Use of statistical technique on the interpretation of routine serologic data produced by poultry industry.

__Autores__: SALLE, Carlos Tadeu Pippi; CÉ, Milene Cristine; SANTOS, Carlos Henrique C.; GUAHYBA, Adriano da Silva; NASCIMENTO, Vladimir Pinheiro do; MORAES, Hamilton Luiz de Souza.
__Referência__: **48**^{th} Western Poultry Disease Conference, 1999, Vancouver - Canadá. Resumos. Kennett Square, PA: American Association of Avian Pathologists (AAAP), 1999, p.130.

**Abstract**
The search for mathematical models that could been able to explain the antibody curves produced by vaccination against infectious bursal disease virus (IBDV), Newcastle disease virus (NDV) and infectious bronchitis virus (IBV) is the main objective of this paper. The data originated from samples collected by 20 breeder flocks during the years 1993, 1994 and 1995 in a Brazilian poultry company. Sera tested for haemagglutination-inhibition (HI) activity against NDV and virus-neutralisation (VN) activity against IBDV and IBV were collected from 5 to 65-week-old birds at 5-week intervals. Geometric Mean Titres (GMT) were transformed into base 10 logarithms and a dispersion diagram plotted, where the X independent variable was the birds age (5 to 65 weeks) and the Y dependent variable was the antibodies titre against the specific vaccine. Variance and regression analyses were used, and the following results had been obtained: the best fitted equation for NDV was a quadratic one, with a coefficient of determination of 0,91, where Y=1.045+0,072X-0,001X^{2}. IBV had obtained a quadratic equation with a coefficient of determination of 0,79, where Y=1.627+0,074X-0,001X^{2}. For IBDV a quadratic equation was also obtained, where Y=1,927+0,116X-0,001X^{2}, with a coefficient of determination of 0,93. Every equation was statistically significant (P<0,01). Use of non-linear models resulted in equations with a better coefficient of determination but higher complexity, becoming useless in practice. A Logistic Model had been used in NDV data, where Y=2,728/(1+1,952*exp(-0,113X)), with a coefficient of determination of 0,92. For IBV, the best model was Exponential Association, where Y=3,137(1-exp(-0.147X) and a coefficient of determination of 0,92. The Hoerl Model, where Y=0,967*(0,987^X)*(X^0,55), had been adjusted for IBDV, with a coefficient of determination of 0,98. From these results, we can conclude it was possible to draw mathematical models that explain the relation between antibodies level after vaccination and birds age.

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