Proceedings of the 10th International Colloquium on Paratuberculosis

Subsequently, (II) under <strong>the</strong> proposed model, we assessed <strong>the</strong> association between time to
MAP infection and fecal shedding status. The risk change over time for seroconversion or
acquiring MAP infection was also estimated under I and II, respectively.
MATERIALS AND METHODS
The model
We assumed that <strong>the</strong> unobserved time to infection (tri) is Weibull distributed:
f ( tr ) = � � � � tr
i
i
��1
i �
e
��
�
i* tri
b zi
,where i e *
� = , zi <strong>the</strong> covariate vector for <strong>the</strong> i th individual, b a vector <strong>of</strong> unknown
regression coefficients and ñ <strong>the</strong> shape parameter <strong>of</strong> <strong>the</strong> Weibull distribution. The
unobserved tri was modeled as a function <strong>of</strong> <strong>the</strong> observed time to detection <strong>of</strong> infection (ti)
and <strong>the</strong> latent infection period (ui):
tr = t � u
i
i
i
With appropriate prior information on ui <strong>the</strong> model is fully specified. Extended model
description with step by step explanation <strong>of</strong> <strong>the</strong> corresponding WinBUGS code is available
upon request from <strong>the</strong> corresponding author.
Data
Data were collected from February 2000 to March 2003 from 1912 cows, in 8 Danish dairy
herds. Briefly, milk samples were obtained 11 times/year from all lactating cows and tested
by an indirect milk ELISA. Fecal samples were collected from all lactating and non-lactating
cows 4 times/year and were cultured on LJ or HEYM. Fecal culture (FC) positive cows were
divided in two shedding groups: FCHigh if positive with high bacterial counts (>10 cfu/g) or
many consecutive FC-positive tests and FCLow o<strong>the</strong>rwise. Animals not shedding or shedding
undetectable levels <strong>of</strong> MAP were classified as FCNeg. An animal contributed a censored
observation if it was still milk-ELISA negative when it exited <strong>the</strong> study for a reason not
associated with MAP infection.
Priors
For <strong>the</strong> proposed model we had to specify prior information about ui from <strong>the</strong> induction <strong>of</strong>
MAP infection to milk seroconversion. For naturally infected dairy cattle, we chose a prior
value <strong>of</strong> ui equal to 1300 days (3.5 years) with a 95% confidence interval extending from
1000 (2.7 years) to 1600 (4.4 years) days: That is a normal N~(1300, 4.4 x 10 -5 ).
RESULTS
Estimated model parameters under (I) <strong>the</strong> standard and (II) <strong>the</strong> proposed Weibull model are
given in Table 1. The shape <strong>of</strong> <strong>the</strong> Weibull hazard – as expressed by ñ – and <strong>the</strong> baseline
hazard – expressed by b0 – differed between models I and II. Median time to milk
seroconversion was 2638 [95%Credible intervals (CrIs): 2542; 2743], 1880 (1758; 2016) and
1722 (1594; 1869) for FCNeg, FCLow and FCHigh cows, respectively. The corresponding median
time to MAP infection was 1726 (1420; 2160), 356 (255; 502) and 227 (153; 339) days. The
risk <strong>of</strong> MAP infection decreases with time (ñ=0.56 (0.51; 0.61) 1 under I). This decrease and increase,
respectively, is significantly steeper for shedders (heavy or low) than cows not shedding or
shedding undetectable levels <strong>of</strong> MAP (see Figure 1).
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