This article discusses issues related to alpha spending, effect sizes used in power calculations, multiple endpoints in RCTs, and endpoint labeling. Changes in endpoint priority is addressed. Included in the the discussion is how Bayesian probabilities more naturally allow one to answer multiple questions without all-too-arbitrary designations of endpoints as “primary” and “secondary”. And we should not quit trying to learn.
To avoid “false positives” do away with “positive”.
A good poker player plays the odds by thinking to herself “The probability I can win with this hand is 0.91” and not “I’m going to win this game” when deciding the next move.
State conclusions honestly, completely deferring judgments and actions to the ultimate decision makers. Just as it is better to make predictions than classifications in prognosis and diagnosis, use the word “probably” liberally, and avoid thinking “the evidence against the null hypothesis is strong, so we conclude the treatment works” which creates the opportunity of a false positive.
Misinterpretation of P-values and Main Study Results Dichotomania Problems With Change Scores Improper Subgrouping Serial Data and Response Trajectories Cluster Analysis As Doug Altman famously wrote in his Scandal of Poor Medical Research in BMJ in 1994, the quality of how statistical principles and analysis methods are applied in medical research is quite poor. According to Doug and to many others such as Richard Smith, the problems have only gotten worse.
The difference between Bayesian and frequentist inference in a nutshell:
With Bayes you start with a prior distribution for θ and given your data make an inference about the θ-driven process generating your data (whatever that process happened to be), to quantify evidence for every possible value of θ. With frequentism, you make assumptions about the process that generated your data and infinitely many replications of them, and try to build evidence for what θ is not.
With the many problems that p-values have, and the temptation to “bless” research when the p-value falls below an arbitrary threshold such as 0.05 or 0.005, researchers using p-values should at least be fully aware of what they are getting. They need to know exactly what a p-value means and what are the assumptions required for it to have that meaning. ♦ A p-value is the probability of getting, in another study, a test statistic that is more extreme than the one obtained in your study if a series of assumptions hold.
Optimum decision making in the presence of uncertainty comes from probabilistic thinking. The relevant probabilities are of a predictive nature: P(the unknown given the known). Thresholds are not helpful and are completely dependent on the utility/cost/loss function.
Corollary: Since p-values are P(someone else’s data are more extreme than mine if H0 is true) and we don’t know whether H0 is true, it is a non-predictive probability that is not useful for decision making.
In trying to guard against false conclusions, researchers often attempt to minimize the risk of a “false positive” conclusion. In the field of assessing the efficacy of medical and behavioral treatments for improving subjects’ outcomes, falsely concluding that a treatment is effective when it is not is an important consideration. Nowhere is this more important than in the drug and medical device regulatory environments, because a treatment thought not to work can be given a second chance as better data arrive, but a treatment judged to be effective may be approved for marketing, and if later data show that the treatment was actually not effective (or was only trivially effective) it is difficult to remove the treatment from the market if it is safe.
Much has been written about problems with our most-used statistical paradigm: frequentist null hypothesis significance testing (NHST), p-values, type I and type II errors, and confidence intervals. Rejection of straw-man null hypotheses leads researchers to believe that their theories are supported, and the unquestioning use of a threshold such as p<0.05 has resulted in hypothesis substitution, search for subgroups, and other gaming that has badly damaged science. But we seldom examine whether the original idea of NHST actually delivered on its goal of making good decisions about effects, given the data.