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.
What are the major elements of learning from data that should inform the research process? How can we prevent having false confidence from statistical analysis? Does a Bayesian approach result in more honest answers to research questions? Is learning inherently subjective anyway, so we need to stop criticizing Bayesians’ subjectivity? How important and possible is pre-specification? When should replication be required? These and other questions are discussed.
(In a Bayesian analysis) It is entirely appropriate to collect data until a point has been proven or disproven, or until the data collector runs out of time, money, or patience.
— Edwards, Lindman, Savage (1963) Introduction Bayesian inference, which follows the likelihood principle, is not affected by the experimental design or intentions of the investigator. P-values can only be computed if both of these are known, and as been described by Berry (1987) and others, it is almost never the case that the computation of the p-value at the end of a study takes into account all the changes in design that were necessitated when pure experimental designs encounter the real world.
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.
In my opinion, null hypothesis testing and p-values have done significant harm to science. The purpose of this note is to catalog the many problems caused by p-values. As readers post new problems in their comments, more will be incorporated into the list, so this is a work in progress.
The American Statistical Association has done a great service by issuing its Statement on Statistical Significance and P-values. Now it’s time to act.
Imagine watching a baseball game, seeing the batter get a hit, and hearing the announcer say “The chance that the batter is left handed is now 0.2!”
No one would care. Baseball fans are interested in the chance that a batter will get a hit conditional on his being right handed (handedness being already known to the fan), the handedness of the pitcher, etc. Unless one is an archaeologist or medical examiner, the interest is in forward probabilities conditional on current and past states.
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.