Longevity is a crucial economic trait in the dairy farming industry. In this study, our objective was to develop a random regression model for genetic evaluation of survival. For the analysis, we used test-day records obtained for the first 5 lactations of 380,252 cows from 1,296 herds in Japan between 2001 and 2010; this data set was randomly divided into 7 subsets. The cumulative pseudo-survival rate (PSR) was determined according to whether a cow was alive (1) or absent (0) in her herd on the test day within each lactation group. Each lactation number was treated as an independent trait in a random regression multiple-trait model (MTM) or as a repeated measure in a random regression single-trait repeatability model (STRM). A proportional hazard model (PHM) was also developed as a piecewise-hazards model. The average (± standard deviation) heritability estimates of the PSR at 365 d in milk (DIM) among the 7 data sets in the first (LG1), second (LG2), and third to fifth lactations (LG3) of the MTM were 0.042. ±. 0.007, 0.070. ±. 0.012, and 0.084. ±. 0.007, respectively. The heritability estimate of the STRM was 0.038. ±. 0.004. The genetic correlations of PSR between distinct DIM within or between lactation groups were high when the interval between DIM was short. These results indicated that whereas the genetic factors contributing to the PSR between closely associated DIM would be similar even for different lactation numbers, the genetic factors contributing to PSR would differ between distinct lactation periods. The average (± standard deviation) effective heritability estimate based on the relative risk of the PHM among the 7 data sets was 0.068. ±. 0.009. The estimated breeding values (EBV) in LG1, LG2, LG3, the STRM, and the PHM were unbiased estimates of the genetic trend. The absolute values of the Spearman's rank correlation coefficients between the EBV of the relative risk of the PHM and the EBV of PSR at 365 DIM for LG1, LG2, LG3, and the STRM were 0.75, 0.87, 0.91, and 0.93, respectively. These results indicated that the EBV of PSR could predict the genetic contribution to survival. The EBV based on the PSR of the STRM was highly correlated with that of the MTM (0.83-0.96). Furthermore, the calculation load of the STRM was lighter than that of the MTM because the rank of the matrix of the STRM was smaller than that of the MTM. These results indicated that the STRM is an appropriate model for estimating survivability by using random regression models.
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