required sample size per group:", n, "\n")## Required sample size per group: 69The function ceiling() rounds up to ensure an adequate number of participants per group.
This calculated sample size provides the minimum number of participants needed in each group to achieve sufficient power to evaluate the non-inferiority hypothesis accurately. Proper sample size calculation in non-inferiority trials reduces the risk of Type II errors (false negatives), which could lead to erroneous conclusions about non-inferiority if the sample is insufficient (Piaggio et al., 2006).
Nielsen et al. used data from previous intertransverse process blocks instead of referencing the standard paravertebral block, potentially impacting the study’s validity. Non-inferiority trials benefit from setting the margin and parameters based on standard, established treatments to ensure clinical relevance (Piaggio et al., 2012). Without considering variability in the paravertebral block, the sample size (powered at 80% and α = 0.05) might be inadequate if the standard deviation differs from that of the chosen reference.
To address this, we recalculate the sample size using an SD of 0.74 from standard paravertebral block studies (Uppal et al., DOI: 10.1097/AAP.0000000000000631), while keeping the same non-inferiority margin.
# Updated parameters for recalculation
sd_standard <- 0.74
# 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: 69This recalculated sample size reflects how differing parameters can influence power and validity.
This analysis demonstrates the importance of tailored sample size calculations for non-inferiority trials. When comparing a new intervention to an established standard, accurate parameter selection is essential. Using established treatment standards as a reference enhances the study’s clinical relevance and validity, thus reducing the risk of underpowered or inconclusive results (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.
Uppal et al. Paravertebral block studies. DOI: 10.1097/AAP.0000000000000631.