Category: Quality – Predictiveness
p-value vs. positive predictive value
Riddle me this:
What does it mean if a result is reported as significant at p < 0.05?
A If we were to repeat the analysis many times, using new data each time, and if the null hypothesis were really true, then on only 5% of those occasions would we (falsely) reject it.
B Without knowing the statistical power of the experiment, and not knowing the prior probability of the hypothesis, I cannot estimate the probability whether a significant research finding (p < 0.05) reflects a true effect.
C The probability that the result is a fluke (the hypothesis was wrong, the drug doesn’t work, etc.), is below 5 %. In other words, there is a less than 5 % chance that my results are due to chance.
(solution at the end of this post)
Be honest, although it doesn’t sound very sophisticated (as opposed to A and B), you were tempted to chose C, since it makes a lot of sense, and represents your own interpretation of the p-value when reading and writing papers. You are in good company. But is C really the correct answer?
Pick one: Genomic responses in mouse models POORLY/GREATLY mimic human inflammatory diseases
About a year ago Seok et al. shocked the biomedical world with the verdict that mice are not humans, or more specifically, that the blood genomic responses in various inflammatory conditions do not correlate at all between human patients, and the corresponding disease models (see previous post , as well as this one). Now another paper, by Takao et al. and also published in PNAS, concludes the exact opposite, that is that there is a near perfect correlation between blood genomic responses in mouse and man.
Meanwhile, the initial publication is among the top cited medical publications of the last year, and hundreds of newspapers and blogs (including this one) have covered it. It will be interesting to see how much media coverage the Takao paper will receive, probably much less. But what happened, which paper should we believe?
Sind die meisten Forschungsergebnisse tatsächlich falsch?
In July, Laborjournal (‘LabTimes’), a free German monthly for life scientists (sort of a hybrid between the Economist and the British Tabloid The Sun), celebrated its 20th anniversary with a special issue. I was asked to contribute an article. In it I try to answer the question whether most published research findings are false, as John Ioannidis rhetorically asked in 2005.
To find out, you have to be able to read German, and click here for a pdf of the article (in German).
Can mice be trusted?
Katharina Frisch ‘Mouse and man’
I started this blog with an post on a PNAS paper which at that time had received a lot of attention in the scientific community and lay press. In this article, Seok et al. argued that ‘genomic responses in mouse models poorly mimic human inflammatory diseases‘. With this post I am returning to this article, as I recently was asked by the Journal STROKE to contribute to their ‘Controversies in Stroke’ series. The Seok article had disturbed the Stroke community, so a pro/con discussion seemed timely. In the upcoming issue of STROKE Sharp and Jickling will argue that ‘the peripheral inflammatory response in rodent ischemic stroke models is different than in human stroke. Given the important role of the immune system in stroke, this could be a major handicap in translating results in rodent stroke models to clinical trials in patients with stroke.‘ This is of course true! Nevertheless, I counter by providing some examples of translational successes regarding stroke and the immune system, and conclude that ‘the physiology and pathophysiology of rodents is sufficiently similar to humans to make them a highly relevant model organism but also sufficiently different to mandate an awareness of potential resulting pitfalls. In any case, before hastily discarding highly relevant past, present, and future findings, experimental stroke research needs to improve dramatically its internal and external validity to overcome its apparent translational failures.’ For an in depth treatment, follow the debate:
Article: Dirnagl: Can mice be trusted
Article: Sharp Jickling: Differences between mice and humans
Why post-hoc power calculation is not helpful
Statistical power is a rare commodity in experimental biomedicine (see previous post), as most studies have very low n’s and are therefore severly underpowered. The concept of statistical power, although almost embarrassingly simple (for a very nice treatment see Button et al.), is shrouded in ignorance, mysteries and misunderstandings among many researchers. A simple definition states that Power is the probability that, given a specified true difference between two groups, the quantitative results of a study will be deemed statistically significant. The most common misunderstanding may be that power should only be a concern to the researcher if the Null hypothesis could not rejected (p>0.05). I need to deal with this dangerous fallacy in a future post. Another common albeit less perilous misunderstanding is that calculating post-hoc (or ‘retrospective )’ power can explain why an analysis did not achieve significance. Besides proving a severe bias of the researcher towards rejecting the Null hypothesis (‘There must be another reason for not obtaining a significant result than that the hypothesis is incorrect!), this is the equivalent of a statistical tautology. Of course the study was not powerful enough, this is why the result was not significant! To look at this from another standpoint: Provided enough n’s, the Null of every study must be reject. This by the way, is one of the most basic criticisms of Null hypothesis significance testing. Power calculations are useful for the design of studies, but not for their analysis. This was nicely explained by Steven Goodman in his classic article ‘Goodman The use of predicted confidence intervals when planning experiments and the misuse of power when interpreting results Ann IntMed 1994‘:
First, [post-hoc Power analysis] will always show that there is low power (< 50%) with respect to a nonsignificant difference, making tautological and uninformative the claim that a study is “underpowered” with respect to an observed nonsignificant result. Second, its rationale has an Alice-in-Wonderland feel, and any attempt to sort it out is guaranteed to confuse. The conundrum is the result of a direct collision between the incompatible pretrial and post-trial perspectives. […] Knowledge of the observed difference naturally shifts our perspective toward estimating differences, rather than deciding between them, and makes equal treatment of all nonsignificant results impossible. Once the data are in, the only way to avoid confusion is to not compress results into dichotomous significance verdicts and to avoid post hoc power estimates entirely.
NB: To avoid misunderstandings: Calculating the n’s needed in future experiments to achieve a certain statistical power based on effect sizes and variance obtained post – hoc from a (pilot) experiment is not called post-hoc power analysis (and the subject of this post), but rather sample size calculation.
For further reading:
Loose cable, significant at p<0.0000002
I just stumbled into a very instructive example which illustrates that p-values should not be misinterpreted as measures of the probablity with which a research hypothesis is true. In 2011 the OPERA collaboration reported evidence that neutrinos travel faster than light, a finding which violates Einstein’s theory of relativity and if true would have shattered physics as we know it! Their analysis was significant at the 6 sigma level, even more stringent than the accepted but already brutal 5 sigma level of particle discovery (p=3.5 x 10-7). Extraordinary claims require extraordinary evidence ! The results were replicated by the same group, published, and hailed by the world scientific and lay press. A short while later it turned out that the GPS systems were not properly synchronized, and a cable was loose. Neutrinos are back at the speed of light, and we can learn from this that p-values are ignorant of simple systematic errors!
Sloppyness and effect size correlate linearly in clinical stem cell trials
Discrepancies in the publication of clinical trials of bone marrow stem cell therapy in cardiology scale linearly with effect size! This is the shocking but not so surprising result of a study in BMJ that found over 600 discrepancies in 133 reports from 49 trials. Trials without discrepancies (only 5!) reported neutral results (i.e. no effect of therapy on enhancement of ejection fraction). The most spectacular treatment effects were found in those trials with the highest number of discrepancies (30 and more).
Exploratory and confirmatory preclinical research
In the current issue of PLOS Biology Kimmelman, Mogil, and Dirnagl argue that distinguishing between exploratory and confirmatory preclinical research will improve translation: ‘Preclinical researchers confront two overarching agendas related to drug development: selecting interventions amid a vast field of candidates, and producing rigorous evidence of clinical promise for a small number of interventions. They suggest that each challenge is best met by two different, complementary modes of investigation. In the first (exploratory investigation), researchers should aim at generating robust pathophysiological theories of disease. In the second (confirmatory investigation), researchers should aim at demonstrating strong and reproducible treatment effects in relevant animal models. Each mode entails different study designs, confronts different validity threats, and supports different kinds of inferences. Research policies should seek to disentangle the two modes and leverage their complementarity. In particular, policies should discourage the common use of exploratory studies to support confirmatory inferences, promote a greater volume of confirmatory investigation, and customize design and reporting guidelines for each mode.’
Systemic flaws of biomedical research ecosystem
In the current issue of the Proceedings of the National Academy of Science (USA), four heavyweights, Bruce Alberts, Marc W. Kirschner, Shirley Tilghman, and Harold Varmus, provide fundamental criticism of the US biomedical research system, and offer ideas for ‘Rescuing US biomedical research from its systemic flaws’. Their main point is that ‘The long-held but erroneous assumption of never-ending rapid growth in biomedical science has created an unsustainable hypercompetitive system that is discouraging even the most outstanding prospective students from entering our profession—and making it difficult for seasoned investigators to produce their best work. This is a recipe for long-term decline, and the problems cannot be solved with simplistic approaches.’ Most of the issues they raise are equally applicable to European biomedical research. Full article: PNAS-2014-Alberts-5773-7
Correlation vs causation
Still not convinced that US spending on science, space, and technology correlates with suicides by hanging, strangulation and suffocation? Or that the number of people who drowned by falling into a swimming-pool highly correlates with the number of films Nicolas Cage appeared in? Check Spurious Correlations, a website that teaches you to understand the difference between correlation and causation!
To infinity, and beyond! 