Epidemiological Surveillance: How It Works

This post is more technical than previous ones: it contains equations. Those who don’t like equations can skip the formulas and read the text only. In [1] we have used a Susceptible-Infected-Recovered (SIR) model mentioned in our post “Fusion of Biosurveillance with Epidemiological Modeling” (December 11, 2011). Here we discuss the SIR model in more details. Its graphical description is simple:

 Mathematically, the SIR model is described by the following first-order nonlinear system of difference equations:

S(n+1) = S(n) – (β/N)S(n)I(n),

I(n+1) = I(n) + (β/N)S(n)I(n)  - δI(n),                             (1)    

R(n+1) = R(n) + δI(n),

where S(n), I(n) and R(n) represent the numbers of susceptible, infected and recovered individuals correspondingly on day n; N is the total population (assumed constant); β is the infection transmission rate and δ is the average rate of recovery from infection. Note that d = 1/δ  is the mean duration of infectivity (in days). Both rates β and δ are supposed to be constant. Unfortunately, variables S(n) and R(n) are not observed or measured systematically in the biosurveillance real-time context. Only I(n) can be estimated, though indirectly, through the assumption that the overall number of infected on each day can be approximated by the sum of the number of patient visits to a hospital emergency department or a clinic or a physician office during the past d days (d is an infectivity period in days.) Therefore, we will work only with the second equation in (1). At the very beginning of an emerging disease or a new pandemic, which is the most interesting moment for early detection and early situational awareness, we can assume that there is no immunity in the population to the new disease, i.e., S(0) ≈ N. Hence, at the early phase of the epidemic, the second equation in (1) is reduced to the closed linear equation which contains only number of infected  
I(n+1) ≈ I(n) + (β – δ)I(n),              (2)       
Equation (2) is approximate (instead of = we have ≈), and taking into account errors of approximations we arrive at the stochastic equation
I(n+1)= I(n)(1 + (β – δ)) + w(n),              (3)                                                                    

where w(n) is an error or noise term (in more details see [1]). Formula (3) is the well-known equation of a first-order autoregression process AR(1). Equations (2) and (3) describe exponential growth if β – δ > 0 and exponential decay if β – δ < 0. Thus, the difference β – δ is a threshold parameter alternative to R₀ mentioned in our previous post “Fusion of Biosurveillance with Epidemiological Modeling” (December 11, 2011). Here R₀ can be expressed as R₀ =β/δ. Obviously, the threshold parameters R₀ and β - δ are equivalent:  

(R₀ > 1) <=> (β – δ) > 0 <=> Epidemic           

(R₀ < 1) <=> (β – δ) < 0 <=> Non-Epidemic

 In the early detection context, the advantage of the threshold parameter β – δ over R₀ is obvious: we have a linear parameter in linear equations (2) and (3) as opposed to nonlinear parameter R₀ =β/δ in a nonlinear setting of system (1). Our approach to computing R₀ is as follows: first, estimating the initial growth rate β – δ  through autoregression model (3) and then evaluating parameter R₀ through formula R₀   = 1 + 7(β – δ) (let us remind that in case of influenza we assume that the mean duration of infectivity d equal to 7 days). Thus, by making statistical inferences  about the only parameter β – δ in AR(1) model (3) we actually make inference about R₀. As a result, we are able to decide whether or not the epidemic has started (early detection task). If the answer is “yes” , we can  get preliminary estimates of the number of infected at the epidemic peak, the total number of infected over the course of the outbreak, the critical vaccination threshold,  etc. needed to develop measures for timely response and consequence management (early situational awareness task). See [1] and previous post “Fusion of Biosurveillance with Epidemiological Modeling” (December 11, 2011). Note that statistical inference methods for AR(1), including  parameter estimating, confidence Intervals constructing and hypothesis testing are well-developed and easily available (see [1]). Though, the situation is not as rosy as it looks. What exactly can be used from this statistical toolkit will be discussed in our next post.

And final remark, our approach could be called “Epidemiological Surveillance” (which is used in the title of the post). Really, on one hand, the approach is based on syndromic surveillance data (numbers of visits); on the other hand, the approach uses epidemiological models and their approximations for analysis and decision making. The problem is that this term (epidemiological surveillance) has been already used with the meaning of biosurveillance related to human health only (animals excluded!) (see [2]). We believe that our understanding of the term “epidemiological surveillance” is more to the point.

References

[1] Shtatland, E. and Shtatland, T. (2011). Statistical approach to biosurveillance in crisis: what is next. NESUG Proceedings. [full text]                                           

[2] Fricker, R. D. (2011a). Some methodological issues in biosurveillance. Statistics in Medicine. [full text]

Biosurveillance for Influenza

Influenza is the most widespread naturally occurring infectious disease in recent human history that has caused countless deaths worldwide. There were three influenza pandemics in the 20th century – the “Spanish” flu of 1918-19 (“the mother of all pandemics”), the “Asian” flu of 1957-58, and the “Hong Kong” flu of 1968-69. The 1918 flu, caused by a strain of H1N1, was by far the most deadly. Between 50 and 100 million people died totally as a result of the Spanish flu, possibly more than during the entire course of The Black Death. It makes the Spanish flu the deadliest natural disaster in human history. For comparison, death toll of WWI is estimated between 10 and 20 million, and WWII – between 62 and 78 million. The 1957 pandemic was due to a new H2N2 strain of influenza virus and killed two million people, while the 1968 pandemic resulted from an H3N2 strain and killed one million. In addition, there were 3 so-called flu pandemic scares (unrealized pandemics). The first pandemic of 21^st century was the Swine flu (April 2009 – July 2010). Fortunately, this H1N1 Swine flu pandemic was mild. It is convenient to show these results in the form of a table:

Pandemic            Years      Strain          Death Toll

Spanish flu      1918 - 1919    H1N1     50 - 100 million
Asian flu        1957 - 1958    H2N2            2 million

Hong Kong flu    1968 - 1969    H3N2            1 million

Swine flu        2009 - 2010    H1N1           25,174 (!)     

The names of influenza strains: H1N1, H2N2, H3N2, etc., are related to the two proteins that play a very important role in the process of influenza transmission: hemagglutinin  (where we get the H) and neuraminidase (from which the N comes from). It is known that there exist 16 different H-proteins: H1 – H16, and 9 different N-proteins: N1 – N9, overall 16 x 9 = 144 combinations. Although the most recent pandemic was rather mild, the uncertainty of “what is next?” is really alarming, Actually, pandemics happen every few decades. They occur when a new subtype of influenza A arises that has either never circulated in the human population or has not circulated for a very long time (so that most people do not have immunity against the virus), and it can spread easily through the human population.

Summarizing one can conclude that influenza is the number one permanent threat to the human population health, which deserves special attention and a particular approach. That is why in all developed countries there exist continuously operating influenza-specific reporting systems (such as FluView (CDC), EuroFlu (the WHO European Region), GoogleFlu (worldwide), FluWatch (Canada) etc. And that is why every day at 10 a.m. during flu season, a report on the number of cases of flu-like illness in the United Kingdom is placed on the desk of the British Prime Minister.

Fusion of Biosurveillance with Epidemiological Modeling

Usually, classical epidemiology is considered to be largely retrospective while biosurveillance should be prospective by definition. Recently, there have been published a few papers which can be viewed as a first step to the so-called real time epidemiology with the possibility of predicting further development of the epidemics (see the corresponding references in [1]). Still, those papers use weekly reporting, which is typical for epidemiology of infection diseases as a whole. In contrast, modern syndromic surveillance operates with daily counts (typically of emergency departments / clinics / doctor offices visits), and relying on weekly data is considered obsolete. And yet, the most important difference between epidemiological approach and syndromic surveillance is in information quality of the data used. Epidemiology uses weekly counts of cases with confirmed diagnosis whereas syndromic surveillance works with pre-diagnostic data. At the first glance, it is unclear whether these two types of data can be connected to each other, and consequently, whether epidemiological modeling can be of any use in syndromic surveillance. If the answer is ‘yes’, then we can use all the wealth of epidemiologic analytics for early detection and situational awareness goals. Below we will see the benefits syndromic surveillance can potentially get from its fusion with epidemiological modeling. The simplest and the most popular epidemiological model is the so-called susceptible-Infectious-recovered (SIR) model. SIR model is one of the early triumphs of mathematical epidemiology (since 1927!), and still it is a workhorse of modern epidemiology. We have also used SIR in [1]. There is a fundamental parameter in SIR, so-called basic reproductive number, R₀, which has a very simple epidemiological interpretation and can answer many questions regarding both early detection and situational awareness. First of all, R₀ is a threshold parameter, determining whether or not there is an epidemic: if R₀ is greater than 1 then the epidemic has started, otherwise there is no epidemic. Thus, R₀ can be used as a natural litmus test for early detection. Secondly, in terms of R₀  one can determine such important characteristics of the epidemic as: (1) the initial rate of increase of the epidemic during its exponential growth phase; (2) the number of infected at the epidemic peak; (3) the total number of infected over the course of the outbreak; (4) the critical vaccination threshold (=1/R₀.) etc. All these characteristics are very important for situational awareness. Therefore, using basic reproductive number R₀ allows us to timely detect an outbreak and simultaneously to evaluate the parameters of the rising epidemic in order to develop measures for timely response and consequence management. See technical details in [1]. However, all these results can be used in syndromic surveillance only if we can connect two different types of data: daily numbers of people with confirmed diagnoses and daily pre-diagnostic counts. Fortunately, it is possible at least in some very important cases (influenza epidemics and pandemics among them). It can be done thru the assumption that the overall number of infected on each day can be approximated by the sum of the number of visits to the emergency department (clinic or doctor office) during the past d days where d is an average number of days of infectivity. This is a reasonable approximation if parameter d is adequately estimated or chosen. In [1] (see also references therein) it has been supposed that for influenza, the mean duration of infectivity d is equal to 7 days. Indeed, most epidemiologists agree that influenza infectivity begins the day before illness onset and can persist for up to 7 days, although some persons may shed virus for longer periods, particularly young children and severely immuno-compromised patients. This assumption is clinically realistic and plays a fundamental role in our approach. It transforms visit counts, which are basic observable variables in syndromic surveillance, into the main epidemiological SIR variable – the number of infected. It is precisely the point where integration of syndromic surveillance with epidemiological predictive modeling is taking place. In this fusion, syndromic surveillance is an information provider (in terms of daily visit counts) and real-time epidemiology contributes to analysis and decision-making. As an additional bonus, 7-day summation allows to compensate for the day-of-week (DOW) effect in number of visits variability. Note that the DOW effect is a primary systematic feature of the data in all recent biosurveillance systems, which drastically influences their performance. The simple 7-day summation procedure is very effective in removing weekly patterns.

Thus, the above mentioned integration of syndromic surveillance and epidemiology can be effectively done in the important case of influenza.

But why influenza is so important?

References

[1] Shtatland, E. and Shtatland, T. (2011). Statistical approach to biosurveillance in crisis: what is next. NESUG Proceedings. [full text]

Biosurveillance in Crisis

Motivated by the threat of bioterrorism, biosurveillance / syndromic surveillance systems are now in crisis: with the original purpose of early detection, and more than 10 years in existence, no health department has reported using them for this purpose. There seems to be almost a consensus in the biosurveillance community that syndromic surveillance systems, based on statistical algorithms, are likely of little value in early detection of bioterrorist outbreaks; but irrespective of whether biosurveillance systems could be useful for detecting bioterrorism or not, their most important contribution to public health practice is detecting and responding to natural disease outbreaks, such as seasonal and especially pandemic flu (see Fricker (2011a and 2011b)).This has led to a shift away from only early detection of bioterrorist attacks. The goal has been expanded in two directions: firstly, to switch the emphasis from bioterrorism only to detecting and responding to natural disease outbreaks; and secondly, to include both early event detection and situational awareness, so that the focus is not simply on detection, but also on timely response and consequence management including vaccination and hospitalization strategies. Even with this expansion, early detection capacity is problematic. There are several reasons for that. One of them is uncontrolled alert rates: there is an alarm nearly every day and most health monitors learned to ignore alarms. It results in distrust in statistical methods and in biosurveillance itself. That is why Fricker, the most outspoken critic of the current state of biosurveillance, concludes in his recent review article [1] in such a pessimistic way: “Returning to the original question of whether statistical methods are useful for early event detection, I suggest that we really don’t know yet. That is, whether the systems and their associated detection algorithms can be modified so that they appropriately minimize false positive signals while maintaining sufficient sensitivity to actual outbreaks is still an open question”. Thus, not only early detection of potentially unpredictable bioterrorist attacks is considered “mission impossible”, but also early detection in general, including natural disease outbreaks. In [2], the rejoinder to the discussion of article [1], Fricker wrote: “And, in spite of my research interest in EED (early event detection) methods, I would suggest that situational awareness is probably the more important function for biosurveillance, since it enhances public health surveillance and management before, during, and after an outbreak“.

In our paper [3] it is shown that the situation is not as bleak and that it is possible, at least in some cases, for example in the case of influenza pandemic, to develop an approach which allows to achieve simultaneously both goals: early detection and early situational awareness, which is a unique ability in biosurveillance. No existing biosurveillance systems are capable of doing this. Such unification of early detection and situational awareness can be possible only through fusion of syndromic surveillance with epidemiological predictive modeling. See more on integration in my next post.

References

[1] Fricker, R. D. (2011a). Some methodological issues in biosurveillance. Statistics in Medicine, [full text]

[2] Fricker, R. D. (2011b). Rejoinder: Some methodological issues in biosurveillance. Statistics in Medicine, [full text]  

[3] Shtatland, E. and Shtatland, T. (2011). Statistical approach to biosurveillance in crisis: what is next. NESUG Proceedings, [full text]