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Infectio

Print version ISSN 0123-9392

Infect. vol.26 no.1 Bogotá Jan./Mar. 2022  Epub Mar 13, 2021

https://doi.org/10.22354/in.v26i1.1003 

CARTA AL EDITOR

The evidence of Bayesian A/B testing in the contrast of clinical events by COVID-19

La estimación de la evidencia de la prueba A/B bayesiana en el contrate de eventos clínicos por COVID-19

Cristian Ramos-Vera1  * 

1 Universidad Cesar Vallejo. Facultad de ciencias de la salud. Área de investi gación, Lima, Perú. https://orcid.org/0000-0002-3417-5701


Sr. Editor:

The clinical investigations reported in this journal employ the standard framework of frequentist statistics based on signifi cance assumptions (p < 0.05). This method leads to a dicho tomization of the results as “significant” or “non-significant” requiring the evaluation of statistical hypotheses1. Therefore, the use of the Bayesian approach is important as an improved way of drawing statistical conclusions from clinical data since it facilitates the answer to the question, what is the proba bility that the effect is conclusive based on the data, which provides greater validity to the significant conclusions. One of the best known methods is the Bayes factor (FB), which esti mates the probability of one hypothesis relative to the other given the data (e.g., null hypothesis vs alternate hypothesis)1,2, this allows estimation of the weight of evidence (10 times the decimal logarithm value of the FB) (3,4, useful for decision ma king of significant findings, where results with evidence values greater than 20 are optimal for clinical decision making.

Replication of clinical results is recommended to validate the practical credibility of such findings by Bayesian inference, useful in various statistical tests1,2, because such estimates are convertible to an effect size (ES), for example, the odd ra tios (OR) measure or the area under the curve ROC (AUROC) (5 using an online calculator as referred to by Ramos-Vera2.

Another Bayesian model of interest is the Bayesian A/B test to contrast two similar clinical events considering the assig nment of prior distributions and the control of such sample data according to the logarithmic odds ratio scale (logOR<0, logOR>0) (6, more suitable for simultaneous evaluation with a normal distribution7. The contrast of variation between both proportional groups is represented by the BF, this is useful for various studies that include participants with and without the clinical event of interest, of greater interest to the current pandemic context given the comorbidity or mortality due to COVID-196. The application of this Bayesian model favors greater precision of difference rates in national and inter national data between two composite proportional groups, where more realistic probabilities are reported given the data by transforming the Bayesian TE obtained: OR to probability = OR/(OR+1) and their respective intervals. Such estimates allow us to determine how likely it really is that participants with the clinical outcome of interest will have such an occu rrence, which has been recommended by Bayesian Neurolo gy Group-Texas (BNG-TX) (6.

For the present letter we considered data reported from a study of the present journal, which included adult patients with serological and molecular tests for COVID-19 from three hospitals in the Peruvian highlands (Ancash and Apurimac) included with clinical suspicion between April and June 2020 (8. The objective was to determine how likely is actua lly the most frequent comorbidity clinical events at positi ve diagnosis of COVID-19 (logOR>0). compared to negative diagnosis (logOR<0).

Table 1 indicates that the clinical outcome of having AT and positive COVID-19 diagnosis was of higher occurrence with a substantial weight of evidence (7.36) with a 66% probability of risk in contrast to the other event. Having a diagnosis of DMT2 with COVID-19 presented a decisive evidence value of 22.67 and a 79% probability of occurrence versus the other event. Such Bayesian findings refer to wide intervals given the small sample sizes, therefore, future studies with larger sample sizes are recommended to pinpoint more stable pro bability distributions.

Table 1 Bayesian A/B test values 

AT: arterial hypertension, DMT2: Diabetes mellitus type 2; *1-5: minimal, 5-10: substantial, 10-15: good, 15-20: very good, 20 to more: decisive3.

Statistical application using Bayesian A/B testing may be very useful in other COVID-19 related research(5,6,9. Therefore, we recommend the articles by Rosenfeld and Orson10, and Kelter1 that can serve as tutorial guides for a better understanding to the investigators of the present journal on various statistical techniques of major clinical use using the Bayesian method.

References

1. Kelter R. Bayesian alternatives to null hypothesis significance testing in biomedical research: a non-technical introduction to Bayesian inference with JASP: BMC Med Res Methodol. 2020; 20:1-12. https://doi.org/10.1186/s12874-020-00980-6Links ]

2. Ramos-Vera CA. The use of Bayes factor in clinical cardiology research. Rev Esp Cardiol. 2021. doi: 10.1016/j.rec.2021.01.020. [ Links ]

3. Weed DL. Weight of evidence: a review of concept and methods. Risk Anal. 2005;25(6):1545-57. doi: 10.1111/j.1539-6924.2005.00699.x [ Links ]

4. Jaynes ET. Probability theory: The logic of science. Cambridge University Press. 2003 [ Links ]

5. Ramos-Vera C. Essential statistical analyses beyond the Bayes factor in intensive care medicine research and COVID-19. Med Intensiva. doi: 10.1016/j.medin.2021.05.007. [ Links ]

6. Arbona-Haddad E, Tremont-Lukats IW, Gogia B, Rai PK; Bayesian Neurology Group-Texas (BNG-TX). COVID-19 encephalopathy, Bayes rule, and a plea for case-control studies. Ann Clin Transl Neurol. 2021;8(3):723- 25. https://doi.org/10.1002/acn3.51288 Links ]

7. Zampieri FG, Casey JD, Shankar-Hari M, Harrell FE Jr, Harhay MO. Using Bayesian Methods to Augment the Interpretation of Critical Care Trials. An Overview of Theory and Example Reanalysis of the Alveolar Recruitment for Acute Respiratory Distress Syndrome Trial. Am J Respir Crit Care Med. 2021;203(5):543-552. https://doi.org/10.1164/rccm.202006-2381CP. [ Links ]

8. Moya-Salazar J, Cañari B, Sánchez-Llanos A, Hernández SA, Eche- Navarro M, Salazar-Hernández R, Contreras-Pulache H. Factores de riesgo en población rural andina con COVID-19: un estudio de cohorte retrospectivo. Infectio, 2021;25(4): 256-61. [ Links ]

9. Hulme OJ, Wagenmakers EJ, Damkier P, Madelung CF, Siebner HR, Helweg- Larsen J, et al. A Bayesian reanalysis of the effects of hydroxychloroquine and azithromycin on viral carriage in patients with COVID-19. Plos One. 2021;16(2): e0245048. https://doi.org/10.1371/journal.pone.0245048Links ]

10. Rosenfeld J, Olson JM. Bayesian Data Analysis: A Fresh Approach to Power Issues and Null Hypothesis Interpretation. Appl Psychophysiol Biofeedback. 2021. https://doi.org/10.1007/s10484-020-09502-y Links ]

Cómo citar este artículo: C. Ramos-Vera. The evidence of Bayesian A/B testing in the contrast of clinical events by COVID-19. Infectio 2022; 26(1): 99-100

There was no financing

Received: June 12, 2021; Accepted: July 26, 2021

* Autor para correspondencia: Correo electrónico: cristony_777@hotmail.com Av. Del Parque 640, San Juan de Lurigancho 15434. Lima. Perú.

No conflict of interest

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