3. Producing Stabilized Rates
The final step of a RSTbx workflow is producing stabilized rates!
Model
The Univariate Conditional Autoregressive (UCAR) model used by RSTbx is based on the model developed by Besag, York, and Mollié (1991) with modifications using inverse transform sampling for restricted informativeness based on Quick, Song, and Tabb (2021):
\[ \begin{split} Y_{i} &\sim \text{Binomial}(n_{i}, \theta_{i}) \\ \theta_{i} &\sim \text{LogitNormal}(\beta_{j} + Z_{i}, \tau^2), \\ i &=\{1,...,N_s\}, j =\{1,...,N_{is}\} \end{split} \]
\[ \begin{split} \beta_{j} &\sim \text{Normal}(0,\sigma_{\beta}^2),\ \sigma_{\beta}^2 \to \infty \\ Z &\sim \text{CAR}(\sigma^2) \\ \sigma^2 &\sim \text{InvGamma}(a_\sigma,b_\sigma) \\ \tau^2 &\sim \text{InvGamma}(a_\tau,b_\tau) \end{split} \]
Additional models are available within the RSTr package.
Requirements
Aggregate event and population table
Aggregate event and population tables should be formated to have one record (aka row) for each region. It would look something like:
| GEOID | EventCount | PopulationCount |
|---|---|---|
| 01001 | 0 | 3430 |
| 01001 | 1 | 7749 |
| 01001 | 0 | 7339 |
| … | … | … |
| 72153 | 5 | 4527 |
| 72153 | 7 | 3223 |
| 72153 | 9 | 571 |
If you would like to produce age-adjusted rates, aggregate event tables should have one record (aka row) for reach region-age group combination. Like this:
| GEOID | AgeGroup | EventCount | PopulationCount |
|---|---|---|---|
| 01001 | 0-4 | 0 | 3430 |
| 01001 | 5-14 | 1 | 7749 |
| 01001 | 15-24 | 0 | 7339 |
| … | … | … | … |
| 72153 | 65-74 | 5 | 4527 |
| 72153 | 75-84 | 7 | 3223 |
| 72153 | 85up | 9 | 571 |
Boundary File
Usage
Producing crude rates
If you haven’t already, set up the Rate Stabilizing Toolbox.
Open up the Catalog Pane.
Right click on Databases, select Add Database, and navigate to where you have downloaded and extracted the RSTbx and find data.gdb.
Within the data.gdb, right click on mi_carto and mi_joined_event_pop, and Add to Current Map.
Open the Rate Stabilizing Tool
Set the following parameters and Run:
Input Table: data.gdb/mi_joined_event_pop
Input Table Fields:- Region ID: GEOID
- Event Count: EventCount
- Population Count: PopulationCount
Input Feature: data.gdb/mi_carto
Input Feature Fields:- Region ID: GEOID
Additional Options:
- Credible Level: 0.95
- Rate Per: 100,000
- Number of Years: 1
Output Table: crude_rates
Age Group Field: Leave blank
Standard Population Year: Leave blank
Standardized Age Groups:- Lower age group: Leave blank
- Upper age group: Leave blank
- Region ID: GEOID
Producing age-adjusted rates
Within the data.gdb, right click on mi_joined_event_pop_strat, and Add to Current Map.
Returning back to the Rate Stabilizing Tool, set the following parameters and Run:
Input Table: data.gdb/mi_joined_event_pop_strat
Input Table Fields:- Region ID: GEOID
- Event Count: EventCount
- Population Count: PopulationCount
Input Feature: data.gdb/mi_carto
Input Feature Fields:- Region ID: GEOID
Additional Options:
- Credible Level: 0.95
- Rate Per: 100,000
- Number of Years: 1
Output Table: age_adj_rate
Age Group Field: AgeGroup
Standard Population Year: 2010
Standardized Age Groups:- Lower age group: 35, 64, 34
- Upper age group: 64, up, up
- Region ID: GEOID
Interpreting estimates
When producing crude rates four columns will be output:
median - The estimated rate. CI{credible level}lower - The lower bound of the estimate at the selected credible level.
CI{credible level}upper - The upper bound of the estimate at the selected credible level.
relLvl - The maximum credible level at which a reliable estimate can be produced.
We typically recommend only utilizing estimates with a reliability level above 0.95.
When producing age-adjusted rate, these same columns will be present for each constituent age group within your data AND the standardized age groups you selected.