I’m really pleased to release my second Guest Blog here at www.pharmascholar.co.uk
Within the piece, Professor Andrea Manfrin and Dr Miland Joshi provide their take on comparator use for application during vaccine studies; a prime example being those studies undertaken during the ongoing COVID-19 pandemic. The text provides the reader with a background to the numbers behind the statistics and calculations used for data analysis alongside recommendations. Both academics are based within the Schools of Medicine, Dentistry, Pharmacy and Biomedical Sciences at the respected University of Central Lancashire, United Kingdom.
Abstract
During the last 12 months, COVID-19 became a global problem. Universities and drug companies are working together for the development of treatments. Vaccines appear to be one of the most promising treatments, and trials are completed, and others are ongoing. All these studies tend to use a common comparator, the percentage of vaccine efficacy (VE%), calculated using the following formula VE=(1-RR) x100. A recent study published in a renowned medical journal presented large trial results using a different formula VE=(1-OR) x100. We compared the analysis using relative risk (RR) versus an odds ratio (OR), and we did not find any large difference in the results. Nevertheless, we would advise using RR instead of OR in the interests of accuracy, for best practice.
Main Body
Logunov et al. (2021) conducted an interim analysis of a randomised controlled phase 3 trial evaluating the safety and efficacy of a vector-based heterologous prime-boost COVID-19 vaccine (1). To calculate the vaccine efficacy, they used the following formula: VE=(1-OR) x100. The odds ratio (OR) is calculated by the formula OR = ad/bc, where a is the number of cases in the vaccinated arm, b is the number of non-cases in the arm, c is the number of cases in the control group, and d is the number of non-cases in this arm.
The Department of Epidemiology of the School of Public Health, UCLA, however, suggests that the formula for the calculation of the vaccine efficacy is VE=(1-RR) (2), where the relative risk (RR) =[a/(a+c)]/[b/(b+d)]. The authors also added that RR must be less than 1 for the vaccination to be preventive.
Vaccine efficacy has been explained by Hodgson et al. (2020)(3); in simple terms, it represents the percentage reduction in disease incidence in a vaccinated group compared to a non-vaccinated group under optimal conditions. The UCLA definition is consistent with the one provided by Spiegelhalter and Masters (4).
The difference between OR and RR may be described as follows: RR represents a ratio of the probabilities (p) or risks of an event or outcome across two groups; OR is a ratio of the odds of an event or outcome across two groups (5). OR is the ratio of two odds; RR is the ratio of two probabilities (P); odds of an event = P/(1-P).
Recommendations
We recommend using RR instead of the OR to calculate efficacy because efficacy is the reduction in the risk effected by the vaccine. To calculate the log-transformed RR standard errors, we used the formula in Altman's Statistics with Confidence (6). We have compared the table in their publication with a table that we created using the formula VE=(1-RR) x100. As shown in Table 1, the differences are small. The only noticeable discrepancy lies in the lower confidence interval for the >60 groups. It should be said that with the large numbers involved in a clinical trial, the prevalence or risk is low, and in such circumstances OR and RR are approximately equal. Nevertheless, we believe that it is important to use the correct formula for the calculation to provide not only the best evidence but also for following best practice.
References
1. Logunov DY, Dolzhikova I V, Shcheblyakov D V, Tukhvatulin AI, Zubkova O V, Dzharullaeva AS, et al. Safety and efficacy of an rAd26 and rAd5 vector-based heterologous prime-boost COVID-19 vaccine: an interim analysis of a randomised controlled phase 3 trial in Russia. Lancet [Internet]. 2021;397(10275):671–81. Available from: http://dx.doi.org/10.1016/S0140-6736(21)00234-8
2. UCLA. Measuring Effectiveness of Immunisation Programs. 1996;(1):1–20. Available from: http://www.ph.ucla.edu/EPI/41508/415cmat/lect14_41508.pdf
3. Hodgson SH, Mansatta K, Mallett G, Harris V, Emary KRW, Pollard AJ. What defines an efficacious COVID-19 vaccine? A review of the challenges assessing the clinical efficacy of vaccines against SARS-CoV-2. Lancet Infect Dis [Internet]. 2021;21(2):e26–35. Available from: http://dx.doi.org/10.1016/S1473-3099(20)30773-8
4. Spiegelhalter D, Masters A. 2021. Behind the numbers: what does it mean if a Covid vaccine has 90% efficacy? Available from: https://www.theguardian.com/theobserver/commentisfree/2021/jan/24/behind-the-numbers-what-does-it-mean-if-covid-vaccine-has-90-per-cent-eifficacy) [Accessed 21 Jan 2021]
5. Ranganathan P, Aggarwal R, Pramesh C. Common pitfalls in statistical analysis: Odds versus risk. Perspect Clin Res. 2015;6(4):222.
6. Altman, Douglas G., Machin, David, Bryant, Trevor N. and Gardner, Martin J. (eds.) (2000) Statistics with confidence: confidence intervals and statistical guidelines, 2nd ed. London. BMJ Books, 254pp.
