1200
Table 2. Results from Analysis of Simulated Data Event 1 Etiologya
SE Method
Full cohortg Traditionalh IPW KM IPW GLM
HR (95% CI)c
2.00 (1.70–2.35) 1.94 (1.56–2.40) 1.98 (1.60–2.45) 1.99 (1.60–2.47)
(Log HR)d 0.08
HR (95% CI)c 0.51 (0.48–0.53)
0.51 (0.39–0.67) 0.53 (0.47–0.61)
Derek Hazard et al
Event 2 Etiologyb SE
(Log HR)d 0.02
0.11 …… 0.11 0.11
0.14 0.07
RR (95% CI)e
3.50 (3.00–4.09) …
3.74 (2.70–5.20) 2.94 (2.37–3.64)
Event 1 Prediction SE
(Log RR)c 0.07 …
0.17 0.11
regression weights. aTrue event 1 HR, 2.00. bTrue event 2 HR, 0.50. cCause-specific hazard ratio for exposure. dCalculated with estimated standard errors for Cox regression and conditional logistic regression, calculated with robust standard errors for IPW and log binomial model. eUsing log binomial model. fDistinct individuals. gCox regression. hConditional logistic regression.
Cohort Sizef
10,000 1,606 1,606 1,606
Note. HR, hazard ratio; CI, confidence interval; SE, standard error; RR, risk ratio; IPW, Cox partial likelihood with inverse probability weighting; KM, Kaplan Meier weights; GLM, logistic
exposure–outcome in simulated data for a subsequent event set- ting. They found that adjusting for matching in the weight esti- mation had little influence on the estimates, whereas adjusting in the Cox regression was essential. Thus, we recommend including possible confounding variables in the weighted Cox model. A further extension proposed by Wolkewitz et al14 is con-
the time-matched risk sets is not recommended. Borgan15 found that reusing controls when close matching is required (eg, in the presence of batch effects for biological samples) can lead to bias in simulation studies. Salim et al16 found that in situations with little overlap in the distributions of the matching variables for 2 separate outcomes, reusing controls was less efficient than simply sampling new time-matched controls. Ohneberg et al17 applied NCC and case-cohort designs to the
ducting subdistribution incidence density sampling and estimat- ing the cumulative incidence function by assuming a Fine and Gray model. In this variation, the patients are available for selection until their (potential) censoring time and the inclusion probability weights are subsequently adjusted. Simulation studies and application to the Spanish ICU data showed IPW estimation to be in good agreement with the full cohort (data not shown). The method could also be extended to a “subsequent event” set- ting where a second event is a subset of a first event. For example, the controls sampled with respect to acquiring infection (first event) could be reused to analyze death from hospital infection (second event). Our study has some limitations. In some situations, breaking
Acknowledgments. We would like to thank the Spanish ICUs for their invaluable contribution to collecting the data.
Financial support. D.H. has received support from the Innovative Medicines Initiative Joint Undertaking (grant no. 115737-2, Combatting Bacterial Resis- tance in Europe—Molecules Against Gram-Negative Infections [COMBACTE- MAGNET]). This work was supported by the German Research Foundation (grant no. WO 1746/1-2 to M.W.). The funders had no role in data collection and analysis, decision to publish, or preparation of the manuscript.
Conflicts of interest. All authors report no conflicts of interest relevant to this article.
References
1. Wolkewitz M, Cooper BS, Bonten MJM, Barnett AG, Schumacher M. Interpreting and comparing risks in the presence of competing events. BMJ. 2014;349:g5060.
2. Andersen PK, Geskus RB, de Witte T, Putter H. Competing risks in epidemiology: possibilities and pitfalls. Int J Epidemiol 2012;41:861–870.
3. Wolkewitz M. Accounting for competing events in multivariate analyses of hospital-acquired infection risk factors. Infect Control Hosp Epidemiol 2016;37:1122–1124.
4. Weber S, Cube M von, Sommer H, Wolkewitz M. Necessity of a competing risk approach in risk factor analysis of central line–associated bloodstream infection. Infect Control Hosp Epidemiol 2016;37: 1255–1257.
same Spanish ICU data set and found that the NCC design had slight advantages in power and precision in assessing the effect of a dichotomous APACHE score on acquiring infection. A further comparison of a case-cohort design and an NCC design reusing controls in a setting with multiple outcomes is of certain interest. Our results indicate that an NCC design does not have the pur- ported disadvantage in such a setting and that a full competing- risks analysis can be performed without collecting new data. This methodology provides a clear improvement over established NCC methods.
Supplementary material. To view supplementary material for this article, please visit
https://doi.org/10.1017/ice.2018.186
5. Aiken AM, Mturi N, Njuguna P, et al. Risk and causes of paediatric hospital-acquired bacteraemia in Kilifi District Hospital, Kenya: a prospective cohort study. Lancet 2011;378:2021–2027.
6. Schumacher M, Allignol A, Beyersmann J, Binder N, Wolkewitz M. Hospital-acquired infections—appropriate statistical treatment is urgently needed! Int J Epidemiol 2013;42:1502–1508.
7. WolkewitzM, von Cube M, Schumacher M. Multistate modeling to analyze nosocomial infection data: an introduction and demonstration. Infect Control Hosp Epidemiol 2017;38:953–959.
8. Obadia T, Opatowski L, Temime L, et al. Interindividual contacts and carriage of methicillin-resistant staphylococcus aureus: a nested case- control study. Infect Control Hosp Epidemiol 2015;36:922–929.
9. O’Fallon E, Kandell R, Schreiber R, D’Agata E. Acquisition of multidrug- resistant gram- negative bacteria: incidence and risk factors within a long-term care population. Infect Control Hosp Epidemiol. 2010;31: 1148–1153.
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