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Confidence with confidence intervals
- Malachy O Columb, Thomson H (7 March 2005)
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Malachy O Columb , Thomson H
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Editor - We would like to congratulate Dr Sell and colleagues on their study that estimated the median effective dose (ED 50) of ropvacaine 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) model [3] for this study. It would appear however that they have reported spuriously tight 95% confidence intervals (95% CI) than the data as preseted in Figure 1 suggests. Similar problems have been highlighted previously [4,5]. 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 1.3mg) are approximately four to sixteen-fold more precise than other methods in a study at nine levels, doses spanning 9mg! 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 (1mg). 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 generally not the case. In any event, any estimate or assumption of SD should be considered in respect of the data as collected. It appears also that the sequences are not stabilised 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 ED 50 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 peform 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. Table of amended results presented as ED50 (95% confidence limits) and 95% confidence intervals (mg). ED50 Levobupivacaine (95% confidence limits) and 95%CI Authors report [1] 11.7 (11.1-12.4) CI 1.3 Independent pairs 11.4 (8.6-14.4) CI 5.8 Modified reversals 11.4 (6.6-16.2) CI 9.6 Dixon & Massey 12.2 (6.2-18.2) CI 12.0 Probit regression 9.7 (4.6-20.2) CI 15.6 ED50 Ropivacaine (95% confidence limits) and 95%CI Authors report [1] 12.8 (12.2-13.4) CI 1.2 Independent pairs 12.8 (10.0-15.6) CI 5.6 Modified reversals 13.0 (6.6-19.4) CI 12.8 Dixon & Massey 13.4 (6.7-20.0) CI 13.3 Probit regression 9.8 (4.1-23.6) CI 19.5 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. British journal of Anaesthesia 2005; 94: 239-42 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 3. Lyons G, Columb MO, Hawthorne L, Dresner M. Epidural pain relief in labour; bupivacaine sparing by epidural fentanyl is dose dependent. Bristish Journal of Anaesthesia 1997; 78: 493-497 4. Palm S, Gertzen W, Ledowski T, Gleim M, Wolf H. Minimum local analgesic dose of ropivacaine vs. ropivacaine combined with sufentanil during epidural analgesia for labour. Anaesthesia 2001; 56: 526-9 5. Columb MO, Maguire S. Up-down sequential allocation. Anaesthesia 2002; 57: 300-1 M.O. Columb H.E. Thomson South Manchester University Hospitals Wythenshawe, Manchester. Conflict of Interest:None declared |
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