Confidence with confidence intervals

* E-mail: mlacolumb{at}doctors.org.uk

Editor—We would like to congratulate Dr Sell and colleagues on their study that estimated the median effective dose (ED50) of ropivacaine and levobupivacaine for postoperative analgesia infused via an intrathecal catheter following hip replacement surgery.1 They used the minimum local analgesic dose (MLAD)2 modification of the minimum local analgesic concentration (MLAC) model3 for this study. It would appear, however, that they have reported spuriously tighter 95% confidence intervals (95% CI) than the data, as presented in Figure 1 of their article, suggest. Similar problems have been highlighted previously.4

A problem with the analysis of up-down sequences is that the observations are not independent. Several approaches have been described to deal with this problem, the Dixon and Massey method being one of the more conservative approaches. For completeness we have included some suggested corrections for the Table including this method, independent pairs, a modified reversal analysis adjusted for testing interval, and probit regression, which we hope the authors and readers will find useful. In this instance we are not interested in the median effective dose (ED50) estimates, rather the 95% CI. Here we see that the authors' estimates (1.2 and 1.3 mg) are approximately four to sixteen-fold more precise than other methods in a study at nine levels, doses spanning 9 mg.

The authors are to be commended for the use of the Figures that depict the data clearly and allow the reader to consider the data in detail. Re-analysis of the data suggests that the SD used to estimate the 95% CI approximated the testing interval (1 mg). Whilst this approach has been recommended for short sequences (nominal sample sizes of six or less) it is based on the assumption that the population SD is known, which is not generally the case. In any event, any estimate or assumption of SD should be considered in respect of the data as collected.


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Table 1 Amended results presented as ED50, 95% confidence limits and 95% CI (mg)

 
It appears also that the sequences are not stabilized in that they are continuing to trend downwards. A simple way to assess this is to note that there are approximately as many ineffective outcomes above the ED50 as there are below. Also, the majority of ineffective outcomes occur within the first ten tests, which suggests the possible bias of a learning effect. A more formal way to assess stability is to perform a logistic regression (analysis of deviance) to assess the effect of dose on outcome and this is not significant (P = 0.43). One would expect dose to be significant where it should be expected to be so in a stable dose–response model.

Other workers wishing to research further these findings should refer to the amended results in the Table in designing future trials and are encouraged to consider doses below the 95% confidence limits reported by the authors, which in a sense, adds more weight to the authors' original conclusions. Despite the error in precision again the authors are to be commended for using estimation rather than simple hypothesis testing in continuing to research such effects.

M. O. Columb* and H. E. Thomson

Manchester, UK

References

1 Sell A, Olkkola T, Jalonen, Aantaa R. Minimum effective local anaesthetic dose of isobaric levobupivacaine and ropivacaine administered via spinal catheter for hip replacement surgery. Br J Anaesth 2005; 94: 239–42[Abstract/Free Full Text]

2 Stocks GM, Hallworth SP, Fernando R, England AJ, Columb MO, Lyons G. Minimum local anaesthetic dose of intrathecal bupivacaine in labour and the effect of intrathecal fentanyl. Anesthesiology 2001; 94: 593–8[CrossRef][ISI][Medline]

3 Lyons G, Columb MO, Hawthorne L, Dresner M. Epidural pain relief in labour; bupivacaine sparing by epidural fentanyl is dose dependent. Br J Anaesth 1997; 78: 493–7[Abstract/Free Full Text]

4 Columb MO, Maguire S. Up-down sequential allocation. Anaesthesia 2002; 57: 300–1[CrossRef][ISI][Medline]





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