Why aren’t deaths rising with cases?

Over the past week or so, there’s been quite a bit of discussion about why we haven’t seen a national increase in COVID-19 deaths alongside the national uptick in COVID-19 cases. There are several important factors that may be contributing to these patterns in the data (see this recent New York Times article for a nice summary). In this post, I’m going to briefly discuss one potential contributing factor, raised recently by epidemiologist Ellie Murray on Twitter.

Here’s how she explains the part of her argument that I want to focus on:

What does this have to do with #COVID19? Well, we switched from only testing people who had really serious severe symptoms to testing a much wider group of people with milder or even no symptoms.

Many of the new cases are much earlier in their disease process.

Lead time bias tells us that we can expect to see a longer delay between detection & death because we are detecting people earlier in the disease process. This does not mean people are surviving longer! That’s the sneaky lead time bias talking!!

https://twitter.com/EpiEllie/status/1280305424005238786

So after reading this, I wanted to know: Do we see a longer lag time between cases and deaths when there are high levels of testing?

After playing around with some data, the answer appears to be yes. When testing levels are low, there’s a shorter lag time between trends in reported cases and trends in reported deaths. Specifically, trends in deaths appear to lag about 1-2 weeks behind trends in new cases when there is not much testing (i.e., percent positive among new tests is 45%) while the lag is more like 2-4 weeks when testing coverage is high (i.e., percent positive among new tests is 5%).

These results are consistent with the idea that when there is more testing, we tend to detect the disease earlier on (well before people typically get sick enough to die from it). That could help to explain why deaths haven’t increased yet when we look at national data, even though nationwide cases have been rising steadily for about 3 or 4 weeks (as of July 7).

Technical details

All the code/data used to run my analysis is available here: https://github.com/favero-nate/covid-underreporting (see files with the name “early_detection”).

I used data from The COVID Tracking Project to measure all my variables. I converted their daily data into weekly (state-level) data. Data on deaths and new cases was converted to indicate death/cases per 100,000 people.

I ran a regression where the dependent variable is the number of newly-reported COVID-19 deaths. The number of new cases is interacted with the percent positive (among new cases), with lags included for either 0-4 or 0-5 weeks in the past (I ran two separate models). Results differ somewhat depending on whether 4 of 5 weeks of lags are used, but both model specifications indicate that there is less of a lag when percent positive is lower.

Here is the output describing the marginal effect of new cases for lags 0-4 when the percent positive is 5%:

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  new_pos_pc |
         --. |  -.0100246   .0046009    -2.18   0.034    -.0192658   -.0007834
         L1. |  -.0012974    .008128    -0.16   0.874     -.017623    .0150283
         L2. |   .0211115   .0074945     2.82   0.007     .0060584    .0361646
         L3. |   .0115612   .0070731     1.63   0.108    -.0026455    .0257679
         L4. |   .0072277   .0078008     0.93   0.359    -.0084406     .022896
------------------------------------------------------------------------------

Notice that the 2- and 3- week lags appear to be the best (positive) predictors of deaths.

When percent positive is 45%:

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  new_pos_pc |
         --. |   .0135866    .017506     0.78   0.441    -.0215751    .0487484
         L1. |   .0264638   .0144514     1.83   0.073    -.0025628    .0554904
         L2. |   .0356483    .009438     3.78   0.000     .0166914    .0546051
         L3. |  -.0076246   .0083358    -0.91   0.365    -.0243675    .0091182
         L4. |   .0135277   .0046214     2.93   0.005     .0042452    .0228101
------------------------------------------------------------------------------

Now, a 1-week or 2-week lag appears to be the best predictor.

If we include 5 lags, we get the following marginal effects when percent positive is 5%:

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  new_pos_pc |
         --. |  -.0078235   .0044692    -1.75   0.086    -.0168001    .0011532
         L1. |  -.0029335   .0088583    -0.33   0.742     -.020726     .014859
         L2. |   .0117092   .0081747     1.43   0.158      -.00471    .0281285
         L3. |   .0200081   .0082513     2.42   0.019     .0034349    .0365813
         L4. |   .0082586   .0054773     1.51   0.138     -.002743    .0192601
         L5. |  -.0006531   .0041305    -0.16   0.875    -.0089493    .0076432
------------------------------------------------------------------------------

The 3-week lag appears to be the best predictor, with 2- and 4- week lags also appearing to have some marginal predictive power.

When percent positive is 45%:

------------------------------------------------------------------------------
             |            Delta-method
             |      dy/dx   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
  new_pos_pc |
         --. |   .0114405   .0195505     0.59   0.561    -.0278279    .0507089
         L1. |   .0115728   .0139244     0.83   0.410    -.0163951    .0395406
         L2. |   .0460193    .008522     5.40   0.000     .0289024    .0631363
         L3. |  -.0022818   .0088022    -0.26   0.797    -.0199616    .0153979
         L4. |    .004343    .006729     0.65   0.522    -.0091726    .0178587
         L5. |   .0046856   .0035725     1.31   0.196    -.0024899    .0118612
------------------------------------------------------------------------------

With this poor testing coverage, the 2-week lag dominates the other predictors.

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