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Evaluating the adjusted expectation

 

For our actual observations we evaluate the adjusted expectations shown above, and so obtain

eqnarray835

Our notation here is that tex2html_wrap_inline9064 refers to our adjusted expectation for tex2html_wrap_inline8866 in the light of the information contained in tex2html_wrap_inline8806 , having observed tex2html_wrap_inline9070 . From the point of view of the Doctor, her belief specifications and the observations tex2html_wrap_inline9036 and tex2html_wrap_inline9038 that she makes when she performs the ogt-test upon herself, are consistent with her revising her expectations upwards for both tex2html_wrap_inline8580 and tex2html_wrap_inline8582 . In the case of the fasting blood-glucose measurement, the analysis shows a revision upwards from 4.16 to 4.71; and in the case of the following two-hour measurement, a revision upward from 6.25 to 6.91.

Informally, as a very rough guide to the locations of tex2html_wrap_inline8580 and tex2html_wrap_inline8582 , we might decide to take intervals of about two standard deviations in either direction from the expectation as being fairly likely to contain the relevant locations. For the prior assessments we have approximately the intervals

displaymath9056

For the assessments after adjusting by tex2html_wrap_inline8806 we obtain the smaller intervals

displaymath9057

The adjusted expectation for the two-hour blood-glucose measurement is 6.91, implying that an average healthy elderly patient will have a two-hour reading on the borderline between being diagnosed as healthy and being diagnosed as having impaired glucose tolerance. Put another way, about half of the elderly will be misdiagnosed according to the threshholds set for this ogt-test. Additionally, the fasting blood-glucose level has adjusted expectation 4.71; suggesting that the elderly have a slightly higher fasting level than do the young. Consequently the analysis suggests that there are static differences between the blood-glucose levels for the young and the elderly; and dynamic differences between their abilities to cope with fluctuations in blood-glucose levels.



David Wooff
Thu Oct 15 12:20:04 BST 1998