## Abstract

### Background

One critical variable in the time series analysis is the change point, which is the point where an abrupt change occurs in chronologically ordered observations. Existing parametric models for change point detection, such as the linear regression model and the Bayesian model, require that observations are normally distributed and that the trend line cannot have extreme variability. To overcome the limitations of the parametric model, we apply a nonparametric method, the Mann-Kendall-Sneyers (MKS) test, to change point detection for the state-level COVID-19 case time series data of the United States in the early outbreak of the pandemic.

### Methods

The MKS test is implemented for change point detection. The forward sequence and the backward sequence are calculated based on the new weekly cases between March 22, 2020 and January 31, 2021 for each of the 50 states. Points of intersection between the two sequences falling within the 95% confidence intervals are identified as the change points. The results are compared with two other change point detection methods, the pruned exact linear time (PELT) method and the regression-based method. Also, an open-access tool by Microsoft Excel is developed to facilitate the model implementation.

### Results

By applying the MKS test to COVID-19 cases in the United States, we have identified that 30 states (60.0%) have at least one change point within the 95% confidence intervals. Of these states, 26 states have one change point, 4 states (i.e., LA, OH, VA, and WA) have two change points, and one state (GA) has three change points. Additionally, most downward changes appear in the Northeastern states (e.g., CT, MA, NJ, NY) at the first development stage (March 23 through May 31, 2020); most upward changes appear in the Western states (e.g., AZ, CA, CO, NM, WA, WY) and the Midwestern states (e.g., IL, IN, MI, MN, OH, WI) at the third development stage (November 19, 2020 through January 31, 2021).

### Conclusions

This study is among the first to explore the potential of the MKS test applied for change point detection of COVID-19 cases. The MKS test is characterized by several advantages, including high computational efficiency, easy implementation, the ability to identify the change of direction, and no assumption for data distribution. However, due to its conservative nature in change point detection and moderate agreement with other methods, we recommend using the MKS test primarily for initial pattern identification and data pruning, especially in large data. With modification, the method can be further applied to other health data, such as injuries, disabilities, and mortalities.