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• Determining the smallest detectable change
  Jane S Angwin
  Published on: 13 April 2016

• Published on: 13 April 2016

  Determining the smallest detectable change

  • Jane S Angwin
  • Other Contributors:
    • Michael Binks, Michael F. James

  Dear Editor,

  The authors [1] are to be congratulated on demonstrating that, when readers view radiographs at 2 time-points simultaneously, they observe the relative change in JSN and/or erosions between the radiographs rather than the absolute state of the joints. Thus, they assign separate scores to the 2 radiographs to reflect this observed change, rather than scoring the 2 radiographs independently. This truth is...

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  Dear Editor,

  The authors [1] are to be congratulated on demonstrating that, when readers view radiographs at 2 time-points simultaneously, they observe the relative change in JSN and/or erosions between the radiographs rather than the absolute state of the joints. Thus, they assign separate scores to the 2 radiographs to reflect this observed change, rather than scoring the 2 radiographs independently. This truth is evidenced in the smaller variance of the ‘change’ data compared to that of the traditional ‘difference’ data [2-4]. Distinct acronyms, SDC and SDD, for smallest detectable change and smallest detectable difference, usefully distinguish cut-offs determined from the two datasets.

  But, when the precision of data is improved, the use of appropriate statistics becomes critical.

  In this paper, SDC is determined as 2.85 using two readers and chronological scoring. In their earlier paper (5), SDC was determined as 1.7 and 2.4 using a single reader, chronological and paired scoring, respectively. Historical estimates of SDD are in the range 4.7 to 11.0 [2- 4].

  The validity of the statistics employed in the earlier paper [5] caused us unease but there was no data or cumulative ‘probability’ plot [6] against which to rationalise our concerns. In the present paper, the situation is remedied by explicitly giving the data for the 10 patients considered, Table 1, and, although the study size is small, it rather neatly proves the point. For 3 of the patients (30%), the difference in score change recorded by the 2 readers exceeds SDC, whereas statistically this number should be around 5%. Further, 2 of the 10 patients (20%) would have been differently assigned as progressors / non-progressors by the two readers.

  Hence, the authors rightly find variation in score change data more appropriate than variation in individual score data, but extrapolation to SDC requires more careful consideration of the data distribution and its correlation to the underlying score change. For this non-normally distributed data, the 97th percentile may be a more meaningful cut-off, but the influences of patient population and different readers’ assessments of change should also be considered more thoroughly. From the data, there is little justification for lowering the SDC (or SDD) cut-off below 4.5.

  References

  (1). Bruynesteyn K, Boers M, Kostense P, van der Linden S, van der Heijde D. Deciding on progression of joint damage in paired films of individual patients: smallest detectable difference or change? Ann Rheum Dis 2004; Published Online First 29/07/2004. doi:10.1136/ard.2003.018457.

  (2). Bruynesteyn K, van der Heijde D, Boers M, Saudan A, Peloso P, Paulus H et al. Determination of the minimal clinically important difference in rheumatoid arthritis joint damage of the Sharp/van der Heijde and Larsen/Scott scoring methods by clinical experts and comparison with the smallest detectable difference. Arthritis Rheum 2002; 46:913-920.

  (3). Lassere MN, van der Heijde D, Johnson K, Bruynesteyn K, Molenaar E, Boonen A et al. Robustness and generalizability of smallest detectable difference in radiological progression. Journal of Rheumatology 2001; 28:911-913.

  (4). Landewé R, Boers M, van der Heijde D. How to interpret radiological progression in randomized clinical trials? Rheumatology (Oxford) 2003; 42:2-5.

  (5). Bruynesteyn K, Landewé R, van der Linden S, van der Heijde D. Radiography as primary outcome in rheumatoid arthritis: acceptable sample sizes for trials with 3 months follow-up. Ann Rheum Dis 2004; Published Online First 22/03/2004. doi:10.1136/ard.2003.014043.

  (6). Landewé R, van der Heijde D. Radiographic progression depicted by probability plots: presenting data with optimal use of individual values. Arthritis Rheum 2004; 50:699-706.

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  Conflict of Interest:
  None declared.

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