West Nile virus (WNV) outbreaks raise the concern of WNV infection in donated blood and blood products destined for transfusion. We describe methods we developed to estimate time-dependent risk of WNV infection in donated blood, including improvements not previously detailed. The methods are then extended for use in estimation of the risk of WNV infection in donated cadaveric tissues by introducing stratification and stratum-specific weighting to address novel aspects of this application. Data from the WNV outbreak in Colorado in 2003 are used to estimate risk for donated cardiac tissue.

Relatively soon after the documentation in 1999 of West Nile virus (WNV) circulation in North America, it was recognized that during a WNV outbreak the probability or “risk” of WNV infection in blood donors may reach sufficiently high levels to pose a threat to the blood supply. In two papers,

Technical details of the initial statistical methods described here were used in the original paper for the Queens outbreak were presented in its appendix, with less formal description provided in the body of the text. Subsequent applications to other geographic areas, time scales, and viruses (

We begin by providing background on the estimation goal and the information needed to reach it in Background & information required. Methodological and computational development then recapitulates and expands the appendix in the original paper for the Queens outbreak (

In Development using a Poisson process model for the underlying case onset times we detail how our resampling implementation can be viewed as assuming an inhomogeneous Poisson process model for the underlying WNND case onset times and estimating the associated cumulative rate function using nonparametric Gaussian kernel smoothing, which we indicated but did not detail in the Discussion of

The recognition that the probability or risk of WNV transmission from donated blood may be unacceptably high during an active, regional outbreak of WNV was the motivation for the original applications discussed here. Because WNV activity is necessarily seasonal in North America, being a mosquito-borne virus, estimation methods were developed to reflect this time-dependence. In the United States, WNND cases are reported through established public health surveillance to the CDC with accompanying information, including the date that the patient first exhibited symptoms. Because WNND is a severe illness, surveillance systems capturing its occurrence in the US are thought to be essentially complete, and so epidemic curves developed using these data can be used to characterize the population-level transmission dynamics in the general population. These WNND case onset data, therefore, form the basis for the estimation methods used here. For the example from the WNV oubreak in Colorado, 2003, the WNND case onset data can be summarized in a epidemic curve, shown in

When focusing specifically on estimation for WNV infection in blood and tissue donations, we restrict estimates of the number infections in the population in two ways. Because transmission of WNV occurs only when a donation contains or is

We develop the methods considering specifically applications to estimation of WNV transmission risk via blood or tissue donation. The details, however, are written to be able to be applied more generally. The intent in the development, therefore, is that whenever densities or distributions or associated parameters are required to be specified, the user would specify such in the application under consideration. Whenever possible in application, we make distributional assumptions and specifications based on published data. For example, below we specify a Weibull distribution for the duration of WNV viremia based on data reported in

For each

The case onset dates

Viewing the smoothed case onset times

We interpret a particular realization of this random function

As we saw, the inapparent-to-apparent infection ratio,

Because we are interested in estimating the probability of a

Our computation of an estimate of

Computation of the integrals in last expression may proceed directly, either analytically or numerically, if we assume particular distributions for the

In the original application for WNV transfusion risk via blood transfusion (

Because we use reported estimates

With the distributional assumptions and approximations given, we compute the estimate of

Resample with replacement

Compute the smoothing parameter

Generate

Generate

In

Generate

We use a Weibull density with mean

Generate a value

We use a Weibull density with mean

Replicate each the resampled case infection time,

Generate a value

We use a beta distribution with mean

Generate

With these values in-hand for each simulation

This curve is an average of

We compute confidence bands based on the simultaneous bootstrap-

for

Finally, the sought-after, time-dependent risk of a WNV-infected donation is computed directly as the estimated number of such infections,

As part of the simulation estimation, we also estimate the mean risk over the course of the outbreak by computing the average height of the risk curve. We do this by computing, for each simulation

In certain applications, as with the motivating example here of estimation of WNV infection in cadaveric tissues, stratification by variables for which key parameters vary should improve estimation. In the present example, the inapparent-to-apparent infection ratio is known to vary by age, with symptomatic infection (and severity of illness) more likely with increasing age. A straightforward refinement of the methods in Methodological and computational development to incorporate this is to use stratification as follows. Assume that the population is stratified into

Combining the strata for a population-level estimate of the risk may proceed naturally by weighting the stratum-specific estimates by relative population size,

In the Monte Carlo evaluation of the integrals in the expression for

We noted without detail in the Discussion section of

Begin by assuming that the WNND case onset dates

Direct estimation of

Operationally, then, using bootstrap resampling and then smoothing the resampled values using Gaussian noise and then using this in the Monte Carlo integrations in

The methods presented were implemented in mostly purpose-written software using the statistical package R (

We implement the updated methods with the application introduced above, estimation of the risk of WNV infected cardiac tissue during the Colorado WNV outbreak in 2003, which remains at the high end of state-level WNV outbreak experience (

As detailed in

The gamma density was assumed for the incubation period, with mean

Finally, the average risk of WNV-infected cardiac tissue donations over the duration of this outbreak was 6.3 (95% CI 3.1, 9.6) per 10,000 deaths, with a maximum risk of 12.3 (95% CI 6.8, 20.5) per 10,000 deaths on August 10.

While the original methods described here were developed for WNV, the underlying ideas were general. Subsequent applications to severe acute respiratory syndrome (SARS) virus (

Application of these methods yields estimates of risks of infected donations before any post-donation testing or processing. In the US, for example, blood donations are now routinely tested seasonally for WNV, using policies implemented shortly after risk estimates were published and WNV transfusion transmission was documented (

One assumption we made was that individuals share common distributions for both the incubation period and the viral infection duration. This is likely not strictly the case in either the donor or the general population, as there may be biological factors that mediate these for different individuals or groups of individuals. For WNV there is not currently evidence that systematic differences by known factors for these quantities would be on a scale to impact the general conclusions drawn from the methods used here, which take account of known uncertainties directly in the estimation. Should such become available, the estimation framework presented allows direct incorporation of such information in an easily implemented way. We also assumed that durations of onset and of infection were the same for individuals who remain asymptomatic or who develop symptoms, as there are not available separate estimates for these durations between these two groups; should such estimates become available, they can be incorporated into the methods presented here easily using the stratification mechanism introduced. Further, if any of the parameters differ by identifiable strata (say, by sex or by age), then one may naturally incorporate any available estimates or information into the framework we introduce here for weighted, stratified analyses, as well. In the absence of such detailed information, however, we may view these assumptions as reflecting a population average distribution across any such relevant factors.

In our approach we relied on Gausian kernel smoothing to underlie the estimation of time-dependent risk curves. Naturally, other methods of smoothing, such as spline smoothing, semi- or fully parametric regression, or wavelet basis smoothing methods may have been used. We adopted the approach we present due to the the direct and ready interpretability of the conversion of the initial, discrete observations to continuous “observations” (

The analysis estimating risk of WNV infection in donated cardiac tissue during the Colorado outbreak of 2003 was part of a more complete analysis reported in

We have detailed and updated our approach for time-dependent risk estimation for arbovirus infection of blood donations, and to address unique aspects of risk estimation for cadaveric tissue donations, we expanded the methods to include stratification and weighting. We expect that these refinements will provide greater flexibility and increased precision for researchers employing this general approach for a general variety of pathogens.

The author thanks the American Association of Tissue Banks for the suggestion to pursue this work, particularly Mr. Frank Wilton, former AATB President and CEO, and also the Scientific and Technical Affairs Committee of the American Association of Tissue Banks for technical guidance, particularly the former committee chair, Dr. Jeffrey Cartmell. Further, the author thanks Dr. Lyle R. Petersen, Division Director, Division of Vector-Borne Diseases, CDC, for his collaboration on these projects and for encouragement in writing this methods paper. Thanks also to the ArboNET team at CDC for curating the data used in this study and to the SciComp team at CDC for access to their computational resources. Finally, thank you to Dr. Mark Delorey of DVBD/CDC for his careful review of the manuscript.The findings and conclusions herein are those of the authors and do not necessarily represent the official position of the US Centers for Disease Control and Prevention.

None declared.

Number of WNND cases aged 13–55 years by date of symptom onset, Colorado, 2003.

Estimated risk of WNV-infected cardiac tissue among potential donations, Colorado, 2003, shown as the black, solid line, with 95% confidence bands shown as black, dashed lines. The gray lines are a sample of the simulated risk curves,

Age group-specific WNND counts for Colorado 2003; inapparent-to-apparent infection ratios,

Age group | WNND |
| |
---|---|---|---|

13–20 | 22 | 742.57 (96.92) | 0.58 |

21–40 | 134 | 526.90 (58.39) | 1.12 |

41–55 | 202 | 286.23 (19.52) | 3.86 |

Total | 358 | Pop = 2,911,979 |