Calculating prevalence

For ease of comparison all of the prevalences on this site are based on the whole practice registered list, not just those in the correct age group - this applies to areas such as diabetes or epilepsy. This is largely because countries other than England do not list the specific number of patients on the practice list over, say, seventeen years old. It is also the prevalence that is used for adjustment of point value.
I was asked this week why the whole list is used for prevalence adjustment rather than the age adjusted subgroup. Is this unfair on practices? Well the answer is no, it is actually more fair the way it is, but for some quite complicated reasons. We have to look at some maths.
$$\begin{array}{c}\mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{\mathrm{PracPrev}}{\mathrm{AvgPrev}}\times \frac{\mathrm{PracList}}{\mathrm{AvgList}}\\ \\ \mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{(\frac{\mathrm{Register}}{\mathrm{PracList}})}{(\frac{\mathrm{AvgReg}}{\mathrm{AvgList}})}\times \frac{\mathrm{PracList}}{\mathrm{AvgList}}\\ \\ \mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{\mathrm{Register}}{\sout{\mathrm{PracList}}}\times \frac{\sout{\mathrm{AvgList}}}{\mathrm{AvgReg}}\times \frac{\sout{\mathrm{PracList}}}{\sout{\mathrm{AvgList}}}\\ \\ \mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{\mathrm{Register}}{\mathrm{AvgReg}}\end{array}$$

We have started from saying that the point value is modified by the practice prevalence relative to the average practice prevalence. Then the point value is modified by the relative size of the practice list overall. The second line expands this a bit by using the register size and the list size against the averages. It is true that this is not exactly how the average prevalence is calculated but it is pretty close.

After simplifying the formula there is a lot we can cancel from the top and bottom until we get to the final formula which basically says that the practice gets a set amount per person on the register but that this drops as the national average register size rises. Nothing else matters.

We can try again using an 'Eligible' denominator for the register.

$$\begin{array}{c}\mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{\mathrm{PracPrev}}{\mathrm{AvgPrev}}\times \frac{\mathrm{PracList}}{\mathrm{AvgList}}\\ \\ \mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{(\frac{\mathrm{Register}}{\mathrm{Eligible}})}{(\frac{\mathrm{AvgReg}}{\mathrm{AvgEgble}})}\times \frac{\mathrm{PracList}}{\mathrm{AvgList}}\\ \\ \mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{\mathrm{Register}}{\mathrm{Eligible}}\times \frac{\mathrm{AvgEgble}}{\mathrm{AvgReg}}\times \frac{\mathrm{PracList}}{\mathrm{AvgList}}\\ \\ \mathrm{Point}\mathrm{value}=\mathrm{\pounds }160\times \frac{\mathrm{AvgEgble}}{\mathrm{Eligible}}\times \frac{\mathrm{Register}}{\mathrm{AvgReg}}\times \frac{\mathrm{PracList}}{\mathrm{AvgList}}\end{array}$$

There is much the same process here but there is a lot less to cancel out. That is not necessarily a bad thing but we can see how this formula behaves. If we assume a practice of average list size then the last term will be one. If it has an average register size for diabetes then the middle term will be one as well. Interestingly in this case the point value would vary with the proportion of over 17 year olds on the practice list (i.e. Eligible would change without changing the overall list size). This is not what we want to see at all as the practice list makeup would alter income without any change to the actual number of patients treated.

So that is why the overall list size is used to calculate prevalence.