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Different methods are available to combine or synthesise different data sources available from literature on the same subject, for instance, if one needs to determine the effect of drug A in reducing cardiac events compared to the effect of drug B in reducing cardiac events.

When head-to-head trials for drug A versus B are available, direct comparison is possible using a pairwise meta-analysis. Alternatively, a network meta-analysis might be required, where head-to-head trials are not available for drug A versus drug B directly, but where there are studies comparing drug A to drug C and drug B to drug C.

Pairwise meta-analysis

To statistically combine data on effect size from different sources with direct comparison data, one would typically employ a pairwise meta-analysis technique. Two different options are most widely available, namely a fixed-effects meta-analysis and a random-effects meta-analysis ^[1].

Fixed effects meta-analyses are usually used where the study does not intend to generalise the results beyond studies included in the analysis. Where there isn’t significant heterogeneity between studies (statistical, methodological, or clinical heterogeneity) and where the number of included studies is low (less than 5 studies)^[1].

When one aims to generalise the results to studies outside of those included in the analysis, have significant heterogeneity between studies, or at least 5 studies included in the analysis, one would typically employ a random effects meta-analysis ^[1].

The outcome of either method would be a pooled effect size. This can be a relative effect size (such as relative risk RR or odds ratio OR for dichotomous variables) or an absolute effect size (such as risk difference RD, for dichotomous variables, or weighted mean difference or standardized mean difference, for continuous variables) ^[1].

The results of meta-analyses are typically reported as forest plots, showing the effect size and 95% confidence intervals for each study included in the analysis, as well as the pooled or summary effect size and 95% confidence intervals.

Network meta-analysis (indirect treatment comparison)

Indirect treatment comparisons or network meta-analyses (NMA) are performed when direct head-to-head trials are not available for drug A compared to drug B, but where there is a common comparator study for both drugs A and B with drug C. Further to this, multiple treatments can be compared at the same time, and by including direct and indirect evidence (mixed NMA) ^[2]. In addition, NMA can be used to rank different treatments.

Different NMA models are available, including the multivariate model and the hierarchical model. A reference treatment must be selected, to which all studies will be compared (usually placebo, or the treatment that is most commonly compared to).

The results are presented in a league or network table, which shows the summary estimates and 95% confidence intervals for the different comparisons. In addition, the ranking probabilities for each treatment in the comparison can be presented as a table or histogram.

Conclusion

Study effects can be synthesised using different statistical techniques, such as pairwise meta-analysis for direct comparisons, or network meta-analysis for mixed or indirect comparisons.

One needs to consider the different assumptions and limitations of each method, as well as the goal of the data synthesis, to select the relevant method.

References

1. 1. Tufanaru C, Munn Z, Stephenson M, Aromataris E. Fixed or random effects meta-analysis? Common methodological issues in systematic reviews of effectiveness. International Journal of Evidence-Based Healthcare. 2015. 13(3): 196-207.
   2. Rouse B, Chaimani A, Li T. Network meta-analysis: an introduction for clinicians. Intern Emerg Med. 2017: 12(1): 103-111.

On December 31, 2019, an official case of the novel respiratory disease of the species of coronaviruses was reported in Wuhan, China (WHO, 2020), marking the beginning of what has now proved to be one of the most devastating viral outbreaks in modern history.

The coronavirus pandemic (COVID-19) came as a rare and unprecedented event. Could this be what economists call a “black swan”? A black swan is an extremely rare event that is often unpredictable beforehand. Black swan events usher catastrophic damage to the economy as they negatively impact financial markets and investments. Some could argue that even the use of robust modelling cannot prevent a black swan (Staff, 2020).

In this article we will argue whether the COVID-19 pandemic is a true black swan event. The Black Swan theory was developed by professor, statistician, and former options trader Nassim Nicholas Taleb, and must meet three criteria:

• • “First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility.
  • Second, it carries an extreme ‘impact.’
  • Third, despite its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.” (Taleb, 2011)

Now, let us discuss the above attributes individually and hope to reach a conclusion.

Is the COVID-19 pandemic an outlier?

History has proven that infectious diseases, epidemics, and pandemics are the number one mass killers. More people died in the 1918 flu outbreak than in the First World War (Jones, 2018), with the 1918 influenza pandemic being the worst severe pandemic in recent history. Scientists have recorded evidence of past possible coronavirus pandemics and according to an article by (Heing, 2020), experts warned of a possibility of a pandemic decades ago. Therefore, COVID-19 cannot be classified as an outlier but is merely part of a pattern of increasingly frequent epidemics that have coincided with urbanization, globalization, and climate change.

Does COVID-19 carry an extreme impact?

COVID-19 is not anticipated to have an impact even remotely close to that of the 1918 flu pandemic which saw at least fifty million deaths. However, with focus on the financial impact of COVID-19, it might be too early to compare previous recessions to the 2020 Coronavirus Crash, but it has been predicted that the current pandemic will continue to have an extreme impact on national economies.

In March 2020, the COVID-19 pandemic began decimating the economy. A mandatory lockdown was imposed across the globe resulting in global economic shutdowns, panic buying and supply disruptions which exacerbated the market, and thus mass hysteria ensued. The global stock market saw multiple severe drops, with the largest drop on Monday the 16^th of March 2020, and this has since been nicknamed “Black Monday II”. Banks and reserves across the world have cut their interest rates, bank rates and cash-flow rates in an attempt to deal with the pandemic (Hutchens & Chalmers, 2020).

Is the COVID-19 pandemic explainable or predictable in hindsight?

Since we are still in the midst of the COVID-19 pandemic crisis it cannot be said with certainty whether this pandemic will be normalized in retrospective.

Conclusion

Even though we cannot answer the third aspect of the Black Swan theory, we can already see that COVID-19 is not a Black Swan event by the mere fact that SARS-coronavirus outbreaks started in 2002 even though the world had nervously hoped that the outbreaks will be controlled before reaching the pandemic status. Instead, the COVID-19 pandemic can be defined as a White Swan event; something that would eventually take place with great certainty (Hutchins, 2020).

References

Heing, R. M., 2020. Experts warned of a pandemic decades ago. Why weren’t we ready?, s.l.: National Geographic.

Hutchens, G. & Chalmers, S., 2020. ABC News. [Online]
Available at: https://www.abc.net.au/news/2020-03-16/coronavirus-fears-see-australian-market-slump-to-start-new-week/12058904
[Accessed 18 November 2020].

Hutchins, G., 2020. Black Swans, Grey Swans, White Swans. [Online]
Available at: https://accendoreliability.com/black-swans-grey-swans-white-swans/
[Accessed 18 November 2020].

Jones, D., 2018. More People Died in the 1918 Flu Pandemic Than in WWI, s.l.: History.

Staff, I., 2020. Investopedia. [Online]
Available at: https://www.investopedia.com/terms/b/blackswan.asp#:~:text=A%20black%20swan%20is%20an,they%20were%20obvious%20in%20hindsight.
[Accessed 19 Nov 2020].

Taleb, N. N., 2011. Chapter 1: The Impact of the Highly Improbable. In: A. Lane, ed. The black swan : The impact of the highly improbable. s.l.:s.n.

WHO, 2020. Novel Coronavirus (2019-nCoV), s.l.: World Health Organization.

Article by Tina Victoria Mhazo

Pharmacoeconomic Analyst
VI Research

October 10^th marked World Mental Health Day.

Here’ a throwback to our days at HeXor (currently VI Research), for Dr Standers interview on SABC entitled; Depression is rife in South African Companies!

Plato’s Allegory of the Cave and lessons for today

If I ask: Why are blackberries red? And I tell you: Because they are green. What would you think? My answer, for some, may be perfectly logic, depending on their background and occupation. For a blackberry farmer, my answer would not only be perfectly logic, but they would actually have the correct answer immediately. However, for most of us, the question and the answer would have been confusing. By simply changing my words, I would have limited this confusion. Why are blackberries red? Because they are not ripe (= green). Blackberries actually go from red to black as they ripen.

If I ask, today, whether humans are living in caves, most will answer: No, of course not.

However, in similar fashion, this might not be true, depending on how we interpret the question? During the COVID 19 pandemic and global lockdown, many people might answer: Yes! This lockdown is a cave I cannot escape from. However, there is a deeper, metaphorical cave we might in fact be living in without even knowing. In this article I turn to the masters from the past and stand on their shoulders to challenge us. Let’s turn to the philosophers, people like Socrates, Plato and Aristotle.

The word philosophy in essence means the love of truth. As scientists and researchers, we are therefore all philosophers as we search for truth. In Plato’s Allegory of the Cave, he challenges society that many people live in caves and in a belief that is not based on truth.

According to Wheeler in Literary Terms and Definitions (Carlson Carson-Newman University) allegories are typically used as “literary devices or as rhetorical devices that convey (semi-) hidden or complex meanings through symbolic figures, actions, imagery or events which together create a moral spiritual or political meaning the author wishes to convey”.

The Allegory of the Cave distinguishes between those who make observational knowledge their source of truth and those who see the real truth. Stated differently (and in line with the late Jack Welsch’s first rule of business): The first rule of success is to confront reality. That means seeing the world the way it really is, and not the way we want it to be.

With that said, let us paint the picture of the Cave as was portrayed by Plato. There are four scenes in this allegory: the cave and its inhabitants; the games the inhabitants play; the escape from the cave; and the return to the cave.

The Cave and its inhabitants: Three prisoners are locked in chains in a cave, all facing an empty cave wall. They have been there all their life. They cannot move at all. Not even turn their heads. Behind them, there is a fire burning and other, free people are walking silently going about their day between the fire and the prisoners. The only thing the prisoners can see are the moving shadows on the wall as the free people pass by. For them, the shadows represent truth, their truth.

The games they play: They invent a game to guess what shadow image will appear next. When someone guesses right, he is hailed as a genius, the other two in awe of his wisdom.

The escape: Then, one prisoner escapes. He exists the cave and sees a world he never anticipated. He sees the sun as the source of true light. While initially he cannot believe it, he experiences beauty and creation and understands that the shadows they saw were only images of the real truth. That the shadows were not truth. It was meaningless.

The return: The escapee then returns to the Cave to share with his fellow prisoners his new knowledge. They do not believe him and threatens to kill him if he sets them free.

The Cave challenges us to always confront reality; to always question, even empirical evidence; to distinguish between perceptions and beliefs and truth. As scientists we need to remain objective and curious. We need to never stop questioning. We need to treat current “truths” as the best possible version of the truth given the evidence at our disposal. We need to be aware that new evidence might be forthcoming that will challenge current wisdom (shadows on the wall?) and we need to open ourselves for those possibilities.

Some truths are most likely irrefutable. For example, that earth is in fact round. Some cause and effect truths are irrefutable, for example that sunset leads to darkness. However, most of today’s empirical evidence is not irrefutable. Drug safety and efficacy for example remains the best version based on existing evidence.

Furthermore, Plato’s Cave teaches us that it is seldom popular or well accepted when we challenge the current convention and beliefs. Think about the concept of glycaemic index. When Jenkins constructed the index in 1981, he was ridiculed by his peers.

Lastly, Plato’s Cave challenges us all to think like philosophers, those who are in love with truth and will continue searching for truth. It challenges us to seek truth outside the basic constructs we were taught. It challenges the belief that, just because someone has an opinion, she or he is a genius. It challenges us to exit the Cave and to let go of the straddling bands that keeps us in the Cave.

“Logic is immaturity weaving its nets of gossamer wherewith it aims to catch the behemoth of knowledge. Logic is a crutch for the cripple, but a burden for the swift of foot and a greater burden still for the wise.”
― Mikhail Naimy, The Book of Mirdad

By Dr Tienie Stander