Joinpoint Methods for Complex Survey Data

NCI's Joinpoint software, which uses joinpoint regression models applied to time-specific estimates, was developed for and is widely used in analyzing trends in population-based disease surveillance systems, such as those from cancer registries. It has also been applied to trends derived from complex survey data. For some complex survey samples, observations may exhibit correlation reflecting a more general covariance structure than the typical heteroscedastic or autocorrelated error assumptions. This can occur when repeated measurements are taken on the same sampled units (e.g., primary sampling units) across multiple time points.

Joinpoint Regression Model for Aggregate-Level Outcomes

The NCI's Joinpoint software (starting with version 4.9) provides the option for modeling trends in aggregated outcomes from complex survey data. This capability incorporates the full variance-covariance matrix of the time-specific estimates. See Variance-Covariance Matrix for additional details. The full methodology is described in Liu et al (2022).

Joinpoint Regression Model for Unit-level Outcomes

Joinpoint models for individual-level (unit-level) data have also been developed. Extended from the aggerate-level models, these models provide a more granular view of the data, incorporating both correlated errors and corrected degrees of freedom to account for the complex sampling design, ensuring accurate statistical inferences. The general model specifications are provided below. The detailed methodology is presented at Liu et al (2025).

For a continuous outcome \(y_{ijl}^{\left(t\right)}\), the following joinpoint model at the individual level is considered:

\[g\left(y_{ijl}^{\left(t\right)}\right)=\beta_0+\beta_1t+\delta_1\left(t-\tau_1\right)I_{\tau_1}(t)+\ldots+\delta_k\left(t-\tau_k\right)I_{\tau_k}(t)+\varepsilon_{ijl}^{(t)}\] (1)

where \(\tau_k\prime\)s are the unknown joinpoints with \(I_{\tau_k}(t)=1\) if \(t>\tau_k\) and \(\varepsilon_{ijl}^{(t)}\) is the error term, \((\varepsilon_{ijl,\ }^1{\ldots,\ \varepsilon}_{ijl\ }^T)~N(0,⅀T×T)\) at given \(i,\ j,\ l\). The link function \(g\left(\bullet\right)\) can be either an identity or a log function. When identity function is chosen, i.e., \(g\left(y_{ijl}^{\left(t\right)}\right)=y_{ijl}^{\left(t\right)}\) , this model could be reduced to the aggregate-level model though this unit-level model has the capacity for inclusion of individual level covariates.

For a binary outcome \(y_{ijl}^{\left(t\right)}\), the following logistic joinpoint model is considered:

\[logit\left(p\left(y_{ijl}^{\left(t\right)}=1\right)\right)=\beta_0+\beta_1t+\delta_1\left(t-\tau_1\right)I_{\tau_1}\left(t\right)+\ldots+\delta_k\left(t-\tau_k\right)I_{\tau_k}\left(t\right)\] (2)

When \(\tau_k\prime\)s are given, Model (1) and Model (2) are similar to regular linear and logistic regression, except that the model fitting is done by segments, as indicated by the additional covariates formed from the time intervals.

The methodology developed addresses the following questions: 1) Is (are) there any joinpoint(s)? If so, then 2) How many joinpoints (or change-points) are there? 3) Where is (are) the joinpoint(s) located? and 4) How reliable are the parameter estimates? These are the same questions that the aggregate-level modeling addresses.

The R algorithms for conducting unit-level joinpoint regression analysis are provided here. The current methodology does not yet support inclusion of additional covariates or predictors (e.g., race/ethnicity). New methods incorporating such covariates into the joinpont regression framework are under development.

References

Liu B, Kim H-J, Feuer E.J., Graubard B.I. (2022). Joinpoint regression methods of aggregate outcomes for complex survey data. Journal of Survey Statistics and Methodology, 00, 1-23. https://doi.org/10.1093/jssam/smac014

Liu B, Kim H-J, Zou J, Feuer EJ, Graubard BI. (2026). Extended Joinpoint Regression Methodology for Complex Survey Data. Statistics in Medicine, 45(1-2):e70374. doi: 10.1002/sim.70374