Statistical analyses

The assumption of normality and homogeneity of variances were graphically evaluated (histogram, normal probability plot of residuals) and tested by Shapiro–Wilk and Barlett, respectively. When needed, dependent variables were transformed in order to meet the assumptions of the statistical model used. The data were presented as mean ± SEM and the results were considered significant at p < 0.05. Statistical analyses were performed using software R (R Core Team, version 4.2.0).

The birth order was categorized into three groups to analyze the IPBI according to the piglet’s expulsion, with 25 being the maximum birth order as the number of piglets from birth order 26 onwards was too low to fit the model adequately. The number of piglets born in each birth order is in Additional File 1: Table S1. For this, a birth order between 2 and 7 was considered as the first tercile (1/3) of piglets born, a birth order between 8 and 16 was considered the second tercile, and a birth order between 17 and 25 was considered the last tercile. If a sow had less than 17 piglets, it was considered only for the first and second tercile. The overall IPBI, as well as the IPBI in each of these three groups, were compared using a linear mixed model where the sow was considered as a random variable.

Univariable models were used to investigate the association between predicted and predictor variables, where each explanatory variable was included as a single fixed effect. Numerical and categorical independent variables with p ≤ 0.20 for the F-test in the simple model were selected and subjected to Pearson’s and Spearman’s correlation analysis to avoid multicollinearity between continuous variables and confounding problems between categorical variables. Based on the results from the univariable models, all factors with p ≤ 0.20 were included as independent variables in a multivariable analysis. After a stepwise elimination procedure, only independent variables with p < 0.05 were included in the final model. The elimination of independent variables in the stepwise procedure was performed according to the p-value; independent variables with higher p-values were eliminated earlier. The complete linear regression models, including inclusion and exclusion criteria and stepwise procedure are shown in Additional File 1: Table S2–S9.

Statistical models that had the dependent variable as a binary variable (piglets’ mortality before 24h post-farrowing, piglets’ mortality between 24h post-farrowing and weaning, and the occurrence of stillbirth) were analyzed by generalized linear mixed models fitted by binomial distribution.

Sow was considered as a random variable in statistical models that analyzed dependent variables at the piglet level (IPBI, piglets’ mortality until 24h post-farrowing, piglets’ mortality between 24h post-farrowing and weaning, and the occurrence of stillbirth).

Interaction between the variables included in the final model was tested and found to be non-significant for all models.

Survival analysis (Kaplan–Meier estimate) was performed using the “survival” package and “survfit” function with a confidence interval of 95%.