Infection Control & Hospital Epidemiology
infection, urinary tract infection, or pneumonia) and 762 (11.6%) died without acquiring an infection. However, 5,359 of 6,563 patients (81.6%) were discharged alive without acquiring an infec- tion, and 10 (0.15%) were administratively censored. (Hereafter, we omit the “without acquiring an infection” description for death or discharge.) The 2 competing events we examined were the risk of acquiringaninfection(definedasafter 24 hoursintheICU) andthe composite event of dying or being discharged. The influence of the Acute Physiology and Chronic Health Evaluation (APACHE) score on these competing events was of interest. For ease of analysis, the APACHE score was categorized into quartiles. Additionally, a dichotomous covariate for treatment with antibiotics within 48 hours of admission (ATB48H) was also analyzed. Entry and event or censoring times were needed for the entire cohort to performa traditional NCC study. This ‘skeleton’ of information was required to select controls at the time of the event as well as to calculate inclusion probabilities.
Time-dynamic sampling
Incidence density sampling was employed to select a reduced sample (ie, subcohort) of the full cohort for statistical analysis. Figure 1 provides a visual representation of the sampling design. We randomly selected 1 control from the risk set each time a subject was observed to acquire an infection (ie, each time the vertical black lines cross the potential controls at each infection time). For example, patient 29 acquired an infection on day 5 and patients 30–50 were potential controls. Whether a subject is selected as a control had no bearing on their potential to be sampled again in the future; individuals may be controls at several infection times. Furthermore, a subject selected as a control may acquire an infection at a later follow-up time. For example, patient 49 was a potential control for both infection case 29 and 45 and later (on approximately day 14) acquired an infection.
Traditional analysis: NCC Design Nosocomial infection cause-specific hazard ratio
estimation.The normal practice for an NCC design is to employ a conditional logistic regression model using the time-matched case-control data.
50 40
Information for Traditional NCC Analysis: Follow−Up Time
30
Nosocomial Infection Sampled Control
20 10 0 0 5 10 15 Days Since ICU Admission
Fig. 1. Nested case-control (NCC) design using incidence density sampling for random sampling of 50 patients from Spanish ICU data. Comparison of information required for established NCC method and extended method. Covariate information collected for nosocomial infection cases and sampled controls.
20 25 30
Additional Information for Full Competing Risks Analysis: Follow−Up Time Death/Discharge
1197
The required cases, controls, and follow-up time (black horizontal lines) information for the traditional analysis is shown in Fig. 1.
Inverse probability weighting (IPW) analysis: case-cohort design
Nosocomial infection, death or discharge cause-specific hazard ratio estimation, nosocomial infection risk ratio estimation In step 1, “inverse probability weighting” calls for noncases in
the sampled subcohort to be weighted with the inverse of their inclusion probabilities. This weighting compensates for controls not selected to the subcohort and thus attempts to reconstruct the original full cohort. Cases are weighted with 1. These weights are fixed for the entirety of the patient’s follow-up time. The time- matching can now be broken and the controls are reused at event times when they are at risk (akin to a case-cohort design). Samuelsen10 reviews 2 inclusion probability estimators. The first
is a nonparametric Kaplan-Meier (KM) type estimator. The second is a standard logistic regression model-type weighting (generalized linear model, GLM11). The first step is to calculate these inclusion probabilities with the ‘skeleton’ from the underlying data. In step 2, the inclusion probabilities from step 1 are subse-
quently used in a weighted Cox partial likelihood to estimate the cause-specific hazard ratio of interest (infection and death or discharge). The remaining competing event (death or discharge, or infection, respectively) is censored. APACHE score quartiles and a variable for antibiotic treatment within 48 hours (ATB48H) are included in the regression. Variance estimation is more complicated due to dependent factors in the weighted likelihood. For this reason, we used robust variances in our analyses. For the NI risk estimates, the weights from step 1 were
included in a log-binomial model. General estimating equations were used for variance estimation.
Results Time-dynamic sampling
As a result of incidence density sampling, a subcohort of 864 individuals was selected for the traditional analysis. Several controls
Individual Patients (Random Sample)
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