I think we need to keep in mind the important distinction between correct frequentist statistics, and simply bad statistics.
@Sander posted a link to a youtube video (I’ve also posted it here in a few different threads) on p-values, confidence intervals, and their common, but incorrect interpretations.
It was mentioned in passing in the video that Jeffries and Fisher would pose statistical puzzles to one another. Jeffries commented that they rarely disagreed in their interpretation using the methods each of them had derived.
(If anyone has a source for this aside from the video, I’d appreciate it).
Just looking at your first link made me very curious as to how they came to this conclusion. I’m no physician, but considering what is known about smoking, I find the idea of “no association” with a serious respiratory disease implausible, to put it charitably.
They did an effect size meta-analysis of 5 studies (!), where 1 study had nearly 90% of the total weight. Their figure 1 lists the CI for odds ratio estimated by this study as 1.51 (0.97 - 2.36).
To call this a “meta-analysis” or “evidence synthesis” when most of the weight is driven by 1 study is misleading at best.
Even worse, they misinterpreted their own data. It is erroneous to use the inclusion of the null in an aggregate CI as a short cut to doing a hypothesis test, especially if the data are of questionable homogeneity. You can aggregate the actual signal from the individual studies by extracting the 1 side p value and combining using one of the many available methods.
As someone who is sympathetic to the Bayesian philosophy, I still find the correct use of p-values helpful. I combined Bayesian reasoning with a frequentist p-value combination procedure in another thread:
There is a Bayesian way to examine this report from the estimation perspective. Robert Matthews has adapted an important technique inititally developed by IJ Good that flips the problem around, and derives the prior that justifies when a finding is credible. It puts frequentist reports in a Bayesian context that is so often missing, leading to errors of interpretation. One of his more recent articles was published by the Royal Society (not long after the ASA’s p-value position paper).
Matthews Robert A. J. (2018) Beyond ‘significance’: principles and practice of the Analysis of Credibility R. Soc. open sci. 5: 171047. 171047 (link)
Taking their aggregate estimate a face value, they report an OR of 1.69 (0.41 - 6.92). Is it credible, from a Bayesian perspective, that there is “no association?”
I set up a spread sheet that uses the formulas Matthews derived in this paper. Using the expression of an “honest advocate”, I’ve derived that the he/she could have a 95% prior credible interval as high as 11.2 to 1 in favor of smoking being a factor in worse outcomes for Covid patients.
These data are entirely consistent with smoking being a negative factor for Covid. Anyone who is skeptical should justify this belief.
As far as philosophy: I recommend an old paper by Bradley Efron (with commentaries), titled:
https://amstat.tandfonline.com/doi/10.1080/00031305.1986.10475342
I come to find the comment by Herman Chernoff on this paper especially wise:
Blockquote
With the help of theory, I have developed insights and intuitions that prevent me from giving weight to data dredging and other forms of statistical heresy. This feeling of freedom and ease does not exist until I have a decision theoretic, Bayesian view of the problem … I am a Bayesian decision theorist in spite of my use of Fisherian tools.
Addendum: @Stephen wrote another paper from a philosophical POV that is worth study.
Senn, Stephen, (2011), You May Believe You Are a Bayesian But You Are Probably Wrong, Rationality, Markets and Morals, 2, issue 42, number 42, https://econpapers.repec.org/article/rmmjournl/v_3a2_3ay_3a2011_3ai_3a42.htm