Surveillance: Quantifying both the absolute incidence or prevalence
of disease and trends in incidence or prevalence over time is critical to the
design and evaluation of control. In
this section we discuss the role of dynamic models in the estimation of disease
burden (e.g. estimating reporting rates, modern state-space methods) and
disease trends (i.e. the relative change in burden over time or space).
Here I refer to disease surveillance as the repeated measurement of a disease system in terms of its states, where the states are the specific quantifiable biological properties that
change through time, such as the population size, the number of susceptible,
infected, and recovered individuals in different classes, or its behavior, where the behavior can be summarized in terms of some aggregate phenomena, such as cycles .
The incidence or prevalence of disease (I will
use the “incidence” as a catchall term for the burden of disease and infection
in a population respectively) in a population is a straightforward,
interpretable, and operational quantity. These quantities can be estimated using classic survey design (e.g.
Morris 2011), however the utility of such estimates is limited
to the scope of the survey. Routine
Cauchemez 2013 or
syndromic surveillance
Mandl 2003 provides an alternative for assessing trends in disease
incidence from measures collected through an existing health system. Translating these measured quantities into
absolute disease incidence presents challenges because these measures are often
imperfect. For example, many cases of
illness occur within the community
Harpaz 2004, but
are not recorded in the health system, thus leading to under-reporting. Case
records for diseases like polio and Zika virus, for which rates of symptomatic
disease are low relative to infection, may reasonably inform disease rates but
will be necessarily insensitive to small changes in the burden of
infection. In the absence of diagnostic
tests, many infections are monitored through clinical symptoms which have low
specificity
Gary 1997Hutchins 2004. Thus many measures could
lead to over-reporting of infection (e.g. ILI, fever and rash, diarrheal
disease). The bias (in either direction)
due to imperfect reporting can be estimated using classic survey methodology or
a combination of clinical diagnosis and lab-confirmation
Page 2014. However, these methods are again limited the
scope and scale of these specific efforts. The problem of imperfect measurement
and observation is common to many dynamical systems and the tools to address
this have been increasingly adopted in epidemiology.
Though reported incidence of disease may reflect temporal trends,
they rarely reflect total burden due to under-reporting. Thus, while a true, unobservable dynamic
process of transmission exists, we are only able to view it through the
imperfect lens of the public health. State-space models are a general class of statistical models that
are designed for such partially observable dynamic processes
Bretó 2009
Chen 2011. The basic structure of a state-space model
consists of a process model that describes the evolution of the states of the
system (where states are measureable biological quantities, such as the numbers
of susceptibles and infecteds) from one time point to the next (formally, these
must adhere to the Markov property that the state in time t+1 depends only on
the parameters and the states at time t), and an observation model that governs
the likelihood of observing a reported level of disease incidence conditional
on the states (i.e. the true incidence).
In the absence of a dynamic link between the states of the system at
time t and time t+1, the absolute value of the states and the reporting process
would be confounded. However, the
temporal autocorrelation in sequential observations induced by the dynamic
process allows these methods to generate simultaneous estimates of both the
state values and the parameters of the observation process (e.g. the rate of
under-reporting). There are many existing strategies to fitting these models – Kalman filter, generalized particle filter, hierarchical MCMC; he specifics of these methods are beyond the scope of this chapter– but further information
can be found at:
Bretó 2009 Chen 2011
Ionides 2006
Clark 2004. The key advance of these methods for application in infectious
disease epidemiology is the ability to provide retrospective estimates of the
states (e.g. suscpetibles and infecteds) of the system. These quantities are critical for
retrospective estimates of true, unobserved disease burden (e.g.
Simons 2012) as well as providing predictions, and associated uncertainty bounds, of current
values which form the initial conditions for forward projections.
Though this has been of fairly limited application in operational
settings (e.g.
Simons 2012), it has become common in research settings
Ionides He 2009 Martinez-Bakker 2015 Cauchemez 2008. The key operational benefit of this approach
is that it provides formal statements of the uncertainty of past
estimates. It is worth noting that an
idiosyncrasy of this approach is that the entire time series is re-fit as new
observations are made – thus, as new surveillance is accrued, the estimates of
the past improve. While intuitively
appealing, this phenomenon can be challenging to explain as past estimates may
be revised upwards or downwards based on subsequent analyses.