Percent Test-Positives Might Be A Spurious Indicator

Even Trump “knows” it: the more diagnostic tests you run, the more cases you’re going to find. One way of compensating for the effect of increased testing is to measure the percentage of tests yielding positive results. Since late April, changes in percent test-positives have generally tracked, and anticipated, changes in death rates. But so have changes in the raw number of test-positives. Yesterday’s post confirmed that states with high test-positives per 100K of population also have high deaths per 100K, which persist for 3 to 4 weeks into the future.

Today I look at the same set of analyses for percent test-positives, to see if they correlate with and predict death rates across states.

The first time I ran analyses on state-by-state data, from the beginning of the epidemic to May 26, covid diagnostic test-positive percentages were correlated strongly and positively with covid-related deaths (r = +.77). I.e., states with tests yielding a high percentage of positive results also had high body counts. Since then the correlation between cases and deaths has nearly vanished, down to r = +.21 as of August 4.

I ran two sets of lagged correlations and compared them with contemporaneous correlations.

Deaths 6/15 – 7/5:

  • correlated with test-positive percentages from 6/15 – 7/5 –> r = -.35
  • correlated with test-positive percentages from 5/26 – 6/15 –> r = -.41

Deaths from 7/5 – 8/4:

  • correlated with test-positives from 7/5 – 8/4 –> r = +.53
  • correlated with test-positives from 6/15 – 7/5 –> r = +.57

Those findings are hard to interpret. Why would there have been a negative correlation between percent test-positives and deaths in the 6/15 to 7/5 interval? Nationwide during that 3-week span, total test positives and test-positive percentages both increased, whereas both before and afterward they decreased. As reported in yesterday’s post, the correlation between total positives and deaths also weakened during the 6/15 to 7/5 interval, but it remained positive.

During both the 6/15-7/5 and the 7/5-8/4 intervals, there was virtually no correlation between the number of tests conducted and the number of test-positives (r = +.11 and +.16, respectively). I.e., the test-positive percentage isn’t consistently raised or lowered by increased testing. In brief, the statistical relationships between percent-positives and other important covid indicators are inconsistent and anomalous.

At this point it would make sense to amp up the analytical power into multivariate regressions. E.g., after controlling for the strongly positive effect of total test positives on total deaths, it might turn out that percent-positives exert either an additive or a countervailing force. That’s how the model-builders do it: throw as many variables as possible into the mix and let the algorithm weight the variables to achieve maximum statistical power.

For now I’ll restrain the impulse to follow the multivariate trajectory. My tentative conclusion from these univariate correlational findings: the parallel trend lines linking test-positive percentages with death rates is a spurious association. Infection rates have increased, leading inevitably to increased death rates. However, ups and downs in the proportion of  tests yielding positive results are likely an artifact of increases and decreases in testing selectivity.


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