Optimal Thresholds, Linear or Nonlinear Relationships of Fracture Risk Reduction With Therapy
Thank you for asking us to comment on the letter by Bauer and Vittinghof. This letter was based on our exploratory analysis of the relationship between bone resorption markers and fracture risk.
Why did we combine the two treatment groups in Tables 1 and 2? The figures from our letter1 show clearly that the smoothed lines overlap and that the treatment as a factor was not significant. These data were therefore combined to more clearly illustrate the relationship between bone turnover markers and fracture risk.
Were the inferences concerning thresholds based on the pooled data in Tables 1 and 2? No. These tables do not allow for time to event; the analysis we conducted was based on Cox regression allowing for treatment and trial.
Why do we say that the on-treatment bone turnover marker is better than the short-term change in bone turnover markers for examining the relationship with fracture risk? The argument is conceptual and is based on our understanding of how bone turnover relates to fracture risk. We know that continuous high bone turnover in postmenopausal woman is associated with increased risk of fracture.2 We relate the level of bone turnover to fracture risk during the period of study; we should do the same in our treatment trials. The argument is not ours—it was put to us by Professor BEC Nordin (personal communication) and we believe him to be correct. There is also a statistical argument that favors the use of on-treatment bone turnover markers. We found a weak correlation between on-treatment and baseline bone turnover markers and thus examining the relationship of percentage change in bone turnover markers and fracture adds further variability and obscures any relationship actually present.
Why do we think that N- and C-telopeptides of type I collagen data are inconsistent? They were inconsistent with respect to a threshold but in many other ways they were quite consistent. Such a level of inconsistency was reported by Bauer3 in his paper about the relationship between bone turnover markers and fracture risk in the FIT study; the bone formation markers bone alkaline phosphatase and procollagen type I N-propeptide showed some results that were similar and some that were discrepant. The most likely explanation is that these are a consequence of chance variation. There may be biological explanation related to differences in enzymatic processing of the N-telopeptide versus C-telopeptide and in the recognition of type I collagen fragments of different stages of maturation, including isomerization.
Did we reanalyze the nonvertebral fracture data? The reader will appreciate from the editorial that we were not responding to a letter to the editor and so we were not clear about the scope of our response. However, because the main issue raised in the popular media was about the concept of a threshold with vertebral fracture, and we had not observed a threshold for nonvertebral fracture, there seemed no point in reanalyzing the nonvertebral fracture data.
Other reports since 2003 have not observed a nonlinear relationship; why did we not refer to these? We were preparing a letter and not a review. However, we now have the chance to comment. One of the articles cited4 did not examine for nonlinearity and so is not relevant. The article by Bauer et al.3 did examine for nonlinearity, but this was not statistically significant at p < 0.05. However, this is a misunderstanding of a p value; it does not mean there is no nonlinearity, only that the authors failed to detect it. They do not state what power they had to detect any important nonlinearity. Nevertheless, they do uncover a misapprehension about the nature of these relationships. Risk must asymptote to zero. It is not to be expected that the relationship between risk and bone turnover markers could be linear over a wide range.
