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Are you rolling?

Patient Safety Quality Monthly, November 23, 2010

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In our world of patient safety and quality, we are inevitably dealing with analyzing and presenting data that we collect. Sometimes we just present last month's values. Unfortunately, that doesn't put the data in any form of context. It makes it hard to answer the questions "So are we getting better or worse?" and "So is our process smooth and under control?"

One good way to help answer these questions is to provide a historical trend. We often try to do that with our data. But if there are a small number of data points or samples, we can often end up with a bad case of the "jaggies." You know those graphs—the high peaks followed by the grand canyons! These jagged graphs can often led the viewer to jump to conclusions and say, "Oh no! That looks terrible!" when there is just one occurrence compared to our normal zero occurrences.

The answer to this is to smooth the data. A smoothed graph can reduce the knee-jerk reactions and help ensure that we are effectively communicating the real underlying trend. A powerful method to smooth our data is to use a rolling or moving average. A rolling average takes a series of prior points, adds them together, and then divides by the number of points. That resulting average is then plotted. We then move over one point and do it again. We just roll across the rest of the graph in this same way. The more points we put into the average, the smoother the trend is. This gives us a nice directional trend for the magnitude of the data.

It is likely that you all have done rolling averages at some point in your analysis, so this isn't really a new concept. Let's take it to the next level. If rolling the averages is a good thing, what else can we roll?

How about rolling standard deviations? The standard deviation tells us how big the spread of the data is. That's useful because it helps us understand if the process that is producing the data is tightly controlled (small spread—highly consistent) or if the process is loosely controlled and producing a larger spread and distribution of the data.

We often take a data stream and calculate the standard deviation based on all the points. But if this is driven by a process, isn't it likely that the process may be getting better or worse? We should assume that the standard deviation might change over time. So, back to rolling. How about if we roll our standard deviation?

Perhaps we have daily data that we collect. Consider calculating a standard deviation based on the daily samples for the past month. Plot that, then move over a month and calculate the standard deviation, and then keep on rolling. This gives us a smoothed curve of the changes in standard deviation over time. Look for major changes. Hopefully you will see a smaller standard deviation after you have implemented a process improvement. Likely you will begin to see an increase in the rolling standard deviation when your process is declining.

One more example for extra credit! Consider two data streams that we all collect—these might be mortality and complications. It is a nice touch to see if they correlate, so we might do an analysis and calculate a correlation value for the entire data set. Consider a rolling correlation. Calculate your correlation on a part of the data, then move over one and do it again. Keep on rolling across your data. Now you will see any changes in correlation between your indicators over time. This can be a great diagnostic tool.

Remember, when you do rolling, you change the magnitude and insert a shift in the data. You have to watch out for that. But expanding your rolling to other areas may open a whole different window on your data. Keep on rolling!

Ken Rohde, Senior Consultant

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