Calculate the estimated number of cases of dementia for each organisation (denominator) by applying the age and sex-specific reference rates to the age and sex structure of its population:

\(E_{k} = \sum ijN_{ijk}\times p_{ij}\)

Where:

\(E_{k}\) is the estimated value for the subject organisation *k*

\(N_{ijk}\) is the population (65+ patient list size) for each combination of age band *i* and sex* j* in subject organisation *k*

\(p_{ij}\)_{ }is the binomial proportion for each combination of age band *i* and sex *j* in the reference population (CFAS II)

Calculate the estimated diagnosis rate for each organisation (indicator value) by dividing its observed dementia diagnoses by its estimated value and express this as a percentage:

\(\lambda_{k} = \frac{O_{k}}{E_{k}}\times 100\)

Where:

\(\lambda_{k}\) is the estimated diagnosis rate for the subject organisation *k*

\(O_{k}\)* *is the recorded 65+ dementia diagnoses in the subject organisation *k*

\(E_{k}\) is the estimated value for the subject organisation *k*

Calculate the upper and lower 95% confidence limits for each organisation’s indicator value by simulation. Repeat the indicator calculation 100,000 times, randomly resampling each time from the age and sex-specific expected distributions, and the recorded diagnoses count distribution, to create a distribution of 100,000 random samples from the overall indicator distribution. Take the 2500th smallest and the 2500th largest values from this distribution as estimates of the 95% lower and upper confidence limits respectively:

\(\lambda LL_{k} = \lambda sim_{k}(n) = n(\lambda sim_{k}1,...,\lambda sim_{k}100,000)\)

\(\lambda UL_{k} = \lambda sim_{k}(100,000-n) = 100,000-n(\lambda sim_{k}1,...,\lambda sim_{k}100,000)\)

Where:

\(\lambda LL_{k}\) is the lower 95% confidence interval for subject organisation *k*

\(\lambda UL_{k}\) is the upper 95% confidence interval for subject organisation *k*

\(n\) defines the threshold of the indicator distribution based on the number of repetitions, 100,000, and level of confidence, 95%: \(\frac{100,000\times(1-0.95)}{2}\)

\(\lambda sim_{k}1,...,100,000\) is the order of randomly sampled indicator values for subject organisation *k* produced by repetition of the following:

\((\lambda sim_{k} = Orand_{k} Erand_{k}\times 100)1,...,100,000\)

Where:

*\(Orand_{k}\)** *is the randomly sampled diagnoses count value for organisation k produced by the inverse cumulative probability function with:

probability: \(R\epsilon(0,...,1)\)

mean: \(O_{k}\)

standard deviation: \(O-\sqrt{\frac{O_{k}}{k}}\)

*\(Erand_{k}\)** *is the randomly sampled expected value for organisation k produced as follows:

*\(Erand_{k} = \sum ijN_{ijk}\times prand_{ij}\)*

Where:

\(N_{ijk}\) is the population (65+ patient list size) for each combination of age band \(i\) and sex \(j\) in subject organisation \(k\)

\(prand_{ij}\) is the randomly sampled binomial proportion for each combination of age band \(i\) and sex \(j\) in the reference population (CFAS II) produced as follows:

\(prand_{ij} = \exp(p_{i}cf_{ij})1+\exp(p_{i}cf_{ij})\)

Where:

\(p_{i}cf_{ij}\) is the inverse cumulative probability function for each combination of age band \(i\) and sex \(j\) in the reference population (CFAS II) with:

probability: \(R\epsilon(0,...,1)\)

mean: \(\log e(p_{ij}100 - p_{ij})\)

standard deviation: \(\frac{(\log e(pUL_{ij}100 - pUL_{ij}) - \log e(pLL_{ij}100 - pLL_{ij}))^2}{1.96}\)

Where:

\(pLL_{ij}\)is the lower 95% confidence limit for each combination of age band \(i\) and sex \(j\) in the reference population (CFAS II)

\(pUL_{ij}\)is the upper 95% confidence limit for each combination of age band \(i\) and sex \(j\) in the reference population (CFAS II)