Joinpoint Regression

Joinpoint regression (Kim et al., 2000), also known as piecewise linear regression, is increasingly used to identify the timing and extent of changes in time series of health outcomes. The basic idea is to model the time series using a few continuous linear segments. These segments are joined at points called joinpoints which represent the timing (e.g., year) for a statistically significant change in rate trend. This analysis can provide a more comprehensive picture of the burden of the disease and generate new insights about the impact of various interventions. Joinpoint regression can also be used to project future trends.

In addition to joinpoints, other parameters estimated by Vesta include:

1. APC Annual Percent Change (slope of segments), and
2. AAPC Average APC over the entire time period.

The number of segments used in a joinpoint regression is dependent on a few things. There is a requirement for a minimum number of observations between joinpoints. Vesta requires a minimum of 1 data point between joinpoints, and 2 data points at both ends of the trend model. This allows the software to generate multiple segments with stronger confidence. Vesta will automatically generate three models of increasing complexity (yellow=0 joinpoint, red=1 joinpoint, and blue=2 joinpoints) and overlay them over the observed time series, in green in the Vesta screenshot below.

Covariates in Joinpoint Regression

Another feature of Vesta is its ability to model residual time trends, i.e. trends that cannot be explained by covariates specified by the user. Covariates include a range of factors (population, environmental, climate, etc.) that can potentially influence observed trends. Covariates can impact the optimal number of joinpoints as well as the significance of rates of change, so it is worth considering how the covariates in your projects can influence the outcome of your analysis.

Spatial Joinpoint Regression

Analyzing temporal trends outside a spatial framework is unsatisfactory because significant variation even within a single state is not accounted for.

Vesta is the only software that allows exploring how characteristics of time series varies spatially through the separate analysis and modeling of individual geographical units.

In the Vesta screenshot above, time trends were modeled using joinpoint regression for four counties of Michigan, identified by their FIPS code (26xxx). New datasets, AAPC and joinpoint years, are created and can be mapped to visualize geographical variations in time series characteristics; see example below for the annual rate of breast cancer late-stage diagnosis across the lower Peninsula of Michigan.

Joinpoint Regression Process

1. Prior to starting a joinpoint regression session, it is important that the column in your dataset with the geographical identifier (e.g., FIPS code for counties) is properly designated as ID variable. From the Data panel, right click on the variable under your dataset, and from 'modify' select 'designate as ID'.
2. From the Methods panel, select "Joinpoint Regression" and click "start"
3. Answer if your data is compositional or not in the first drop down menu
4. Select your dataset from the drop down menu
5. Select your dependent variable in your dataset from the drop down menu
6. Select your independent variables from the display by clicking the plus sign, and remove independent variables by clicking the minus sign
7. The data can be grouped in different ways:
   • Separate by ID
   • Combine all - all time serries are averaged and a single joinpoint regression model is fitted to that temporal average
   • by ID variable
8. Select your desired error calculation
   • Homoscedastic - calculated by ordinary least squares regression
   • Weighted by standard deviation - select the calculated standard deviation from your dataset. The standard deviation cannot be calculated in Vesta and need to be brought in with the data file at import.
9. Click "Run". Joinpoint regression results are viewable from the Data panel after the process completes.

Joinpoint Regression Results

Results from a Joinpoint regression analysis are created in a Results folder that is saved under the respective dataset in the Data panel.

A new workspace entitled "Joinpoint Results" is automatically created with a joinpoint time plot and report. Specific geographies can be selected from the dropdown in the top left corner, and the time plot and report updated to present the selected geography results.

The time plot is interactive and allows users to capture trend values and behaviors across multiple joinpoint curves.