C-19: Importance of testing at speed

Updated: May 11

We utilise a cross correlation method to gauge a more robust estimate of test delays and timeliness of death reporting from country to country; in order to complement and refine our previous approach of curve fitting daily infection and death statistics. We then postulate possible implications that a higher or lower testing speed may have on exploring future strategies that a country may undertake to keep the virus under control. Intuitively, a longer delay between actual infections and detection, verified via testing, would mean authorities would struggle to monitor the spread of infections - leading to an inability to prevent further spread and increase dependency on lockdowns as the only means to abate it.

TL;DR

  • It is possible to directly measure median times for 'infection-to-detection' and 'infection-to-death' for each country by cross-correlating mobility changes with reported statistics, assuming mobility changes are large enough to affect changes to virus transmission

  • Case detection delays are significant, ranging between 0 days to 22 days depending on country based on our previous analysis. A generalised takeaway is that high test delays are associated with weaker ability to abate infection spread, in absence of the effects of lock-downs; as such a country exhibiting longer test delays means they are less able to handle infection spreads

  • If any country is to devise an effective exit strategy from lock-downs, it would need to reduce test delays below an estimated 5 days or less in order to have an effective test, track and trace strategy that would help overcome spread of the virus in the population. Several countries have in fact achieved this


A brief background and history of our methodology

  • In earlier projections we had assumed a relatively short median time between actual infections and death, based loosely around available statistics at the time. This was set preliminarily at 8 days; and would mean the 'real-world' infection curve (not to be confused with case detection) would lead that of deaths by 8 days

  • We then studied more closely the change in real-world transmission factor, ascertained from official death and case detection statistics and estimated a new median time between infection and death of 14 days, which we found to be relatively consistent from country to country. All our daily projections now utilise this estimate, regardless of country in question

  • Fitting case detection statistics to this new real infection curve yields an estimated case detection delay for each country - this is estimated between a range of 0 days and 22 days, with median around 9-10 days. At this median delay most countries would fail to abate epidemic spread of the virus, I.e. the transmission of the virus would be >1

  • However, the issue with this approach of computation is that in introduces any potential error in the timeliness of death reporting into the estimation of case detection speed, i.e. if deaths are delayed by 1-2 days, the same delay is introduced into the real infection curve, and thus also the case detection delay computation

  • In this article we attempt to directly correlate the changes in mobility to reported case detection and death statistics to determine an exact estimate of the two metrics: time between infection and death, and time between infection and detection for each country


Introductory discussion: Importance of reducing delays vs. wide ranging performance from country to country

  • A shorter test delay would mean that the infected person can be isolated and their contacts traced at a faster speed, thus abating any further spread early. With a doubling time ranging between 2-5 days in the early stages, reducing this delay as much as possible is crucial to keep infections under control.

  • A recent study by researchers in Oxford University have quantified the effects, including as well different possible phases of pre-symptomatic, symptomatic and asymptomatic transmission rates - see excerpted graphic from their article below. In general they found that 3 days to detect and isolate infected persons may already be too late to reduce the transmission factor to non epidemic levels I.e. >1. Link to article: https://science.sciencemag.org/content/early/2020/04/09/science.abb6936

Source: Science Magazine, 31 March 2020, "Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing". The solid black line showsr=0, i.e., the threshold for epidemic control.

  • The daily projections that we publish include an estimate of each country's testing delay - to recap again for the reader what this is: the estimated time, in general, it takes for health authorities to detect cases after the initial infection. This delay is an amalgamation of a very wide range of factors; from test-kit availability, availability of healthcare capacity, differences in regimes and procedures across healthcare systems, to physical proximity and ease at which patients are able to seek care. Below is an excerpt from our daily reports for reference with the computed test delay highlighted in red;

  • We estimate this figure by computing the time delay between the case detection curve in yellow, and the theoretical real infection line in red (see the arrow in figure below), with an assumed 14 day delay between this line and model fitted deaths;

  • Tabulated below are the estimated case detection delays for a range of countries, along with other salient statistics for reference. The last two columns are estimates based on our fitting of reported statistics in terms of initial growth (Phase 1), and tapering growth (Phase 2) due to control and abatement activities

  • See plot below the table. Contrary to intuition, there does not seem to be much correlation between initial growth phase and test delays - suggesting more complex factors are at play to accelerate or slow down the virus transmission in this early phase. However, we do see positive correlation between delays and the effectiveness of the taper phase, or how fast the taper is. It should be noted, however, that we cannot disaggregate lock-down effects that occur concurrently during this phase. It is intuitive however to imagine that track and trace activities are escalated during such lock-downs as authorities escalate their actions to combat the virus spread, thus possibly leading to a more rapid test timeframe

Table: Testing delay estimates by country

Figure: Initial and taper phase growth (y-axes) vs. testing delay (x-axis) - lower on the y-axis the better (i.e. slower initial growth and faster the taper to transmission <1)

Cross-correlation analysis: computing median time between infection and death from death statistics

  • Across most countries we studied, mobility records in general shows a weekly cadence - with weekends (Saturday, Sunday) increasing or decreasing in mobility; before, during or after lockdowns. We noticed the same observation in death and infection statistics, suggesting that it could be possible the two factors are correlated to mobility changes - an intuitive observation as with more mobility there is greater interaction and therefore transmission

  • It should be stated that reported case detection and death statistics are rather erratic, and are themselves respectively influenced by a number of factors - from test queues to administrative paperwork and presumably multiple layers of reporting procedures. However as we already have a strong hypothesis of the median estimate (i.e. 14 days) it should bound our consideration set of results from the cross-correlation computation

  • Cross-correlation was conducted with respect to (i) the day on day changes in mobility, and (ii) the day on day changes in reported daily infection or death figures. Windowing was applied to focus on larger infection and deaths to improve statistical significance of the computation

  • The results below are a selection of computations for a number of countries. By assuming the onset of increased transmission coincides with that of increased mobility we see good agreement to the timeframe of 14 days for the median time between infections and death, with some, but minimal variation from country to country

Malaysia: 16 days (previous 14 days)

United States: 13-14 days (previous 14 days)

United Kingdom: 13-14 days (previous 14 days)

Belgium: 14 days

Sweden: 14-15 days (previous 14 days)


Cross-correlation results: computing median time between infection and case detection from case detection statistics

  • Whereas death statistics had a clear starting baseline hypothesis, the situation for case detection statistics is a bit different as this would be wide ranging across countries

  • We thought it might also be interesting to understand how testing delays have changed over the period since the pandemic started - reflecting potential resource constraints within healthcare systems. A static computation such as the one conducted above for death statistics may thus not be suitable for this intended purpose

  • Instead, we conducted a rolling cross-correlation of the case detection data with time window varying between 7-10 days across the period of study; in order to create a 2-dimensional cross correlation map (see examples below)

  • Correlation scores for fitting ranged between 0.5-0.9 indicating a reasonably good fit, however we should warn that given the erratic data with weekly 'rhythms', the data should be viewed 'suspectedly' at best. The rhythms could be caused by a number of factors, included cyclical workload within the healthcare systems, creating aliasing errors in the correlation data (repeated higher correlations in 7 day intervals). To note; a cross correlation score of 0.5 would mean that for a 1% growth in mobility there would be a 0.5% growth in daily infections on any given day

  • In summary, there is good agreement with our previous method of estimating delays in case detection, and we will therefore maintain that approach as primary indicator of test delays in our daily projections. However, this method has the added advantage of allowing investigation of how test delays may have changed with time, which itself is a very interesting topic to explore further.

  • Results are shown below for select countries;

Netherlands (test delay baseline est 9 days, refined ~9-11 days)

Sweden (test delay baseline est 0 to -1 days, refined 0-2 days)

Malaysia (test delay baseline est 10 days, refined 10-11 days)

Germany (test delay baseline est 2 days, refined ~0-4 days)


Belgium (test delay baseline est 6 days, refined ~8-10 days)

Japan (test delay baseline est 7 days, refined ~6 days)

Brazil (test delay baseline est 12 days, refined ~10 days)

Switzerland (test delay baseline est 4 days, refined ~5 days)

Implication and discussion

  • Testing speeds need to improve. As countries finalise their plans to reopen their economies and end lockdowns it is of great importance that testing is improved - both in terms of speed and sufficiency. Our estimates of testing speeds from country to country suggest a lot more needs to be done to improve on the current situation, where many countries are still testing at median delays of 10-14 days from infection

  • Test speeds are not entirely consistent. It should be noted that the exact delay in testing at any one time varies; we explore this below utilising data from Austria. Note the cumulative infection curve does not follow the logistic curve fit (modelled utilising death statistics). The likely reason is a change to test regime where later tests in the month of April were done faster (vs. date of contraction) than those before 24 March. The rolling cross correlation below that confirms this, where test delays since early April may have dropped as low as 1-3 days compared to 6 days previously.


  • A note on test sufficiency. This is a discussion not elaborated here, i.e. are test regimes able to test the vast majority of infected persons in the population. As we had explained in another article, this is not easily determined without a priori knowledge and understanding of the prevalence of asymptomatic carriers - a topic which itself is challenging with many unknowns

  • Smart tactics should be explored. To reduce the burden on precious test-kit and human resources, for a start, healthcare authorities could explore smarter test tactics. A number of researchers have suggested strategies such as; cluster/pooled testing, where up to 50-60 individuals are tested at once in a single test vial boosting efficiency and speed significantly if infected numbers are low enough; or sewer testing, where samples are collected from sewage waste - both these methods are elaborated in this article here. In South Korea, drive through testing is available affordably, leading to higher speed of detection as the mass population drives the rapidity of testing due to their own personal need for certainty and security. Ultimately these methods achieve greater effectiveness and speed through smarter tactics not just simply more testing

  • Time will tell if the human population has the ingenuity, willpower and coordinative ability to solve this problem efficiently. To reiterate, it is extremely important for each country to reach a test speed which is able to combat infection spreads and bring down transmission rates to below 1. The scientists agree this is a delay of maximum 3 days; we think that there may be some leeway for countries where initial growth rates are more manageable, perhaps this should bring it up to 5 days or less. Still, not an easy target given current levels

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