Raw surveillance data on a novel influenza strain, especially from established systems with background data on nonpandemic influenza, can broadly illustrate the trajectory of symptomatic infections in time and space. To inform many decisions, however, surveillance data must be processed to estimate particular quantities—for example, transmissibility and severity measures or the cumulative proportion of the population infected to date—and to define the pandemic's possible course through formal prediction or plausible planning scenarios.

3.1.

Estimating Severity and Disease Burden

Severity estimation and disease burden estimation are different approaches to answering interrelated questions: How many cases? How many deaths (burden)? What is the ratio of deaths to cases (severity)?

As described in

section 1, case-fatality or other case-severity ratios are probably the most important quantitative inputs for early decision making. However, estimating both the numerator and denominator of these ratios is challenging. For discussion purposes here, we focus on symptomatic case-fatality ratios, where the numerator is fatalities and the denominator is symptomatic cases.

Symptomatic case number estimates can come from surveys (with some correction for the proportion of symptomatic cases truly due to pandemic virus infection

^{67,81,82}) or from data at other levels of the “severity and reporting pyramid,”

^{38} such as confirmed cases

^{38} or hospitalizations

^{81} combined with an estimate of the proportion of symptomatic cases hospitalized.

^{81} If one made assumptions about the proportion of asymptomatic cases, these estimates could be converted into estimates per infection (see sidebar:

Large-Scale Serosurveillance).

Case ascertainment will always be less than 100% and will vary over space and time in the pandemic. If unaccounted for, ascertainment can bias severity estimates. In the earliest phases of a pandemic, symptomatic case numbers can be biased by the preferential detection of the most severe cases, leading to substantial overestimates of severity, since these cases are more likely than typical cases to be fatal.

For example, as of May 5, 2009, Mexico had reported almost 1,100 confirmed H1N1 cases and 42 deaths from H1N1,^{10} a crude case-fatality proportion of about 4%. In hindsight, this high apparent severity was largely, or entirely, attributable to the underascertainment of mild cases, of which there were probably several orders of magnitude more than the number confirmed.^{5,6} As public health efforts scaled up and an increasing number of milder cases were detected, this bias declined,^{34} but it did not disappear, showing how even with the most intense efforts, only a minority of symptomatic cases may be virologically confirmed.^{38}

The numerator—fatalities—can be directly estimated in jurisdictions with routine viral testing of fatal cases. Experience in 2009 showed that some fatal cases are diagnosed only on autopsy,^{36,76} posing a risk for underestimating the numerator. A second source of variability is differences between jurisdictions in the definition of influenza deaths, which may include all fatalities in individuals in whom the virus was detected or only those in whom the virus was judged to have caused the death. Another potential source of error in estimating the number of deaths is the delay from symptom onset to death from pandemic influenza, which can be a week or longer.^{11,82,83} For this reason, deaths counted at time *t* may not correspond to all the cases up to time *t* but to the cases that had occurred up to a week or more before *t*. In the exponentially growing phase of the pandemic, there may be many recently infected individuals who will die but have not yet died; they are counted in the denominator but not the numerator. If unaccounted for, this “censoring bias” can lead to an underestimate of severity as much as about 3-fold to 6-fold during the growing phase of a flu pandemic.^{11} Two basic approaches can address this bias: One is to correct for it based on the growth rate in disease incidence and the lag time between case reporting and death reporting.^{11} Another is to perform analyses after transmission has subsided in a population, by which time most deaths will have been registered in the data set.^{44}

Notwithstanding these sources of bias, it is particularly challenging to precisely estimate the case-fatality proportion when the true proportion is low. In any population with a statistically robust number of deaths (eg, more than 10 cases) and a symptomatic case-fatality proportion of 1 in 10,000 (0.01%), it would require 100,000 documented symptomatic cases (or a correspondingly large number of confirmed cases) to directly estimate the ratio—an impractical approach.^{1} The 2009 pandemic highlighted the need for other approaches.

One alternative is to conduct surveys within defined outbreak populations to estimate the number who are ill and relate this number to the directly measured number of severe outcomes. For example, in an early H1N1 outbreak at the University of Delaware, 10% of student respondents and 5% of faculty and staff on a campus of 29,000 reported ILI that resulted in 4 hospitalizations but no deaths.^{55} While this could not yield a precise estimate of the symptomatic case-fatality or case-hospitalization proportions, it provided useful upper bounds. A telephone survey yielded similar estimates in New York City.^{67}

Another approach to estimating case-fatality proportion is to decompose the severity “pyramid,” instead relying on some types of surveillance to estimate the ratio of deaths to hospitalizations and on other types to estimate the ratio of hospitalizations to symptomatic cases.^{44} Bayesian evidence synthesis methods^{84} are a natural framework for combining the uncertainty in the inputs to such estimates into a single estimate of uncertainty in severity measures.^{44}

Overall, the presence of countervailing biases (the underascertainment of both numerator and denominator) made initial severity assessment challenging in the 2009 pandemic. Although both biases were recognized, it was difficult at the time to identify the more severe bias. In retrospect, censoring bias was minor compared to the underascertainment of mild cases, making early estimates of severity higher than current estimates based on more complete data. There was also important uncertainty about whether estimates differed between populations (eg, U.S. versus Mexico) because the severity was truly different or because ascertainment patterns differed. These conclusions are outbreak-specific; in SARS, for example, ascertainment was relatively complete, but censoring bias—perhaps more acute than in 2009 because of the longer delay from symptom onset to death—led to substantial underestimates of severity until the bias was corrected for.^{85}

All of these considerations, described in the context of attempting to estimate overall risk of mortality, are relevant as well to more complex measures of severity, such as years of life lost.^{29}

Because influenza is seasonal, experiences in one hemisphere can—and did—inform planners and decision makers in the other. In 2009, the southern hemisphere was the first to have a full, uninterrupted winter season with the novel H1N1 virus. Rapid reviews of the experience in the southern hemisphere's winter season^{86,87} provided evidence for northern hemisphere planners that the capacity of intensive care units would likely be adequate overall, though local shortages might occur.

3.2.

Interpreting Clinical Data

Data on the characteristics of severe clinical cases are directly relevant to decisions about prioritizing prevention (eg, vaccination) and using scarce resources to treat those most likely to benefit. Choosing priority groups for such preventive measures as vaccination should depend in part on the *per capita* relative risk of having various groups suffer severe outcomes without vaccination.^{30} For a particular group—pregnant women, for example—this risk can be estimated by dividing the proportion of pregnant women among individuals with severe outcomes by the proportion of pregnant women in the general population.

This same measure of comparative severity applies to prioritizing other measures that are distributed to uninfected people. In 2009, it was proposed that certain groups might benefit from predispensed (or easier access to) antiviral drugs to aid in early treatment. The potential benefits of such a policy depend mainly on the per capita risk of severe outcomes in the priority groups compared to the general population.^{88}

To prioritize treatment of symptomatic individuals, the relevant measure of comparative risk is severity *per case*, not per capita, since the decision involves a person with presumed or known infection, not a randomly chosen group member. The distinction between these 2 measures is that per capita severity is equal to per case severity times the risk of becoming a case. For example, in most countries, people over age 50 showed considerably higher severity per case, but only modestly higher per capita severity, because they were less likely than younger people to be infected.

The goal for all the purposes outlined above is to identify predictors of severe outcome rather than understand why the predictors are associated with the severe outcome.^{88} In the 2009 pandemic, morbid obesity was identified in some case series as a predictor of hospitalization and death,^{89} prompting much discussion about whether morbid obesity itself caused the outcomes or whether it was a marker of other conditions that did so. This question of etiology is unimportant when allocating resources; if high-risk individuals can be identified, they can receive priority for prevention or treatment and the benefit will be the same, regardless of whether the identifying factor is causal or only a marker.

3.3.

Estimating Transmissibility

A standard summary measure of transmission intensity is its reproductive number—the mean number of secondary cases caused per primary case. When this exceeds 1, incidence grows; below 1, incidence declines. Absent mitigation measures, an estimate of the reproductive number of a strain at baseline can inform how intensely transmission must be reduced to slow or stop the growth in the number of cases.^{90} To halt growth, the critical proportion of transmission events that must be blocked is given by 1 minus the reciprocal of the reproduction number. Estimates of changes in the reproduction number over time^{91,92} can indicate the impact of control measures^{37} or of intrinsic changes in transmissibility due to depletion of susceptible individuals, seasonality, or other changes.^{93}

A common approach to estimate transmissibility of a newly emerging infection relies on estimates of 2 quantities: the exponential growth rate of the number of cases and the distribution of the serial interval or generation time—that is, the time from infection to transmission.^{94} The minimal data required to derive the reproductive number from these 2 estimates are a time series of the number of new cases (ideally, a daily time series) and an estimate of the serial interval distribution,^{92} which can come from early outbreak investigations.^{5,95} The assumption is that the distribution of intervals between symptom onsets approximates that of the intervals between times of infections.^{96} Remarkably, with certain assumptions, one can infer both the serial interval distribution and the reproductive number using only the time series of new cases.^{34,97}

Key challenges in estimating reproduction numbers from epidemic curve time series include changes over time in the fraction of cases ascertained—which can affect apparent growth rates and therefore bias reproductive number estimates—and reporting delays, whereby, even in a growing epidemic, recent case incidence will appear to drop off due to recent, unreported cases.^{7} There is growing methodological and applied literature on addressing these challenges^{34,37,94,96,98} and obtaining corrected estimates or bounds for the reproductive number. Analyzing viral sequence data, discussed below, can provide a partially independent estimate of transmissibility and validate conclusions made from purely case-based estimates.

3.4.

Real-Time Predictive Modeling

Transmission-dynamic models can be used to predict the possible future course of an epidemic (eg, the number of infections per day in various groups) given certain assumptions. These assumptions, or model inputs, include such quantities as the reproductive number of the infection, the relative susceptibility and infectiousness of different groups in the population, the natural history of infectiousness, and the nature and timing of possible interventions. Transmission-dynamic models have been widely used as planning tools to assess the likely effectiveness of interventions for pandemic influenza^{19,25,99–101} and many other infections.^{102,103} In these cases, the models are applied to hypothetical epidemics, and the input assumptions are taken from past epidemics of similar viruses. In this section, we consider a distinct though related application of transmission-dynamic models: predicting the dynamics of a pandemic as it unfolds by using real-time data on the incidence and prevalence of infection to date in various population subgroups.

Since reliable predictions of a pandemic's time course are tremendously helpful for response planning and decision making (

sections 1.5–

1.6), it would be valuable if transmission-dynamic models were employed in real time to make and update predictions of the course of transmission. This would require 3 ingredients: (a) a sufficiently accurate mathematical model of the key processes that influence transmission; (b) data on the current and past incidence of infection with the pandemic strain, population immunity, and other parameters needed to set initial model conditions; and (c) an assumption that the biological properties of the influenza virus would not change within the time scale of prediction.

Transmission-dynamic models are now computationally capable of including virtually unlimited amounts of detail in the transmission process,^{104} but knowledge of some of their inputs is limited. For example, while much is known about the factors that affect influenza transmission, areas of uncertainty remain, including the exact contributions of household, school, and community transmission;^{104} the contribution of school terms, climatic factors, and other drivers to transmission seasonality;^{93,105–107} and the role of long- and short-term immune responses to infection with other strains in susceptibility to pandemic infection.^{108} Our understanding of behavioral responses to pandemics is also at an early stage.^{109}

During a pandemic, incidence data are imperfect and subject to substantial uncertainty in the “multiplier” between observed measures of incidence and true infection (see sidebars:

Syndromic Surveillance and

Large-Scale Serosurveillance). Since infection and resulting immunity drive the growth, peaking, and decline of epidemics, this conversion factor is crucial to setting model parameters. Finally, changes in the antigenicity, virulence, or drug resistance of a circulating strain could invalidate otherwise reliable model predictions.

Efforts at real-time modeling in the 2009 pandemic showed that uncertainty in the number of individuals infected in various age groups at any given time hampered efforts to forecast the pandemic using transmission-dynamic models. Despite this limitation, the 2009 experience illustrated the potential of predictive models to provide policy guidance by generating plausible scenarios and, as important, by showing that certain scenarios are less plausible and thus of lower priority for planning.

In one published case study, Ong and colleagues set up an ad hoc monitoring network among general practitioners in Singapore for influenzalike illness and used the reported numbers of daily visits for ILI to estimate, in real time, the parameters of a simple, homogeneously mixed transmission-dynamic model, which they then used to predict the course of the outbreak.^{62} Early predictions of this model were extremely uncertain and included the possibility of an epidemic much larger than that which occurred. This uncertainty reflected the limitation of the input data (here, physician consultations). Without a known multiplier, it was impossible to scale the number of infections anticipated by the model to the number of consultations. By late July, the growth in the incidence of new cases had slowed, providing the needed information to scale the observed data to the dynamics of infection, allowing for more accurate and more precise predictions.^{62}

Data on healthcare-seeking behavior were used in a similar effort in the United Kingdom, but with a more detailed, age-stratified transmission-dynamic model. Here, too, the timing and magnitude of the peak were difficult to predict because of uncertainty in the conversion factor between observed consultations and true infections—although in this case the authors, by their own description, had made a guess that was roughly accurate^{63} when tested against serologic data.^{65}

A third effort was made in late 2009 to assess the likelihood of a winter wave in U.S. regions. Based on estimates of the rate of decline of influenza cases detected by CDC surveillance in November to December, combined with estimates of the possible boost in transmissibility that might occur due to declining absolute humidity,^{107} it was anticipated that any winter wave would be modest and likely geographically limited. Further analysis after the fact showed that the southeastern U.S. was the region most likely to experience further transmission due to a seasonal boost in transmissibility, a finding consistent with observations.^{93}

These experiences indicate that real-time predictive modeling is possible but will also include considerable uncertainty if undertaken responsibly. For transmission-dynamic modeling, the most important source of uncertainty lies in the multiplier between cases observed in surveillance systems and infections. Modelers must therefore seek out the best data to estimate parameters for models by paying careful attention to publicly available data and by building relationships with those who conduct surveillance prior to pandemics, so that information transfer is facilitated in the midst of an event. As noted by the authors of the studies described above, and in reviews by several consortia of transmission modelers,^{7,61} the factor that could most improve the reliability of real-time models is having nearly real-time estimates of cumulative incidence—whether through serosurveillance or other means.

The real-time, predictive modeling described above is one of the developing frontiers within the broader scope of transmission-dynamic modeling. These approaches differ from scenario-based modeling, which may be performed before or during a pandemic to provide robust estimates of the possible effects of interventions under particular assumptions rather than predict the short-term dynamics of the infection. Scenario-based modeling^{18,19,23,25,90,104,110} has significantly improved our understanding of epidemic dynamics and the likely responses to interventions, but it is most helpful when predictions are robust to variations in assumptions that may be difficult to pin down during an epidemic.

3.5.

Interpreting Virologic Data

Simple virologic confirmation of pandemic H1N1 infection was an integral part of case-based surveillance, especially early on and for severe cases. The proportion of viral samples that are positive, alone or in combination with ILI data, provides a measure of incidence (with the caveats described in previous sections). A more novel approach is to use viral sequence data to time the origin, rate of growth, and other characteristics of a pandemic,^{5} applying methods that rely on the coalescent theory developed in recent decades in population genetics, in which the quantitative history of a population can be inferred from the pattern of branching in a phylogenetic tree.^{111}

Work is still under way to assess the quality of inferences made from methods for viral sequence data, although very early transmissibility estimates were broadly consistent with those from case-count data.^{5} However, one early finding is that the strength of inferences can be improved by consistently associating epidemiologic data (in particular, data on the geographic and temporal origin of a strain) with sequence data. Unfortunately, while easy to gather, these “metadata” often do not appear together with sequences in online databases.

3.6.

Detecting Changes in the Virus

On the minds of many analysts and decision makers in 2009 was the 1918 experience, in which a wave of clinically mild infection with a pandemic virus occurred in the spring, followed by a wave of much more virulent influenza in the fall.^{112–114} The appearance of a more virulent virus strain is one of several hypotheses for how such a change occurred. Speculation aside, such an event reinforces the public health importance of detecting changes in drug resistance or antigenicity during a pandemic. Ongoing sampling of viral isolates from diverse sources, along with surveillance to detect unusual clusters of severe illness, are valuable in maintaining awareness of any variation in a virus that could be biologically and epidemiologically significant.

The 2009 pandemic showed it is possible to detect mutations that, on biological grounds, may affect virulence and transmissibility, but it also illustrated the challenge of interpreting such genetic changes. The E627K mutation in the PB2 gene, detected in several isolates of pH1N1, was expected to dramatically increase virulence; however, animal studies showed the mutation had little effect in the genetic background of the 2009 strain, and it has not appeared to spread widely in the viral population.^{115} In contrast, the hemagglutinin D222G substitution, which alters receptor binding,^{116} was associated in several populations with more severe disease.^{117–119} The exact mechanistic consequences of this mutation remain uncertain, and it has not replaced the wild-type sequence in the viral population. It would be valuable to develop more specific strategies for obtaining and characterizing novel or unusual variants of pandemic viruses that may be associated with important phenotypic changes and to implement and test these principles during interpandemic periods. Targeted approaches, including systematic sampling from a defined mix of mild, severe, treated, and untreated infections, could be one component of such a strategy.^{1}