Appendix 2 for Busch et al. manuscript in March 2006 EID

Average Period of Time that West Nile virus RNA is Detectable

The average period of time during which RNA is detectable, T_MP-NAT, can be estimated using minipool-NAT yield data and an estimate of the seasonal West Nile virus incidence. In a region where IgM yield data was collected (North Dakota) the peak West Nile virus seroprevalence, max_IgM, is an estimate of the seasonal West Nile virus incidence, , provided the epidemic is short (about 2 months) and provided data is collected beyond the end of the epidemic (about 3 weeks);

For a week, j, the weekly proportion of donations with West Nile virus RNA (weekly minipool-NAT yield) is the number of West Nile virus minipool-NAT positives in the week divided by the number of donations screened in the week;

An  incidence rate is the number of incidents divided by person-time. The weekly average incidence rate can be estimated from the weekly West Nile virus minipool-NAT data and from a person-time estimate (34,35). On average, each donation can be considered at risk for being minipool-NAT positive during the average period of time in which RNA is detectable by minipool-NAT (T_MP-NAT). The person-time can be estimated as the number of donations in the week multiplied by T_MP-NAT.  Hence, the weekly average incidence rate can be estimated as:

The estimated weekly average incidence rate, , is a rough approximation to the actual average weekly incidence rate but is considered adequate for this study (e.g., although some minipool-NAT positives may be incident in the previous week, this is counter-balanced by incident positives occurring late in the week that would not be identified by minipool-NAT in a given week). The weekly West Nile virus incidence (i.e., proportion of blood donors who were infected during the week) is estimated from the weekly average incidence rate. That is, the weekly West Nile virus incidence is equal to the weekly average incidence rate times the number of days in the week;

The seasonal West Nile virus incidence (i.e., proportion of blood donors who were infected during the 2003 season) can then be estimated by summing the estimated weekly West Nile virus incidences over the epidemic period (36);

Equating the two expressions for seasonal West Nile virus incidence yields an estimate for the average period of time in which RNA is detectable by minipool-NAT, T_MP-NAT;