This forum is about wrong numbers in science, politics and the media. It respects good science and good English.
The early part of an exponential (for time much less than the time constant) is linear. Bit of a coincidence, isn’t it, that the allegedly discrepant group continues exactly at the same event rate as both groups started at? I find your arguments in justification for the claim rather circular and in need of a trim from Occam’s razor.
I'm not convinced its a coincidence, I've seen similar behaviour in similar data too many times. Curves that look like that (albeit with radically different numbers and duration of treatment) are used to claim efficacy for cancer treatments, so you can't just ignore them when they turn out to be bad news for a drug.
Again for emphasis, we are talking about data from human subjects here, not physics experiments. Whatever type of curve you might want to fit to the data, it is the data that matter not the theory behind your distribution of choice. The crucial thing that is going on here is the removal of subjects that have events from the population. Every time you do this you reduce the inherent risk of events in the remaining population (because those at inherently higher risk will on average have their event earlier in the trial). That is why you expect to see the event incidence per unit time tail off.
If we do indeed see that in one group and not in another, in a randomised, double-blind, placebo-controlled clinical trial powered to look for the effect and with the effect as a predefined endpoint, we are entitled to conclude (with all the usual caveats) that there is a treatment effect.
I'd be delighted for you to take Occam's razor to my arguments or point out where they are circular, I'm here to learn.
Since it's come up again, Vioxx was not seen off by junkists, it was voluntarily withdrawn from the market by the manufacturer. I believe it still has a valid marketing license in the USA, which means the FDA is all fine about it.
There was no statistical blunder. The behaviour of the placebo group is completely normal for a clinical trial setting. It comes down to whether you think the benefit of the product outweighs the risk. Even given this data, that trade-off might be positive for the customers, but especially in the USA with its class-action suits and huge personal injury claims egged on by a drug-company-suing industry, the manufacturer did not think it worthwhile continuing to flog these pills.
Our bending author is spot on when it comes to most abuses of statistics, but this one really doesn't cut it. The criticisms rightly applied to post-hoc analysis of multiplicit data-dredges on retrospectively-reported exposures and unreliable outcome data do not apply to single predefined endpoints with predefined analyses on prospective empirical data. Even when it's the control group you think is odd.
You lost me in the first paragraph at the top of this page, particularly with its last sentence.
I have so often seen these great breakthroughs in the work of research students. I have always told them “You need to demonstrate that this is repeatable”, which was, unfortunately, always the end of the matter. I conceived the Law of Experiments long before I started Number Watch. Only the second corollary appeared much later, but well before the vioxx fiasco.
The attrition of the cohorts appears considerably greater than the number of incidents, which leads me to conjecture that the premature termination of the trial was motivated by the shortage of participants rather than for ethical reasons. I also note that the results were presented as percentages of the remaining cohorts rather than their actual numbers, which does not lend support to your explanation.
This discussion is a variant of the smoking/lung cancer discussion to me. The analysis is of the RR (HR, OR, Whatever ratio you wish to use). The RR is inevitably a ratio of bad to basis for each group. In my over simplified model, it is the probability of rolling a six on one throw of the die and comparing that to the chance of rolling a six on a different die.
Continuously lost in the discussion is the survivability ratio, aka, what is the chance in x rolls of the dice that I won't roll a six. Smokers continue to flaunt the huge risks of smoking, leading active productive lives surviving way longer than they are suppose to. The risks associated with Vioxx are microscopic compared to smoking.
The smoking death toll requires great minds to extract from the data. Other great minds can come back and twist the result without too much difficulty because it fiddles with a variable that isn't all that well defined. The unit of life is the period between birth and death. Rosebuds come to mind. There is quite possibly more science behind "carpe diem" than all the sophisticated analysis of epidemiology. Vioxx made it infinitely more likely for a person seize more moments and enjoy them. Apologies in advance, but I will sneer heavily in the direction of anyone suggesting they can accurately measure enjoyment. A Nun on her knees praying can effectively be enjoying life every bit as much as Paris Hilton.
Imagine a collection of atoms of radioactive elements. Any and all - we have a range of half-lives ranging from a few seconds to millenia.
We stick them in a box and watch them decay. At the beginning of the experiment the decay rate, the number of decays per unit time per number of remaining atoms, is higher than it is later in the experiment.
Your average group of patients being watched for some event is like this mixture of different nuclei, they are not a group of the same type of nuclei at constant risk of decay irrespective of time. The analogy is not perfect of course - in humans risk of bad stuff tends to rise with age, radioisotopes don't care how old they are. But in this human experiment we are looking at two groups with one systematic treatment difference, and all the other differences controlled for, as far as possible, through randomisation.
Cohort attrition at later stages is because of the trial being stopped.
It's not ethical to stop a trial in a marketed product for lack of participation, not that there was any such lack anyway. It is ethical to stop it because the drug is harming people. The highest ethic in clinical trials is the good of the participants in that trial - the greater good of humanity takes a back seat (cf. Declaration of Helsinki). You might not like that scientifically, but that's the decision that has been reached and in many places legislated for.
Once you have this kind of result it's **** hard to find volunteers for a repeat of the experiment. Like I said, you are absolutely right with most of your criticisms of statistical abuse in the life sciences. However, as it's "life" and in this case human life, we have to live with a lower degree of certainty than the physicists.
Rutherford said if you need statistics you need better experiments. Unfortunately in drug research it is not ethically possible (or financially possible) to put any question of efficacy or safety beyond all doubt. Beyond reasonable doubt (even at p=0.05) can be hard enough. and the risk/benefit evaluation is by its nature not a simple formula.