Detecting Human-to-Human Transmission of Avian Influenza A (H5N1)

Effective surveillance, containment response, and field evaluation are essential to contain potential pandemic strains

We model the within household spread by the household transmission probability ( 1 p ), defined as the probability that an infectious household member infects another household member in a 1 day period. The between household transmission probability ( 2 p ) is the probability that an infectious person infects a person from a household different from his or her own in a 1 day period. Finally, b is the probability that any person is infected from a zoonotic source due to 1 day of exposure. By prospective design we mean that a population of size N are free of the disease at the beginning and followed up from day 1 to some day T . We assume the whole population is exposed to a constant zoonotic infective source throughout the observation period. Let i t be the symptom onset day for an infected person i . People who do not show any symptom by day T will have indicate whether there is a close contact (1) or a casual contact (0) between persons i and j . The probability that an infective person j infects a susceptible person i on day t , is given by is the distribution of the infectious period. The probability that a susceptible person i escapes infection from all infective sources on day t is then given by Assume that the duration of the latent period δ has the distribution

The Likelihood in Case-Ascertained Design
Real epidemic data, such as the avian A(H5N1) influenza clusters discussed in this paper, generally come with the case-ascertained design instead of the prospective design, i.e., the whole cluster is ascertained upon the development of disease (i.e., symptom onset) of one or more index cases. To reduce the selection bias, the likelihood should be conditioning on the symptom status on the day when the index cases are ascertained. Let The joint conditional likelihood will be maximized to obtain the maximum likelihood estimates. By conditioning, index cases do not contribute to the joint conditional likelihood.

The Permutation Test The Hypotheses
Testing the existence of human-to-human transmission is equivalent to testing the hypotheses , 0 0 : . 0 : Η is the null hypothesis and 1 Η is the alternative hypothesis.
Not infected, Otherwise.

The Test Statistic
When there is no person-to-person transmission, i.e., 0 denote the likelihood for the null model. The test statistic is defined as the likelihood ratio statistic: Then the p-value is given by

The Null Distribution Based on Resampling
. This permutation test can be refined by varying symptom onset days of infected individuals in any given permuted data, as long as the null likelihood c L 0 is unchanged. The refined permutation test resamples data from a much larger sampling space and thus can attain higher statistical power. Technical details of these resampling methods can be found in Yang et al. (2). However, an important distinction from Yang et al. (2) is that the index cases should not be involved in the refinement stage for the case-ascertained design, because changing the symptom onset days of the index cases also changes the index or non-index status and makes it difficult to keep c L 0 constant.
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Three Important Functions of Estimated Parameters
We summarize the degree of transmissibility of the infectious agent by the household secondary attack rate (SAR 1 ), where SAR 1