Abstract
Evaluation of conception rates in dairy livestock requires specific statistical methods because of the followings: (i) some cows are still alive after the follow up period and their fate is not known, which means that records of these animals should be censored, (ii) the risk factors connected with fertility are not perform linearly and may vary with time, (iii) not all lactation records are normally distributed. Therefore, this study was undertaken to assess factors influencing days open (DO) and conception rates of dairy cattle, using nonparametric and semi-parametric survival functions. Parity, season of calving, milk yield levels (MYL), age at calving (AAC), days to first estrus (DFE), days to first insemination (DFI), number of inseminations per conception (NIPC) were significantly associated with days open for a number of 1980 lactation cows, of which 12.73 % were censored. The overall median of DO was 123 days (95 % CI = 119.55-126.44). For the first five parities studied, medians of DO were 111, 121, 128, 123 and 152 days, respectively. The Kaplan-Meier survivor functions and log-rank tests denoted highly significant differences (p < 0.001) among parities, seasons of calving and levels of milk yield in terms of time to conception. Proportions of pregnant cows were estimated at every postpartum time point alongside their cumulative probabilities. The overall percentages of pregnant cows were 0.5, 34.7, 67.2, 92.07 and 99.34 % at days 50, 100, 150, 200 and 250 postpartum. Cox PH models reveled significant contribution of all studied factors as hazards for conception. The hazard ratios (varied from 0.632 to 1.393) were used to quantify the exact differences between all categories. The present study has provided important survival functions that were used to identify and quantify the economic risk factors associated with days open length and conception rates of dairy cattle in Egypt.

Key words: Survival analysis, Kaplan-Meier plots, log-rank test, Cox proportional hazard models, dairy cattle, days open.