Box 1: The WCE method in more detail RESULTS Participating hospitals Seven hospitals (9% of all Dutch hospitals) participated for different periods (1‐3.5 years) during the eight years of the VAP surveillance module (2004–2011). Four of the seven hospitals were top clinical (“high cure”) hospitals and three were general hospitals. University hospitals did not participate. The nation‐wide distribution of the three hospital types is 29 (top clinical), 61 (general) and 10% (academic). The WCE model uses the Cox PH framework and time‐varying covariates to generate, for each covariate, a function that describes the delayed and immediate effect of (past) exposures/levels on the outcome[22].The WCE model requires as input (1) the time‐window in which past exposures are considered to have an impact on the risk of the outcome, (2) a pre‐specified number of internal knots, which determine the flexibility of the cubic B‐spline, and (3) whether the impact of past exposures reaches zero at the earliest point of the time‐ window (i.e., constraining the effect of the covariate to the null at that point). When insufficient prior information is available to make an informed choice on these inputs, as in our case, the data may be used to determine which inputs provide the best model fit. The approach used to select the optimal WCE model for each factor involved fitting multiple WCE models using all possible time‐windows (up to 2, 3, 4, …, 28 days back); 1, 2 or 3 internal knots; and with the effect of the exposure at the most historical time point included in the time‐window either unconstrained or constrained to the null. From these 162 (27 x 3 x 2) models, the best‐fitting WCE model for each factor was selected as the WCE model with the lowest Akaike information criteria (AIC). Since we selected the best of multiple models, p‐values for WCE univariate models are likely to be artificially low. For each factor, we therefore simulated 1000 datasets in which there was no association, keeping the exposure patterns and outcome times consistent with the original dataset. For each of the 1000 simulated datasets, we ran the same set of WCE models (with alternative time‐windows, numbers of internal knots, and weight‐function constraints), and selected the best‐fitting model using the AIC, as above. The distribution of the 1000 p‐values was plotted and the proportion of the 1000 p‐values that were smaller than the p‐value of the optimal WCE model was recorded as the p‐value corrected for multiple testing[25]. 4 65 Risk factors for VAP using flexible methods
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