## Statistical Methods:

As one can imagine, this project relies heavily on various statistical methods to model the outcome of subjects with chronic diseases. A brief, simplified summary of the methods being employed for the project is as follows.

There are two parts to the Statistical Method: estimation and simulation . Estimation is the process of determining the probability of moving from one state to another in a subprocess (complication or comorbidity) of the disease model. Simulation is the process of using the estimated probabilities to simulate what will happen to a single subject or sample population as they progress through the disease model.

### Estimation:

View Estimation Movie

- The Lemonade Method estimates progression rates between model states by combining parameter estimates from studies published in research journals (Isaman et al., 2006)
- Sometimes there are several studies that estimate the transition probabilities between a pair of states; this makes generating progression rates fairly simple because all of the necessary information is readily available.
- However, some studies may omit certain states or there may not be any studies that estimate some of the transitions in the model. This makes determining progression rates more complicated. If a study omits an intermediary state, the estimated transition rates must be imputed for the omitted stages so that the overall rate is estimated correctly.
- Some studies may not be completely representative of the US population, and this makes it more challenging to find progression rates that will be representative when simulation is done on individuals with many different backgrounds and medical histories.
- The Lemonade method also allows users to calculate transition probabilities that depend on an individual's characteristics, such as age or BMI.
- Because the accuracy of the simulation relies on the progression rates generated during estimation, it is very important that these estimates are as good as possible.

### Simulation:

View Simulation Movie

- Simulation uses estimated probabilities of transitions to simulate what will happen to a single individual or sample population as they progress through the disease model.
- The estimated probabilities may either be specified by the user or generated in the estimation step described above.
- In our example, subjects are identified as having various complications due to diabetes (as seen in the pictorial model ).
- For every year of the patient's simulated life, the patient's complication may progress as indicated in the pictorial model at the rates defined by the model.
- As a person progresses, the probability of various transitions can change.
- For instance, someone with non-proliferative retinopathy will have a much higher probability of developing blindness compared to someone who simply has diabetes and shows no other problems. Similarly, a person's risk of Myocardial Infarction (MI) can increase when the individual has a history of MI.

Ultimately, the estimation and simulation steps can be used together to predict the outcome of an unknown individual or sample population based on various symptoms and medical histories.

### References:

- Isaman, D.J.M., Herman, W.H., & Brown, M.B. A discrete-state and discrete-time model using indirect estimates. Statistics in Medicine 2006 25(march): 1035-1049. DOI: 10.1002/sim.2241