The standard two-arm, randomized clinical trials compare an intervention to standard treatment with equal (usually) numbers of patients randomized to each treatment arm. To prevent heterogeneity, only data from within the current trial, as opposed to historical data, are used to assess the treatment effect that defines equivalence between the two treatments.
The USFDA guidance for developing therapeutics states that the equivalence limit represents a consensus for that particular circumstance and claim. Small statistical differences between the arms can be considered clinically insignificant, therefore, allowing the treatments to be ‘proved’ as equivalent. Another definition for such trials is that the equivalence limit should be statistically small with little or no consequence within the range of clinical variability between the two testing arms.
There is no consensus between USFDA and EMA for choosing an equivalence limit in clinical trials. The factors that can be used to classify an equivalence limit are based on the following three criteria:
- The margin between the intervention and standard arm is small enough to conclude an effect of the intervention
- The smallest margin value that represents a meaningful difference, or a large value that represents a meaningless difference between the two arms
- A value that is small compared to background clinical variability or has other good statistical properties.
In this article, we put together some of the factors that are relevant in deciding an appropriate margin of the clinical trials focussed on establishing non-inferiority, superiority, or equivalence to an existing treatment.
Sample size and margin
The number of patients in each arm of the clinical trial should be large enough so that the margin is higher than the lower bound of the 95% confidence interval difference between the treated group and the control group.
The sample size is usually calculated under the assumption that the intervention and control treatment have equal effects i.e. when the margin is zero. This is often the case and is also desirable that the new treatment is slightly better. In such cases, the required sample size would decrease considerably (Table 1).
Despite the theoretical and statistical principles, uncertainty in deciding the sample size still exists regarding how these principles can be applied to actual clinical studies. Even if so, these trials should provide proper explanations of the rationale for margin.
Table 1. Sample size required for non-inferiority comparisons (Schumi et. al, 2011).
| True proportion in active control | Non-inferiority bound using 10% margin | Approximate sample size per group assuming 1:1 randomization to new treatment and control required under: | ||
|
Equal effects |
5% benefit | 10% benefit | ||
|
0.1 |
0.09 | 19,200 | 8,725 |
5,050 |
|
0.2 |
0.18 | 8,500 | 3,900 | 2,250 |
|
0.3 |
0.27 | 4,970 | 2,260 |
1,300 |
| 0.4 | 0.36 | 3,200 | 1,450 |
825 |
|
0.5 |
0.45 | 2,100 | 1,000 | 550 |
| 0.6 | 0.54 | 1,440 | 640 |
360 |
| 0.7 | 0.63 | 930 | 405 |
225 |
Interchanging from superiority to non-inferiority and vice versa
Switching from non-inferiority to superiority is feasible provided that the margin (with respect to the control) is predefined or can be justified during the analysis. An important consideration for non-inferiority trials is that proving the margin may be difficult. It is limited to some cases where there is a widely accepted value or a non-inferiority margin already available in the literature. The statistical sensitivity should be sufficiently high. This ensures that relevant differences between the two arms are detected if they exist or are found during the analysis. Therefore, evidence or results-based approach is required to prove equivalence or superiority, or noninferiority of the intervention in the clinical trial when comparing it with the standard treatments.
Limitations for crossover trial designs
It is inevitable that some patients crossover from the intervention arm to the standard arm before or during the clinical study due to complexities in trial planning or subject preference. Although the intention-to-treat (ITT) analysis is the preferable approach for deciding the outcome of such trials, its role in non-inferiority trials is still under question. This has led to the use of other approaches like Per-Protocol (PP) or As-treated (AT) analysis, although inherent biases in such approaches usually exist. If minimal crossovers occur, the AT approach would have the lowest type I error with a small opportunity for bias. Results of clinical trials with a high number of crossovers should be interpreted with caution, especially when the crossover is non-random. Therefore, crossovers are usually prevented in such clinical trials.
In superiority or equivalence trials, analysis according to the ITT principle and PP analysis shows higher confidence intervals and significance (P) values which is similar to inferiority trials without crossover design.
Perspectives
- Presently, success in two-arm randomized clinical trials depends upon success in the primary outcomes. It is rare that secondary or exploratory outcomes such as other aspects of benefit, such as safety, and regulatory success are considered. Therefore, these trials require more than one clinical study or a multicentric approach to prove statistical outcomes more appropriately.
- Adding composite endpoints to primary outcomes like efficacy with quality of life, cost or safety, would make the analysis complicated but more rightful and significant
- We propose the revision or modification of the regulations to consider multiple interconnected dimensions of a new product. This would make the analysis become more complicated, but would also lead to multi-factorial and robust approvals
#non_inferiority #equivalency #clinicaltrials
Sources
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3153695/
https://pubmed.ncbi.nlm.nih.gov/22232060/
https://bmjopen.bmj.com/content/4/10/e006531
https://trialsjournal.biomedcentral.com/articles/10.1186/1745-6215-12-106