Update: Application of Hybrid Shewhart Charting to Covid Data Series
We have just passed the one-year anniversary of the first reported deaths from Covid-19 in the United States.
During the pandemic, decision-makers have been most interested in the local trajectory of cases, hospitalizations, and deaths and the effect of actions to reduce pandemic impact. Exponential growth phases in the pandemic deserve special attention and detection.
The display shows a series of summary lines (solid) and limit lines (dashed) that represent the trajectory of the reported daily deaths worldwide over the past 13 months. Our method uses control chart rules to assess whether a series is ‘about the same’ or shows signs of a change in trajectory.
The series is adjusted for day-of-week effect; many series related to the pandemic show persistent differences between days, a special cause related to the reporting processes.
The Hybrid Shewhart Chart Method
10 months ago I posted an initial description of our method to help decision-makers distinguish signals from noise.
Over the summer and fall, I worked with my colleagues Lloyd Provost, Shannon Provost, Gareth Parry and Rocco Perla to modify the initial method.
Our current approach distinguishes between different ‘epochs’ of a data series to support effective decision-making.
| Epoch | Description | Data Structure |
|---|---|---|
| 1 | pre-exponential growth | Relatively rare events, summarized by average counts and limits based on the Poisson distribution |
| 2 | exponential growth | Values rapidly increasing that can be described by a straight line with positive slope on the log scale, with limits based on day-to-day differences in counts |
| 3 | post-exponential growth: flat trajectory or exponential decline | Values declining or approximately constant that can be described by a straight line (negative slope or zero slope on the log scale, with limits based on day-to-day differences in counts |
| 4 | stability after descent | Relatively rare events, summarized by average counts and limits based on the Poisson distribution |
We implemented the current method using R. The method accounts for unusually large values as well as the day-of-week effect mentioned above. The R code is available on a public GitHub repository. I give a detailed description of the method in this repository’s ReadMe file.
The R code drives a display of the Covid-19 death counts for countries and U.S. states and territories maintained by the Institute for Healthcare Improvement.
I have also generalized the naming convention in the core functions that drives the IHI display. The new naming convention makes it easier to plot any Covid-related series like ICU cases or hospitalizations using the hybrid Shewhart method. The generalization is documented in this GitHub repository. The repository also has RMarkdown files that will produce interactive plots based on plotly. Click on this markdown file to produce an interactive plot of the world deaths shown in the display at the top of this post.
More information
Lloyd, Shannon, Rocco, Gareth and I published an early description of our approach last June. We are completing the draft of a new paper that describes the current method. I will update this post with the link when the paper is available. I will also add links to other papers that apply the method as these are published.
Colleagues in the Irish government health services are applying the method to Covid pandemic data; their first report is published here.
