The calculations of the logistic method detailed in the paper [1] are appropriate when the factor-specific event rates of the local population are not too dissimilar. We have found that when these rates are very heterogeneous, weighting the logits to give a standardised rate will give an unreliable estimate of the standardised rate. We propose that in such cases the estimated probabilities (of disease) derived from the logistic regression model, are weighted by the standard area populations to obtain the standardised rate. The corresponding approximate standard error of the standardised rate being a function of the estimated probabilities and logits. The downside of weighting the probabilities rather than the logits sometimes results in the lower confidence limit being negative. However this is also a shortcoming of the arithmetic direct standardisation method. If this is the case then we recommend that the lower interval be truncated at zero. The resulting confidence interval produced will be at least at the 95% level. While continuing to propose that the logistic regression method of standardisation has advantages over the usual arithmetic direct standardisation, we suggest that weighting the probabilities given by the logistic regression, rather than the logits will give a more reliable standardised rate in general. We wish to thank Sarah Lewington (CTSU, University of Oxford) for bringing this limitation to our attention.
Reference 1. Roalfe AK, Holder RL, Wilson S: Standardisation of rates using logistic regression: a comparison with the direct method. BMC Health Services Research 2008,8:275
Limitation
14 January 2010
The calculations of the logistic method detailed in the paper [1] are appropriate when the factor-specific event rates of the local population are not too dissimilar. We have found that when these rates are very heterogeneous, weighting the logits to give a standardised rate will give an unreliable estimate of the standardised rate. We propose that in such cases the estimated probabilities (of disease) derived from the logistic regression model, are weighted by the standard area populations to obtain the standardised rate. The corresponding approximate standard error of the standardised rate being a function of the estimated probabilities and logits. The downside of weighting the probabilities rather than the logits sometimes results in the lower confidence limit being negative. However this is also a shortcoming of the arithmetic direct standardisation method. If this is the case then we recommend that the lower interval be truncated at zero. The resulting confidence interval produced will be at least at the 95% level. While continuing to propose that the logistic regression method of standardisation has advantages over the usual arithmetic direct standardisation, we suggest that weighting the probabilities given by the logistic regression, rather than the logits will give a more reliable standardised rate in general.
We wish to thank Sarah Lewington (CTSU, University of Oxford) for bringing this limitation to our attention.
Reference
1. Roalfe AK, Holder RL, Wilson S: Standardisation of rates using logistic regression: a comparison with the direct method. BMC Health Services Research 2008,8:275
Competing interests
none