Homeopathy paper published

So, this is the moment you’ve all been waiting for. A while ago I wrote a comment on an article that was published in Homeopathy. This article, among other things, purported to show that the authors of a Lancet meta-analysis (Aijin Shang and co-workers) that had negative results for homeopathy had engaged in post-hoc hypothesising and data dredging. That was an outrageous slur on what is a perfectly reasonable paper, if you understand it properly. My comment has now been published, along with a response from the authors. If anyone needs a copy of my comment and doesn’t fancy paying for it, drop me a line and I’ll bung you a PDF. In any case, the original version appears on my blog here.

Meanwhile, the reply by original authors Rutten and Stolper is an exercise in evasion and obfuscation, and doesn’t really address most of the points that I made. This seems to be fairly typical (and to be fair isn’t only restricted to non-science like homeopathy). In their original paper, Rutten and Stolper claimed that “Cut-off values for sample size [i.e. the number of subjects in a trial, above which the trial was defined as “large”] were not mentioned or explained in Shang el al's [sic] analysis”. This is simply not true. So what do Rutten and Stolper have to say about this embarrassing error?

“Wilson states that larger trials were defined by Shang as “Trials with SE [standard error] in the lowest quartile were defined as larger trials”. According to Wilson this was done to predefine 'larger trials'. We agree with Wilson that this is indeed a strange way of defining 'larger trials', but it is perfectly possible to simply define larger studies a priori according to sample size in terms like 'above median' as we suggested in our paper. Shang et al did not mention the sensitivity of the result to this choice of cut-off value: if median sample size (including 14 trials) is chosen homeopathy has the best (significantly positive) result, if 8 trials are selected homeopathy has the worst result. In the post-publication data they mentioned sample sizes but not Standard Errors. Isn't it odd that the authors did not mention the fact that homeopathy is effective based on a fully plausible definition of 'larger' trials, but stated that it is not effective based on a strange definition of 'larger', but that this was not apparent because of missing data?”

So, nothing there about how they failed to properly read the paper to check what Shang et al.’s definition of larger trials was, while essentially accusing them of research misconduct. Instead, they shift the goalposts and decide that they don’t like the definition that was provided. Now, it certainly would be possible to define larger studies as being “above median” sample size. By doing this you would be including studies of smaller size than would be included using Shang’s definition. As is well understood, and as Shang et al. clearly showed, including studies with smaller sample size will give you more positive but, crucially, less reliable results. So I don’t think it was particularly odd that Shang et al. failed to abandon their definition of larger trials in favour of someone else’s definition, published three years later, that would inevitably lead to less reliable results. Rutten and Stolper state that using 8 larger, high quality trials gives the worst results for homeopathy: but to get a positive result, you would have to include at least 14 trials, as Ludtke and Rutten show in another paper in the Journal of Clinical Epidemiology. And, again, it was perfectly apparent what definition Shang et al. used to define larger trials: it is clearly stated in their paper.

OK, so why use standard error rather than simply using sample size directly, as Rutten and Stolper want to do? In meta-analyses, a commonly used tool is a funnel plot. This plots, for each study included in the analysis, standard error against odds ratio. The odds ratio is a measure of the size of the effect of the intervention being studied. If the value is 1, there is no effect. If it is less than one, there is a positive effect (the intervention outperformed placebo), if greater than one there is a negative effect (placebo outperformed the intervention). The plot is typically used to identify publication bias (and other biases) in the set of trials: to simplify, if the plot is asymmetric, then biases exist. Using their funnel plot of 110 trials of homeopathy (Figure 2 in the Lancet paper), Shang et al. were able to show, (to a high degree of statistical significance, p<0.0001)that trials with higher standard error show more positive results. It then makes perfect sense to screen the trials by standard error rather than sample size, because it has been demonstrated that standard error correlates with odds ratio. Of course, you could plot sample size against odds ratio, but that is not the recommended approach.

Rutten and Stolper also claim to be "surprised" that one apparently positive trial of homeopathy was excluded from Shang's analysis. Since it was excluded based on the clearly stated exclusion criteria, I didn't find that surprising myself. How do Rutten and Stolper respond?

"We were indeed amazed that no matching trial could be found for a homeopathic trial on chronic polyarthritis by Wiesenauer. Shang did not specify criteria for matching of trials. We would expect the authors to explain this exclusion because Wiesenauer's trial would have made a difference in meta-regression analysis and possibly also in the selection of the eight larger good quality trials".

This routine is now wearily familiar. Someone makes a claim that Shang et al. didn’t do something, in this case specify criteria for matching of trials; I check the Lancet paper, and find that claim to be false. What did Shang have to say about matching of trials? On page 727, they say “For each homoeopathy trial, we identified matching trials of conventional medicine that enrolled patients with similar disorders and assessed similar outcomes. We used computer-generated random numbers to select one from several eligible trials of conventional medicine”. And, of course, the authors did explain why the trial was excluded; it met one of the pre-defined exclusion criteria. To me, that seems clear enough. As it stands, Rutten and Stolper’s point is nothing more than an argument from incredulity. They are amazed! Amazed that no matching trial could be found. But they haven’t actually found one to prove their point. It’s possible that this Weisenauer trial might have made a difference to the selection of 8 large, high quality trials. But I doubt it would have made any significant difference to the meta-regression analysis, which was based on 110 trials.

Having wrongly accused Shang et al. of doing a bad thing by defining sub-groups post-hoc, Rutten and Stolper applied all kinds of post-hoc rationalisations for excluding trials they don’t like. For example, they decided to throw out all the (resoundingly negative) trials of homeopathic arnica for muscle soreness in marathon runners, on the basis that homeopathy is not normally used to treat healthy people, and these trials therefore have low external validity. I argued that Shang et al. had to include those studies, since they met the inclusion criteria and did not meet the exclusion criteria. On what basis could they exclude them? From Rutten and Stolper, answer came there none:

"Wilson's remark about prominent homeopaths choosing muscle soreness as indication is not relevant. Using a marathon as starting point for a trial is understandable from a organisational point of view, although doubt is possible about external validity. Publishing negative trials in alternative medicine journals is correct behaviour. There is, however, strong evidence that homeopathic Arnica is not effective after long distance running and homeopathy as a method should not be judged by that outcome".

Yes, publish the negative trials. But why shouldn’t the negative trials be included in a meta-analysis? Because they’re negative, and that just can’t be right? I don’t see any rationale here for excluding these trials.

Rutten and Stolper also take the tine-honoured approach of arguing about statistics:

“…the asymmetry of funnel-plots is not necessarily a result of bias. It can also occur when smaller studies show larger effect just because they were done in a condition with high treatment effects, and thus requiring smaller patient numbers”.

I think this is nonsense, but anyone with more statistical knowledge should feel free to correct me. If the high treatment effects are real, then the larger studies will show them as well, and there will be no asymmetry in the funnel plot. The smaller studies are always going to be less reliable than the larger ones.

Finally, Rutten and Stolper conclude that:

"The conclusion that homeopathy is a placebo effect and that conventional medicine is not was not based on a comparative analysis of carefully matched trials, as stated by the authors".

Homeopaths do want this to be true, but no matter how many times they repeat it, it continues to be false. I think the problem is that they have become fixated on the analysis of the subgroup of larger, higher quality trials, which was only one part of the analysis. The meta-regression analysis for all 110 vs 110 trials gave the same results; the analysis of the “larger, higher quality” subgroup merely lends support to those results. So after all that palaver, there’s still no reason to think that there is anything particularly wrong with the Shang et al. Lancet paper, and there is certainly no excuse for accusing its authors of research misconduct.

Homeopathy meta-analysis comment accepted for publication

Just a short post to say that the article I wrote pointing out some problems with a re-analysis (Rutten and Stolper 2008) of the Shang et al. Lancet meta-analysis has been accepted for publication by Homeopathy. I have also been sent the reply by the authors of the re-analysis. My comment and the reply will not actually appear in print until April, so I'd better not address the content of the reply at this point. I will say that I don't think it adequately addresses the points that I made. In particular, the authors don't have much to say in response to the point that information they claim is missing from the Shang paper is in fact clearly stated in that paper. More to come on this in April.

The Rutten and Stolper paper, and a companion paper in the Journal of Clinical Epidemiology by Ludtke and Rutten, were the subject of a press release titled "New Evidence for Homeopathy" claiming to cast doubt on the Shang meta-analysis. Perhaps I should issue a press release titled "New Evidence Against Homeopathy". Then again, maybe it would be better titled "New Evidence Against Homeopaths".

Now, despite apearances, I have to say that the subject of meta-analyses of homeopathy is not one that particularly fascinates me. It's just that a number of prominent homeopaths have made claims that the Shang study is flawed and/or fraudulent. In checking the claims that have been made, mainly be simply checking the Shang paper and its supplementary data, I have almost invariably found that they are false. Apgaylard has found similarly. I find it amazing that these false accusations have propagated across the internet and been accepted as truth, without anyone apparently doing the most basic of fact checking.

News on latest Homeopathy submission

A while ago a submitted a comment to the journal Homeopathy, discussing a paper published in the journal by Rutten and Stolper, claiming to find a number of serious flaws in the Shang et al. meta-analysis that appeared in the Lancet in 2005. I had a slightly cryptic e-mail back from the journal last week:

Dear Dr Wilson,

Thank you for sending us this article. We have sent the article to the authors for comment.

We will be in touch again shortly.

I assume that means that the comment will be published, with a reply by the authors. I'll be interested in what they have to say, because at this point some of the errors in their paper seem to be indefensible.

Science by press release (epic fail)

While I was messing about at the University of Google, doing some research for the thing that I've just sent to homeopathy, I came across this [pdf]. Yes, the homeopaths (in the form of the International Homeopathic Medical League and the European Committee for Homeopathy) have put together a press release, based on the study in Homeopathy by Rutten and Stolper, and the study by Ludtke and Rutten in the Journal of Clinical Epidemiology. Both studies criticise (mostly wrongly) a perfectly good meta-analysis of homeopathy from the Lancet. The headline is "New evidence for homeopathy". No question mark, no caveats. You might guess that the International Homeopathic Medical League and the European Committee for Homeopathy would not be entirely unbiased sources of information. In fact, these studies are very far from being evidence for homeopathy, as I've tried to point out (and not just me). I suppose two studies sounds better than one, but the truth is that these are essentially the same study, with extra nonsense in the part that got published in Homeopathy. The studies apply a post-hoc analysis to the data from the Lancet article, and claim to be able to produce a positive result for homeopathy if you squint at the data and stand on one leg. Then they accuse the Lancet paper of data dredging. What a laugh riot.

Unfortunately, lots of scientific studies get reported based on their press releases. This means that the people who read the reports get no sense of the flaws in the study and the caveats that should be applied to its conclusions; these come from independent scientific scrutiny of the study once it has been peer-reviewed and published. Pushing press releases on your research may be a good way to get brownie points from your university, but it's not usually a good way of fostering an improved understanding of the scientific process. To be fair, it's by no means only homeopaths and their ilk who do this, as Ben Goldacre has pointed out.

Still, the good thing about this is that a search on Google News for this release shows that, at the time of writing, it has only been picked up by a few woo-ish magazines: mainstream western news seems to have ignored this more or less completely. Maybe the press has got fed up of this particular manufactured controversy, at least for now.

I know I said life was too short...

I wrote a little about a paper by Rutten and Stolper recently published in the amusing pseudo-journal Homeopathy. The paper performed the usual homeopath party trick of throwing incorrect allegations of research misconduct at the Shang et al. meta-analysis of homeopathy that was published in the Lancet, while also engaging in dubious statistical analysis. I've now had a little time to put together something a bit more meaty, with proper references and everything, and send it off as a letter to the editor of Homeopathy. I reproduce the text below.

Rutten and Stolper [1] have conducted a re-analysis of the data used in the landmark Lancet meta-analysis (Shang et al.) [2] of trials of homeopathy and conventional medicine. However, their approach to this work seems to have been influenced by a belief that the Shang analysis was deliberately skewed against homeopathy, and in favour of conventional medicine. I argue here that the evidence does not support that contention, and that the re-analysis by Rutten and Stolper does not show that the Shang et al. study was invalid.

Rationale for the re-analysis

In the abstract of their paper, Rutten and Stolper state “There is a discrepancy between the outcome of a meta-analysis published in 1997 of 89 trials of homeopathy by Linde et al and an analysis of 110 trials by Shang et al published in 2005, these reached opposite conclusions”, and on page 170 they write “The contradiction between Linde's conclusion based on 89 trials, and Shang et al's conclusion, based on 110 trials seems odd”. But there is nothing particularly surprising about this discrepancy. The Linde paper referred to was published in the Lancet in 1997 [3]. The same team re-analysed the data in a paper published in 1999 [4]. They concluded that because trials of higher methodological quality had smaller effect sizes, and that because a number of newly published high-quality trials showed negative results for homeopathy, their meta-analysis had over-estimated the effectiveness of homeopathy. Hence there is no reason to see to the discrepancy between Shang et al. and Linde et al. (1997) as being particularly “odd”.

Trial quality

Rutten and Stolper make statements about the “pre-specified hypotheses” of the Shang et al. study, but these are not consistent through the paper. In the introduction, they state:

“The hypotheses predefined mentioned in the introduction of Shang et al's paper were: ‘Bias in conduct and reporting of trials is a possible explanation for positive findings of placebo-controlled trials of both homeopathy and allopathy (conventional medicine)’; and: ‘These biases are more likely to affect small than large studies; the smaller a study, the larger the treatment effect necessary for the results to be statistically significant, whereas large studies are more likely to be of high methodological quality and published even if their results are negative’.”

Yet, in Rutter and Stolper’s section on “Pre-specified hypotheses” they include “quality in homeopathy is worse than in conventional medicine” as a hypothesis of Shang et al., and say that this hypothesis was falsified in the Shang et al. study. This is a straw man: it is not a hypothesis that was discussed in the Shang et al. paper, and Rutten and Stolper have missed the point of including a matched set of trials of conventional medicine. As Rutten and Stolper state (p. 170) “Pooling of results is…questionable if homeopathy works for some conditions and not for others”. This is a reasonable point. However, it is clear that some experimental conventional treatments work and some do not. The results of the analysis of conventional medicine were not consistent with the placebo hypothesis, showing that it is possible to obtain a positive result using the methods of Shang et al., even there is considerable heterogeneity in the results [5].

Post-hoc analysis?

Rutten and Stolper make the claim that the sub-sets of larger, higher quality studies were chosen post-hoc, presumably to make homeopathy appear less effective than it really is. In their paper, Rutten and Stolper state [p. 172-173]:

“Cut-off values for sample size were not mentioned or explained in Shang el al's [sic] analysis. Why were eight homeopathy trials compared with six conventional trials? Was this choice predefined or post-hoc? Post-publication data showed that cut-off values for larger higher quality studies differed between the two groups. In the homeopathy group the cut-off value was n = 98, including eight trials (38% of the higher quality trials). The cut-off value for larger conventional studies in this analysis was n = 146, including six trials (66% of the higher quality trials). These cut-off values were considerably above the median sample size of 65. There were 31 homeopathy trials larger than the homeopathy cut-off value and 24 conventional trials larger than the conventional cut-off value. We can think of no criterion that could be common to the two cut-off values. This suggests that this choice was post-hoc.”

The first thing to note is that it is not true that cut-off values for sample size were not mentioned or explained in the Shang et al. analysis. In the original Shang paper, on page 728, it is stated that “Trials with SE [standard error] in the lowest quartile were defined as larger trials”. In other words, the cut-off was not defined in terms of numbers of subjects, but in terms of standard error. It might be argued that this is a strange way of defining “larger” trials (and perhaps it should have been phrased as “lower standard error”). But it makes sense when criteria must be stated a priori. If a number of subjects were stated as a cut-off value, there would be no way of knowing how many studies would meet that criterion before looking at the data. You might find that a very large or very small number of studies met the criterion, making further analysis difficult. So, there is no mystery as to why the “cut-off values” were different between trials of homeopathy and trials of conventional medicine: it is because the distribution of standard errors is different between the two populations. This could be discovered simply by reading the original paper, and the conclusion that the groups were chosen post-hoc cannot be sustained.

A further point here is that the group of “larger” homeopathy trials contains smaller trials that would not have made the cut for “larger” trials in the conventional medicine group. Those smaller trials are more likely to show spurious positive results. It follows that had the authors engineered the groups to get the result they wanted, they had engineered them in favour of homeopathy.

Another paragraph in Rutten and Stolper states “We did not further investigate possible selection bias by excluding trials, but we were surprised by the exclusion of Wiesenauer's trial on chronic polyarthritis. This was a larger trial (n = 176), of good quality according to Linde, with positive results. This trial would have contributed positively to the outcome of the larger higher quality trials. Shang excluded this trial because no matching trial could be found” (page 171). Since the trial was excluded on the basis of the clearly stated, pre-specified exclusion criteria, what is surprising about it having been excluded? Including it would have made a nonsense of the design of the study and violated the pre-specified exclusion criteria, and would have been a gross error.

Another possible outcome?

Rutten and Stolper conduct a sensitivity analysis, but, as they note, the decisions they make in this analysis are highly subjective. They decide to exclude all trials of homeopathy for muscle soreness [6-9], on the grounds that “treatment of healthy individuals is very rare in homeopathic practice [and] this outcome has low external validity to judge the effect of homeopathy as a method” (page 173). Yet, the trials were conducted with the participation of prominent homeopaths, and some were published in homeopathic or alternative medicine journals [8, 9], so at least some homeopaths seem to be of the opinion that there is enough external validity for it to be worth conducting a trial. So how can the external validity of the trials be judged in a transparent way? In a meta-analysis based on clear, pre-specified criteria, there could be no justification for omitting the studies.

It is also notable that one of the authors was a co-author of another re-analysis published in the Journal of Clinical Epidemiology [10]. That analysis showed that if random-effects meta-analysis is used, it is possible to add smaller trials to Shang’s set of “larger, higher quality” trials of homeopathy, and get a statistically significant (although clinically unimpressive) benefit for homeopathy. All this really shows is that a finding in favour of homeopathy is not robust, and as Shang et al. showed, including smaller trials also decreases the reliability of the findings. The re-analysis also showed that the benefit for homeopathy was statistically insignificant when a meta-regression analysis was used: this negative finding was strangely not mentioned in the Homeopathy paper. Because the results differed between meta-regression and random-effects analyses, and because Shang et al. showed highly significant evidence of funnel-plot asymmetry in their complete dataset of 110 trials of homeopathy, it is arguable that meta-regression analysis is a more appropriate choice.

Overall, it is clear that “another outcome” (i.e. one favourable to homeopathy) is possible, as long as negative studies are excluded without good reason, smaller and less reliable studies are included, and a particular method of statistical analysis is used. In a paper that (wrongly) criticises a study for analysing data based on criteria established post-hoc, this seems like an odd point to make.

Conclusion

The analysis by Rutten and Stolper contains misconceptions of Shang et al., contains some important errors, and does not show that the Shang et al. study was an invalid analysis. In particular, there is no evidence that the Shang et al. study involved post-hoc choice of subgroups. The results of meta-analyses can be debated, but scientists should not be accused of research misconduct on the basis of no evidence, or on the basis of having failed to read their work properly.

References

1. Rutten ALB and Stolper CF. The 2005 meta-analysis of homeopathy: the importance of post-publication data. Homeopathy 2008; 97: 169-177.

2. Shang A, Huwiler-Müntener K, Nartey L et al. Are the clinical effects of homeopathy placebo effects? Comparative study of placebo-controlled trials of homeopathy and allopathy, Lancet 2005; 366: 726–732.

3. Linde K, Clausius N, Ramirez G et al. Are the clinical effects of homeopathy placebo effects? A meta-analysis of placebo-controlled trials, Lancet (1997); 350: 834–843.

4. K. Linde K, Scholz M, Ramirez G, Clausius N, Melchart D, Jonas WB. Impact of study quality on outcome in placebo-controlled trials of homeopathy, J Clin Epidemiol 1999; 52: 631–36.

5. Shang A, Jüni P, Sterne JAC, Huwiler-Müntener K, Egger M. Are the clinical effects of homeopathy placebo effects? A meta-analysis of placebo-controlled trials: Author’s reply, Lancet 2005; 366: 2083-2084

6. Vickers AJ, Fisher P, Wyllie SE, Rees R. Homeopathic Arnica 30X is ineffective for muscle soreness after long-distance running – A randomized, double-blind, placebo-controlled trial. Clin J Pain 1998; 14: 227–231.

7. Vickers AJ, Fisher P, Smith C, Wyllie SE, Lewith GT. Homoeopathy for delayed onset muscle soreness - A randomised double blind placebo controlled trial. Brit J Sports Med 1997; 31: 304–307.

8. Jawara N, Lewith GT, Vickers AJ, Mullee MA, Smith C. Homoeopathic Arnica and Rhus toxicodendron for delayed onset muscle soreness - A pilot for a randomized, double-blind, placebo-controlled trial. Brit Hom J 1997; 86: 10–15.

9. Tveiten D, Bruset S, Borchgrevink CF, Norseth J. Effects of the homeopathic remedy Arnica D30 on marathon runners: A randomized, double-blind study during the 1995 Oslo Marathon. Complement Ther Med 1998; 6(2): 71–74.

10. Lüdtke R, Rutten ALB. The conclusions on the effectiveness of homeopathy highly depend on the set of analyzed trials. J Clin Epidemiol 2008; 61: 1197-1204