Vinculatoriedad jurídica del Acuerdo de Paz

The outcome of interest for this study was an estimate of the duration of vaccine acquired immunity, expressed in days. Duration of immunity was defined as the date on which a bird was first identified as seronegative to the H5 HI test minus the date of the last H5N1 vaccination event. A key assumption here was that H5 HI seropositivity occurred follow- ing a vaccination event. Birds were sampled at each of the sampling rounds which equated to sampling intervals of approximately one month during the two high risk periods and two and half months during the single low risk period. The two high risk periods (rounds 1 to 5 between December 2008 and March 2009 and rounds 10 to 14 between Decem- ber 2009 and March 2010) and one low risk period (rounds 6 to 9 between April 2009 and November 2009) were defined on the basis of a frequency analysis of previous HPAI H5N1 outbreaks in Viet Nam (Pfeiffer et al. 2007, Minh, Morris, Schauer, Stevenson, Benschop, Nam & Jackson 2009).

Survival analyses were used to quantify the timing of seronegative events relative to the date of the last H5N1 vaccination. Because assessment of immune response occurred intermittently throughout the study period (i.e. at each sampling date) the exact date on which a seropositive bird became seronegative was not known. For this reason sur-

vival analyses were carried out using an interval censoring approach (Kleinbaum & Klein 2012).

Initially, 20 poultry were selected from each study flock and then assigned to a vaccinated (n= 10) and an unvaccinated, sentinel group (n= 10) group, as described above. As the aim of this study was to estimate the duration of immunity developed from vaccination, only data from vaccinated birds (n = 2,233 birds, equivalent to 5,387 serum samples tested) were used for the interval censored survival analyses (Figure 5.2).

A survival analysis respecting the presence of interval censoring requires a data set that has the dates on which individual birds entered the study, the dates on which birds were last identified as H5 HI positive, and the dates of each of sampling round on which birds were identified as H5 HI negative. It should be noted that many birds had several vacci- nation events throughout the study period which meant that the total number of observed bird-vaccination intervals (n = 3,797) was greater than the total number of vaccinated birds (n= 2,233, Figure 5.2).

Details of 17 factors (explanatory variables) thought to influence the duration of immu- nity were collected throughout the study period. These explanatory variables were broadly grouped into those related to geographical location (e.g. the village in which a flock was located), time of vaccination (the two high and one low risk periods) and bird (production type, flock size, age at the time of vaccination). Other, time varying covariates, included whether or not birds were moved out of their home district, the origin of birds introduced into a flock, changes in flock size, the presence of sick birds in the household between sampling rounds, the presence of sick birds in the home village between sampling rounds, the presence of multiple animal species in the household, the presence of pigs in the household, whether or not the household was visited by poultry traders between two con- secutive sampling rounds, whether or not the household flock was visited by other poultry flocks (shared rice fields) between two consecutive sampling rounds, whether the flock owner purchased feed for poultry between consecutive sampling rounds, and the presence or absence of cleaning activities between two consecutive sampling rounds. Continuously distributed variables, for example age at the time of vaccination (expressed in days) and flock size were re-coded as categorical variables. The turnover of birds in the population, stratified by production type, was described using a Lexis diagram (Keiding 1990). The effect of each candidate explanatory variable on the duration of immunity was as-

5.2 Materials and methods 65 sessed using the Kaplan-Meier technique (Kaplan & Meier 1958). The homogeneity of time to event was tested using the log-rank statistic. Explanatory variables associated with time to event at P <0.20 were selected for inclusion in the multivariate analyses. The logarithm of the negative log of survival probability was plotted as a function of the logarithm of follow-up time, and was approximately linear. On this basis we assumed that the time taken for seropositive birds to become seronegative was consistent with the Weibull distribution.

The effect of the identified putative explanatory variables on time to event was quantified using an acceleration failure time (AFT) model (Kalbfleisch & Prentice 1980):

S(t) = exp(−λtp) = exp −(λ1p_t)p (5.1) where λ1p =exp −(β0+β1x1ij +...+βmxmij+Fi +Bj) (5.2) In Equation 5.1S(t)represents the probability that a bird remains seropositive up to time t. In Equation 5.2 the termsλandprepresent (respectively) the scale and shape parameter for the Weibull distribution. The term β0 is the intercept term and β1,...m represent the

regression coefficients for each of the m explanatory variables included in the model. The termsBj andFi represent (respectively) frailty terms for each of thej birds within

each of theiflocks.

With this formulation the median duration of immunity (expressed in days) as a function of the parameterised explanatory variables is given by:

t= [−lnS(t)]p1 ×

λ1p

−1

(5.3) Equation 5.3 The results of an AFT model can be expressed in terms of a time ratio, representing the increase (or decrease) in time to event as a function of the parameterised explanatory variables, compared with a specified reference category.

A backward-stepwise procedure was used to build the Weibull AFT model, which started with inclusion of all putative explanatory variables that were associated with time to event with a P-value of less than 0.20. Putative explanatory variables that were not statistically

significant were removed from the model one at a time, beginning with the least signifi- cant. Only those explanatory variables that had estimated regression coefficients that were significant at P<0.05 or those that were biologically plausible were retained in the final model. A frailty term was included to account for multiple vaccination intervals per bird and clustering at the individual flock level. All biologically plausible interactions between each of the explanatory variables remaining in the final model were assessed.

The final model is reported in terms of an adjusted time ratio for each explanatory vari- able. An adjusted time ratio (and its 95% confidence interval) of greater than one indicates that, after accounting for other explanatory variables in the model, exposure increased the length of time taken for a bird to become seronegative following vaccination. An adjusted time ratio (and its 95% confidence interval) of less than one indicates that exposure de- creased time taken to become seronegative. Statistical analyses and model development were conducted using the survival package (Therneau & Lumley 2012) in R, version 2.15.2 (R Development Core Team 2012).