Stephen, I don't know anything about Cox proportional hazards (except what I read in Wikipedia). I do know, however, that chi-square is not a very powerful test, and that it is is extra-lousy when the contignecy table it badly skewed, as it is here (you did include the non-occurrences (of death), right?). That is why it is conventional medical research (where most conditions are rare and, therefore, most contingency tables are badly skewed) to use odd ratios. There is no significance test I know of associated with odds ratios (but apparently there isn't one associated with Cox either). In this case, the odds ratio for cancer death would be:
25/88 .2841 -------- = --------- = 1.4205 19/95 .2000 which meas that you are 42% more likely to die of breast cancer without the therapy, which sounds pretty important. But the whole point of Gigerenzer et al's piece was that relative measures of this sort can be misleading if the base rate is low, viz., that saying (if I recall the numbers in his article correctly) that mammography cuts the risk of breast cancer death by 33% sounds impressive, but when you tell people that it means, say, 2 fewer deaths in a thousand cases (*before* you even factor in the negative side effects of the procedure itself), they are (rightly) much less impressed. In the research that concerns you, however, the authors are claiming about 5.5 fewer deaths per 100 ([25/113 - 19/114]*100), which is more worthy of consideration that 2 in 1000, but is still not nearly the slam dunk that 42% sounds like. However, do not fret. I note that in their description of the aims of therapy was included the phrase, "maintain adherence to cancer treatment." Now, if that was even partly accomplished by the therapy (that some people who would have otherwise quit conventional medical treatment were persuaded to continue to instead) then you have your answer without having to resort to spooky mind-over-matter claims. It was the medical treatment that saved these extra lives. What the therapy did was to ensure that a few extra people stayed with their medical treatments. Regards, Chris -- Christopher D. Green Department of Psychology York University Toronto, ON M3J 1P3 Canada 416-736-2100 ex. 66164 [EMAIL PROTECTED] http://www.yorku.ca/christo/ ========================== [EMAIL PROTECTED] wrote: > While indolent Americans are sleeping off their turkey comas, hard- > working Canadians, who would never indulge in such gormandising excess, > continue to think big thoughts on psychology. Here¨s one. > > It is widely believed, despite the absence of convincing evidence, that > cancer can be influenced by psychological factors, such as thinking > positive thoughts, having a healthful lifestyle, attending support > groups, or receiving therapy. This drives me nuts. It¨s hard enough for > psychology to show any direct benefit from psychological intervention. > How much less likely that psychology can influence the course of a dread > disease with a clear biological basis. And this claim carries the > pernicious implication that if you¨ve got cancer, it must be because > you¨re doing something wrong. > > Yet. A just-published study (Andersen et al, 2008) reports on the > progress of disease in women surgically treated for breast cancer and > continuing with medical treatment. They report that women additionally > exposed to 12 months of intensive group therapy, which included > "strategies to reduce stress, improve mood, alter health behaviours, and > maintain adherence to cancer treatment", produced significant long-term > benefits against their disease. > > In particular, these women had "a reduced risk of breast cancer > recurrence...and [a reduced risk of] death from breast cancer". I¨ve saved > the best for last. In contrast to our usual complaints about > correlational studies, this was a _randomized_ study, in which the > control group received assessment only. True, there was no placebo, but > I¨m nevertheless gobsmacked that _anything _ like that, whatever it was, > could produce such a striking outcome. Even more remarkable, they also > reported "a reduced risk of death from all causes", which Gigerenzer > (2008, see comments below) considers the ultimate bottom line, one which > is rarely achieved. And the results were analyzed on an "intention to > treat" basis, which means that dropouts were counted as failures. > > Do we therefore accept these exceptionally-encouraging conclusions? This > is where I bring in Gigerenzer (and you, gentle readers). There¨s been a > lot of admiration expressed on this list lately for Gigerenzer et al > (2008), and justifiably. Their paper is clear and insightful and I¨ve > learned a lot from it. I¨ve been trying to use Gigerenzer¨s ideas in > evaluating this paper, but I¨m not sure I¨ve got it right. > > Gigerenzer recommends transparent framing of information, and recommends > that data be expressed as natural frequencies. The Andersen paper uses > "Cox proportional hazards analysis" (which is not transparent to me) in > an analysis of survival times. Gigerenzer criticizes the use of survival > time data and says it is uncorrelated with mortality, which he recommends > should be used instead. Yet his argument is based on the use of survival > times when methods of diagnosis differ (e.g. his Rudy Giuliani/prostate > cancer example). This is not the case here, as the groups are randomized > after receiving diagnosis by the same method, so any improvement in the > therapy group in survival time should be meaningful, and not subject to > this criticism . > > But I¨m concerned that while the analysis is for survival time and the > critical finding is displayed as a set of three graphs (Figure 3) of > recurrence-free survival time, breast cancer specific survival time, and > overall survival time, the language is frequently that of mortality (e.g. > the abstract claims "reduced...death from breast cancer [and]...from all > causes". I don¨t see how they get from one to the other, and I wonder > whether this is just sloppy language for survival time data. > > Then there¨s this. Their Figure 2 provides all the data necessary at the > study end (median of 11 years follow-up) to do a natural frequency > analysis as recommended by Gigerenzer (but they don't). For the control > group (assessment only) 25 of 113 died of breast cancer; for the therapy > group, it was 19 of 114. For all causes of death, for the control, 30 of > 113 died, while for the therapy group it was 24 of 114. Deaths in each > case are reduced by about 6% after therapy compared with control, which > seems meaningful (Hazard ratios around 0.8). But neither control vs > therapy comparison is even close to significance by a chi-square test > (e.g. Fisher¨s exact), which means either there¨s nothing there, or not > enough subjects were studied to show it. > > So, what¨s going on? Can Cox proportional hazards analysis demonstrate > something not evident by simple statistics? Are they justified in using > their mortality language when analyzing by survival times? Or are they > playing with statistics, and avoiding using an analysis which turns out > negative? My own feeling is that they should have explicitly carried out > the analysis I did, noted their failure to show an effect on mortality, > and discussed the implications for their Cox analysis. The press release > I have, BTW, prominently refers to the mortality claim, "The study also > found that patients receiving the intervention had less than half the > risk (44 percent) of death from breast cancer compared to those who did > not receive the intervention, and had a reduced risk of death from all > causes, not just cancer" (Science Daily, 2008/11/08). Not according to > my analysis of their data, though. > > I would really like to hear from our statistics experts on this. The > abstract is here: http://tinyurl.com/5z8fn2, although it would be better > to read the paper. If you don¨t have access to it, I can supply a copy, > or you can get it direct from the author, who answered my request > promptly. She¨s a psychologist at Ohio State University. Her address is > [EMAIL PROTECTED] > > (As usual, I¨m thinking about going the letter-to-the-editor route. But > I¨m not sure I¨ve got it right). > > Stephen > > > Andersen, B. et al (2008). Psychological intervention improves survival > for breast cancer patients: a randomized clinical trial. _Cancer_, 113: > 3450-8 [published on-line November 17, 2008]. > > Gigerenzer, G. et al (2008). Helping doctors and patients make sense of > health statistics. _Psychological Science in the Public Interest_, 8: 53- > 96. > > ----------------------------------------------------------------- > Stephen L. Black, Ph.D. > Professor of Psychology, Emeritus > Bishop's University e-mail: [EMAIL PROTECTED] > 2600 College St. > Sherbrooke QC J1M 1Z7 > Canada > > Subscribe to discussion list (TIPS) for the teaching of > psychology at http://flightline.highline.edu/sfrantz/tips/ > ----------------------------------------------------------------------- > > --- > To make changes to your subscription contact: > > Bill Southerly ([EMAIL PROTECTED]) > > > --- To make changes to your subscription contact: Bill Southerly ([EMAIL PROTECTED])
