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Table 5 Cox proportional hazard model for time of maximum proportion resistant of the peaked behavior mode

From: Expanding behavior pattern sensitivity analysis with model selection and survival analysis

Standardized Input Parameter Time Strata Coefficient Exponentiated Coefficient Standard Error
p r 1 −2.133 0.118 0.33
2 −1.274 0.280 0.30
3 −1.199 0.302 0.166
p i 1 2.156 8.639 0.311
2 1.748 5.745 0.305
3 0.691 1.996 0.136
start r 1 1.945 6.996 0.321
2 1.249 3.485 0.291
3 1.299 3.666 0.164
start i   −0.856 0.425 0.110
λ in 1 0.810 2.248 0.245
2* 0.164 1.179 0.250
3 1.038 2.822 0.143
λ out   0.581 1.787 0.099
log10(βsr)   0.206 1.228 0.098
MICs 1 −8.913 0.0001 1.474
2 −3.631 0.026 0.763
3 −0.824 0.439 0.159
δ   −0.343 0.710 0.131
V LI   −0.481 0.618 0.113
η LI   −0.384 0.681 0.096
  1. The example mathematical model was for the proportion of tetracycline-resistant enteric Escherichia coli in a beef steer during and after administration of oral chlortetracycline. The Cox model presented here uses right-censored data. In 80% of peaked behavior simulations the maximum proportion resistant occurred at the last time step of chlortetracycline administration and these simulations were considered to not have a maximum event occur in the Cox model (right-censored). Coefficients, exponentiated coefficients, and standard errors are listed for the standardized parameters that were included in the most parsimonious model. Time stratification, which allows the effect of a parameter to vary as a step-function between time strata, was used to meet the assumption of proportional hazards for pr, pi, startr, λin, and MICs. The maximum times were divided into three time strata: (1) Day 10 to Day 16.6, (2) Day 16.7 to Day 23.3, and (3) Day 23.4 to Day 30. Coefficients for these five parameters were constant within a time stratum and different between time strata. Parameters that do not have time strata listed met the proportional hazard assumption without stratification and have just one coefficient, constant across time. For this model, Cox and Snell’s R2 was 0.248 (maximum possible 0.584). *P > 0.05