# Extended Joinpoint Regression Methodology for Complex Survey Data

## TL;DR

This paper introduces a new method for analyzing trends in health survey data that accounts for complex sampling designs and improves accuracy in identifying changes over time.

## Contribution

The paper proposes individual-level models and a modified design-based AIC for joinpoint regression in complex survey data.

## Key findings

- The new individual-level model outperforms aggregate-level models in identifying joinpoints with moderate to large ICC.
- Simulation studies show improved accuracy in detecting true joinpoints using the proposed methodology.
- The modified M-dAIC helps in model selection for complex survey designs.

## Abstract

Joinpoint regression can model trends in time‐specific aggregated estimates. These methods have been developed mainly for non‐survey data such as cancer registry data, and only recently have been extended to utilize survey data that accounts for complex sample designs resulting in non‐zero correlation between the time‐specific estimates. This correlation can occur for surveys with data from the same sampled units used across time points, for example, the annual National Health Interview Survey with multistage cluster samples using the same first‐stage sampled clusters over consecutive time points. Another issue when modeling aggregated data is that the degrees of freedom for joinpoint analyses of multistage cluster samples are based on the number of time points, not the number of first‐stage sampled clusters as used in survey methods. To address this, we propose models of individual‐level data that incorporate both the correlation between time points and correct the degrees of freedom due to the sampling design that is needed for accurate inferences. Also, a modified design‐based Akaike Information Criterion (M‐dAIC) for model selection is proposed to account for complex sample designs. These new methods are empirically compared to existing methods using simulation studies and health survey data examples. The simulation studies indicated that this new individual‐level model identified the true number of joinpoints more accurately than the established aggregate‐level models for data collected using complex survey designs with moderate to large interclass correlation coefficients (ICC).