1198 Kaplan−Meier Logistic Regression
Derek Hazard et al
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Fig. 2. Dots represent the weights of individual controls at the time they were sampled. For example, a patient with weight 10 represents 10 patients in the analysis. The aim of this weighting is to reconstruct the full cohort from the selected subcohort.
were sampled multiple times resulting in a subcohort of 760 distinct individuals for the weighted analysis. Among 760 infection cases, 432 (56.8%) were automatically included. Of all 760 cases, 2 cases (0.3%) were censored and 326 death or discharge cases (42.9%) were sampled with respect to infection. From the subcohort, 137 cases (18.0%) were in the first APACHE quartile, 189 (24.9%) were in the second, 184 (24.2%) were in the third, and 250 (32.9%) were in the fourth. Furthermore, 209 (27.5%) were treated with an antibiotic within 48 hours of admission, while 551 (72.5%) were not. Figure 2 shows the weights assigned to the selected controls.
Patients with longer stays in the ICU have a higher chance of being selected as a control (and consequently lower inverse probability weights) than patients with shorter stays. Thus, the weights are higher for sampling times early after admission and lower for later sampling times (when only patients with longer stays can be selected).
Infection cause-specific hazard analysis
Table 1 shows the results from the full cohort estimation (the “gold standard”) as well as the IPW and traditional estimation from a reduced cohort for the infection endpoint. From the full cohort, we can conclude that an increasing APACHE score is associated with an increasing hazard for acquire an infection. The same inter- pretation would result from the IPW and traditional methods, even though the reduced cohort estimates did not reach statistical sig- nificance (P <.05) for the second APACHE quartile. All 4 estimates indicate that antibiotic treatment within 48 hours is associated with a lower infection hazard. We observed little difference in accuracy and precision among the traditional, KM, and GLM estimates.
Death or discharge cause-specific hazard analysis
Table 1 shows the results for the full cohort and IPW estimation with reused controls for the combined death-or-discharge end- point. Importantly, traditional estimation (conditional logistic regression) is not possible for this competing event with the given
data. Here, IPW methods conform to the full cohort interpreta- tion that higher APACHE scores have a statistically significant decreasing effect on death or discharge. The estimates for anti- biotic treatment within 48 hours are also in agreement: full, 0.64 (95% CI, 0.60–0.69); KM, 0.64 (95% CI, 0.44–0.95); and GLM, 0.65 (95% CI, 0.53–0.81). The logistic regression weights have a slight advantage over the KM weights in precision.
Infection risk analysis
Using a log binomial model to predict risk, the IPWestimates are in good agreement with the full cohort estimates. Once again, tradi- tional estimation is not possible for this analysis with the given data. Interestingly, we observed a far more pronounced influence of the fourth-quartile APACHE score on the risk ratio (6.92, full cohort) for acquiring a NI than on the corresponding hazard ratio (2.14, full cohort). This finding is explained by the strong decreasing effect a high APACHE score has on the death-or-discharge hazard; these patients stay longer in the ICU and thus have a higher risk of acquiring an NI. This phenomenon also explains the seemingly paradoxical result that ATB48H has a statistically significant decreasing influence on the NI hazard ratio (0.75) but no influence on the NI risk ratio. Again, ATB4H is associated with an increased length of stay in the ICU (decreased death-or-discharge hazard) and thus a greater risk of acquiring an infection.
Simulated data
In addition to the successful implementation of the methodology with prospectively collected real data from 2 Spanish ICUs, the methodology was also applied to simulated competing risks data with similarly impressive results (see Table 2). Both IPW methods match the accuracy and precision of the traditional method for the first simulated event while displaying good agreement with the full simulated cohort estimates for the second event and risk analysis. Software code in R for the real and simulated data analysis is provided in the supplemental material section.
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Inverse Probability Weight
Inverse Probability Weight
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