Background
Osteoporosis increases the risk of fragility fracture in both genders. In a population-based study of Canadians age 50 years by the Canadian Multicenter Osteoporosis Study Group, the prevalence of vertebral fractures was found to be 23.5% in men and 21.5% in women [
1]. Alendronate, a potent oral bisphosphonate, decreases the risk of fractures in postmenopausal women with low bone mass or prevalent fractures, as established in a recent meta-analyses examining outcomes in thousands of women [
2‐
4]. Less is known about the effect of alendronate in men, due to a paucity of randomized controlled trials. However, osteoporotic fractures are common in aging men; in fact the lifetime risk of a fracture of the spine, hip or distal radius is 13% for white men older than 50 years [
5]. Our objective was to determine whether alendronate decreases risk of vertebral and non-vertebral fractures in men.
Upon initiating our review, we were aware of the paucity of trials examining anti-fracture efficacy of bisphosphonates in men. However, given that bisphosphonates decrease osteoclastic resorption in a mechanism independent of sex steroid status [
6], we believed that the effect of alendronate in men would be similar to that previously observed in women. Therefore, the anti-fracture efficacy of alendronate in women would be relevant prior information to be incorporated in assessing treatment effects in men. Classical, frequentist, statistical methods do not offer the flexibility to incorporate relevant prior knowledge or beliefs in analysis of data, thus we sought an alternative statistical approach to analyze the results of our systematic review and we turned to Bayesian methods.
Bayesian statistical methods can explicitly and quantitatively incorporate relevant prior evidence in health technology assessment [
7]. The foundation of Bayesian statistical methodology is Bayes' theorem, which is "a formula that shows how existing beliefs, formally expressed as probability distributions, are modified by new information" [
8]. In Bayesian methodology, the conclusions of the analysis (known as the "posterior" inferences) are a result of modification of the "prior" data (in this case, known anti-fracture efficacy of alendronate in post-menopausal women), by new data collected (known as the "likelihood function", in this case, the data collected in men) [
9]. Bayesian methodology is similar to clinical practice, as typically a clinician has a strong "prior" belief of, for example, a diagnosis such as osteoporosis prior to diagnostic testing, based on the clinical profile of the patient (such as age, gender, risk factors) and the results of diagnostic testing (analogous to a "likelihood function"), are used to confirm or refute those clinical suspicions and formulate a final conclusion (analogous to a "posterior" inference). Thus, Bayesian approaches are clinically intuitive. Moreover, results of Bayesian analyses are also more easily clinically translated than those of frequentist analyses [
8]. For example, a Bayesian result tells us how likely is the result (such as an odds ratio), given the data [
8]; as opposed to a frequentist result, which tell us how likely are the data given the null hypothesis. For these reasons, Bayesian methodology may be incorporated in healthcare medical decision-making [
9]. Justification for the use of Bayesian approach in this study is the ability to directly answer the clinically relevant question: how likely is an osteoporotic man treated with alendronate to be protected from fracture given the current evidence in men and prior evidence in women? A classical frequentist analysis does not allow the flexibility to incorporate prior relevant information in the analysis and all relevant data from women would be ignored in such an analysis. Thus, a Bayesian approach was chosen as the primary analysis method for our study.
Discussion
Limitations of our systematic review include the paucity of trial data from men, the small sample sizes in trials, the variations in trial duration between studies, and the inconsistency of calcium and vitamin D formulations between trials (with the possibility that the alfacalcidiol used in the Ringe study could be considered a form of active therapy [
23]). We were also unable to perform a per protocol sensitivity analysis of the anti-fracture efficacy of alendronate in men who were compliant with therapy as these data were not published in the primary trials. We did not include unpublished data. We also did not contact author to clarify details of the randomization procedures. Merits of our study include its systematic nature, including both Bayesian and traditional frequentist analyses of available data, and the examination of clinically relevant fracture outcomes. Of note, the numerical estimates of odds ratios and their respective credibility or confidence intervals were similar using Bayesian and frequentist analyses in this study. These findings are not surprising, given that the treatment effects of alendronate in women, from whom prior information was derived, were similar to those observed in men. The precision of our estimate was however slightly improved using a Bayesian approach for the outcome of non-vertebral fractures as seen by the slightly narrower credibility interval than confidence interval for that outcome. Credibility intervals can be narrower using a Bayesian approach than confidence intervals obtained using a frequentist approach because of additional data provided by the priors [
9].
Given that the results of our Bayesian and frequentist meta-analyses were similar, was there any advantage to the Bayesian approach? The basic question posed using a frequentist approach is how likely are the data given the null hypothesis? In contrast, the question posed from a Bayesian perspective is, how likely is the odds ratio, given the data [
8]? Furthermore, the interpretation of a traditional 95% confidence interval is that given a long series of such intervals, 95% of them should contain the true value of the odds ratio [
9]. In contrast, in interpreting a 95% credibility interval, there is a 95% probability that the true value of the parameter lies within this interval [
9]. Thus, the clinical question posed and the interpretation of the probability interval, are more clinically intuitive from a Bayesian perspective. Moreover, the Bayesian approach allowed the flexibility to incorporate clinically relevant evidence from trials in women in this meta-analysis of alendronate treatment in men.
In the future, more trials of active osteoporotic therapies and their effects on fracture outcomes need to be performed in both genders.
Appendix
Electronic search strategy for potentially relevant studies
For Medline and Medline-in-Process (1966 to May 24, 2004), Cochrane Central Register of Controlled Trials (1800 to May 24, 2004): "alendronate" or "fosamax" - restricted to adult male humans (age ≥ 19 years), clinical trials, controlled clinical trials, and randomized controlled trials.
For Embase 1996 to May 24, 2004: "alendronate" or "fosamax" AND "male" or "men"- restricted to adult male humans (age ≥ 19 years), clinical trials, controlled clinical trials, and randomized controlled trials.
For PubMed (up to May 24, 2004): name and initials of authors of included studies AND "alendronate" or "fosamax"
Competing interests
Dr. Sawka is a Skeletal Health Scholar funded, in part, by the Canadian Institutes of Health Research. Dr. Sawka is also a Fellow in Health Economics at McMaster University, partly funded by an unrestricted educational grant from Hoffmann-La Roche.
Dr. Papaioannou's competing interests include: Aventis, Eli Lilly, Merck, Novartis, and Procter and Gamble.
Dr. Adachi, Consultant to: Amgen, Astra Zeneca, Aventis, Eli Lilly, Glaxo Smith Kline, Merck, Novartis, Procter and Gamble, and Hoffman-La Roche.
Dr. Hanley's competing interests include consultancies with, honoraria for speaking from, or involvement in research with, the following companies or organizations : Amgen, Astra-Zeneca, Aventis, the Dairy Farmers of Canada, Eli Lilly, Merck, Novartis, NPS Pharmaceuticals, Pfizer, Procter and Gamble, Hoffman-La Roche, and Wyeth.
The other co-authors have no competing interests to declare.
Authors' contributions
All co-authors reviewed the manuscript and made suggestions for revisions. The project idea was conceived by Dr. Sawka. Analyses were performed by Dr. Sawka, with input from Dr. Thabane. The manuscript was written and revised by Dr. Sawka.