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:

Ek=∑ijNijk×pijEk=∑ijNijk×pij

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:

λk=OkEk×100λk=OkEk×100

Where:

λkλk 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:

λLLk=λsimk(n)=n(λsimk1,...,λsimk100,000)λkLL=λsimk(n)=n(λsimk1,...,λsimk100,000)

λULk=λsimk(100,000−n)=100,000−n(λsimk1,...,λsimk100,000)λkUL=λsimk(100,000−n)=100,000−n(λsimk1,...,λsimk100,000)

Where:

λLLkλkLL is the lower 95% confidence interval for subject organisation *k*

λULkλkUL 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%: 100,000 * (1-0.95) / 2

λsimk1,...,k100,000λsimk1,...,k100,000 is the order of randomly sampled indicator values for subject organisation *k* produced by repetition of the following:

(λsimk=OrandkErandk×100)1,...,100,000(λsimk=OrandkErandk×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: Rϵ(0,...,1)Rϵ(0,...,1)

mean: OkOk

standard deviation: O−−√kOk

*Erand*_{k}_{ }is the randomly sampled expected value for organisation k produced as follows:

Erandk=∑iiNijk×prandijErandk=∑iiNijk×prandij

Where:

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

prandijprandij 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:

prandij=exp(picfij)1+exp(picfij)prandij=exp(pijicf)1+exp(pijicf)

Where:

picfijpijicf is the inverse cumulative probability function for each for each combination of age band *i* and sex *j* in the reference population (CFAS II) with:

probability: Rϵ(0,...,1)Rϵ(0,...,1)

mean: loge(pij100−pij)loge(pij100−pij)

Standard deviation: loge(pULij100−pULij)−loge(pLLij100−pLLij)2/1.96loge(pijUL100−pijUL)−loge(pijLL100−pijLL)2/1.96

Where:

pULijpijUL is the lower 95% confidence limit for each combination of age band *i* and sex* j* in the reference population (CFAS II)

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