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Lies, Damn Lies, and Statistics: Overview on various statistical measures in Science (& economics)

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  • Lies, Damn Lies, and Statistics: Overview on various statistical measures in Science (& economics)

    Full article here (summary below),_Its_Wrong

    BOX 1: Statistics Can Confuse
    Statistical significance is not always statistically significant.
    It is common practice to test the effectiveness (or dangers) of a drug by comparing it to a placebo or sham treatment that should have no effect at all. Using statistical methods to compare the results, researchers try to judge whether the real treatment’s effect was greater than the fake treatments by an amount unlikely to occur by chance.
    By convention, a result expected to occur less than 5 percent of the time is considered “statistically significant.” So if Drug X outperformed a placebo by an amount that would be expected by chance only 4 percent of the time, most researchers would conclude that Drug X really works (or at least, that there is evidence favoring the conclusion that it works).
    Now suppose Drug Y also outperformed the placebo, but by an amount that would be expected by chance 6 percent of the time. In that case, conventional analysis would say that such an effect lacked statistical significance and that there was insufficient evidence to conclude that Drug Y worked.
    If both drugs were tested on the same disease, though, a conundrum arises. For even though Drug X appeared to work at a statistically significant level and Drug Y did not, the difference between the performance of Drug A and Drug B might very well NOT be statistically significant. Had they been tested against each other, rather than separately against placebos, there may have been no statistical evidence to suggest that one was better than the other (even if their cure rates had been precisely the same as in the separate tests).
    “Comparisons of the sort, ‘X is statistically significant but Y is not,’ can be misleading,” statisticians Andrew Gelman of Columbia University and Hal Stern of the University of California, Irvine, noted in an article discussing this issue in 2006 in the American Statistician. “Students and practitioners [should] be made more aware that the difference between ‘significant’ and ‘not significant’ is not itself statistically significant.”
    A similar real-life example arises in studies suggesting that children and adolescents taking antidepressants face an increased risk of suicidal thoughts or behavior. Most such studies show no statistically significant increase in such risk, but some show a small (possibly due to chance) excess of suicidal behavior in groups receiving the drug rather than a placebo. One set of such studies, for instance, found that with the antidepressant Paxil, trials recorded more than twice the rate of suicidal incidents for participants given the drug compared with those given the placebo. For another antidepressant, Prozac, trials found fewer suicidal incidents with the drug than with the placebo. So it appeared that Paxil might be more dangerous than Prozac.
    But actually, the rate of suicidal incidents was higher with Prozac than with Paxil. The apparent safety advantage of Prozac was due not to the behavior of kids on the drug, but to kids on placebo — in the Paxil trials, fewer kids on placebo reported incidents than those on placebo in the Prozac trials. So the original evidence for showing a possible danger signal from Paxil but not from Prozac was based on data from people in two placebo groups, none of whom received either drug. Consequently it can be misleading to use statistical significance results alone when comparing the benefits (or dangers) of two drugs.
    __________________________________________________ _____________________
    BOX 2: The Hunger Hypothesis
    A common misinterpretation of the statistician’s P value is that it measures how likely it is that a null (or “no effect”) hypothesis is correct. Actually, the P value gives the probability of observing a result if the null hypothesis is true, and there is no real effect of a treatment or difference between groups being tested. A P value of .05, for instance, means that there is only a 5 percent chance of getting the observed results if the null hypothesis is correct.
    It is incorrect, however, to transpose that finding into a 95 percent probability that the null hypothesis is false. “The P value is calculated under the assumption that the null hypothesis is true,” writes biostatistician Steven Goodman. “It therefore cannot simultaneously be a probability that the null hypothesis is false.”
    Consider this simplified example. Suppose a certain dog is known to bark constantly when hungry. But when well-fed, the dog barks less than 5 percent of the time. So if you assume for the null hypothesis that the dog is not hungry, the probability of observing the dog barking (given that hypothesis) is less than 5 percent. If you then actually do observe the dog barking, what is the likelihood that the null hypothesis is incorrect and the dog is in fact hungry?
    Answer: That probability cannot be computed with the information given. The dog barks 100 percent of the time when hungry, and less than 5 percent of the time when not hungry. To compute the likelihood of hunger, you need to know how often the dog is fed, information not provided by the mere observation of barking.
    __________________________________________________ _____________________
    BOX 3: Randomness and Clinical Trials
    Assigning patients at random to treatment and control groups is an essential feature of controlled clinical trials, but statistically that approach cannot guarantee that individual differences among patients will always be distributed equally. Experts in clinical trial analyses are aware that such incomplete randomization will leave some important differences unbalanced between experimental groups, at least some of the time.
    “This is an important concern,” says biostatistician Don Berry of M.D. Anderson Cancer Center in Houston.
    In an e-mail message, Berry points out that two patients who appear to be alike may respond differently to identical treatments. So statisticians attempt to incorporate patient variability into their mathematical models.
    “There may be a googol of patient characteristics and it’s guaranteed that not all of them will be balanced by randomization,” Berry notes. “But some characteristics will be biased in favor of treatment A and others in favor of treatment B. They tend to even out. What is not evened out is regarded by statisticians to be ‘random error,’ and this we model explicitly.”
    Understanding the individual differences affecting response to treatment is a major goal of scientists pursuing “personalized medicine,” in which therapies are tailored to each person’s particular biology. But the limits of statistical methods in drawing conclusions about subgroups of patients pose a challenge to achieving that goal.
    “False-positive observations abound,” Berry acknowledges. “There are patients whose tumors melt away when given some of our newer treatments.… But just which one of the googol of characteristics of this particular tumor enabled such a thing? It’s like looking for a needle in a haystack ... or rather, looking for one special needle in a stack of other needles.”
    __________________________________________________ _____________________
    BOX 4: Bayesian Reasoning
    Bayesian methods of statistical analysis stem from a paper published posthumously in 1763 by the English clergyman Thomas Bayes. In a Bayesian analysis, probability calculations require a prior value for the likelihood of an association, which is then modified after data are collected. When the prior probability isn’t known, it must be estimated, leading to criticisms that subjective guesses must often be incorporated into what ought to be an objective scientific analysis. But without such an estimate, statistics can produce grossly inaccurate conclusions.
    For a simplified example, consider the use of drug tests to detect cheaters in sports. Suppose the test for steroid use among baseball players is 95 percent accurate — that is, it correctly identifies actual steroid users 95 percent of the time, and misidentifies non-users as users 5 percent of the time.
    Suppose an anonymous player tests positive. What is the probability that he really is using steroids? Since the test really is accurate 95 percent of the time, the naïve answer would be that probability of guilt is 95 percent. But a Bayesian knows that such a conclusion cannot be drawn from the test alone. You would need to know some additional facts not included in this evidence. In this case, you need to know how many baseball players use steroids to begin with — that would be what a Bayesian would call the prior probability.
    Now suppose, based on previous testing, that experts have established that about 5 percent of professional baseball players use steroids. Now suppose you test 400 players. How many would test positive?
    • Out of the 400 players, 20 are users (5 percent) and 380 are not users.
    • Of the 20 users, 19 (95 percent) would be identified correctly as users.
    • Of the 380 nonusers, 19 (5 percent) would incorrectly be indicated as users.

    So if you tested 400 players, 38 would test positive. Of those, 19 would be guilty users and 19 would be innocent nonusers. So if any single player’s test is positive, the chances that he really is a user are 50 percent, since an equal number of users and nonusers test positive.

  • #2
    Re: Lies, Damn Lies, and Statistics: Overview on various statistical measures in Science (& economic

    Bayesian Statistics has always made more sense than the classical testing of hypothese for most purposes.

    FDA has now accepted the use of Bayesian statistics in earlier trials, though to my knowledge, no drugs have been approved on the basis of Bayesian statistics.

    There are some very good articles on the use of Bayesian statistics in clinical trials.


    • #3
      Re: Lies, Damn Lies, and Statistics: Overview on various statistical measures in Science (& economic

      Originally posted by Rajiv View Post
      Bayesian Statistics has always made more sense than the classical testing of hypothese for most purposes.
      But they are less well suited for the main purpose of drug trials - to increase drug profits
      Most folks are good; a few aren't.