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Time since enrollment or time on study is one of the most frequently used time scales, though there has been considerable debate about whether this choice has always been the most appropriate [ 4 — 6 ]. The use of calendar time as the basic time scale for longitudinal observational data the so-called real-time approach treats the population of interest as a dynamic population rather than a closed cohort [ 7 , 8 ]. An application is, for instance, the impact of environmental exposure on pregnancy outcomes [ 6 ].
For ICU-acquired infections caused by transmissible pathogens such as MRSA and Vancomycin-resistant Enterococci, calendar time is often a natural choice when studying the effect of interventions on the ICU-level [ 9 ]. This is because hazards of acquiring the infection are likely to vary over calendar time as a result of fluctuations in the prevalence of the pathogen on the ward [ 3 ]. These fluctuations are typically unobserved as they result from asymptomatic carriage, making direct adjustment for the ICU-level prevalence impossible.
In addition to patient-individual characteristics, the risk of acquiring a MRSA infection in an ICU might also depend on spatio-temporal factors, i. The choice of calendar time as the basic time scale also controls for time-varying factors acting on the ICU-level such as changes in medical management, hygiene practices, patterns of antibiotic usage, staffing levels, and seasonal factors [ 3 , 9 — 11 ].
This ICU exposure time is one the most important determinants for ICU-acquired infections and is frequently used for studying patient individual risk-factors such as age, morbidity, patient-individual antibiotic treatment or invasive devices [ 12 ].
Ignoring these competing events can easily lead to heavily biased risk estimates [ 15 ] and wrong conclusions about the impact of risk factors [ 16 ]. Due to the presence of competing events, there are two metrics the rate and the risk metric in a risk factor analysis [ 17 , 18 ].
Thus, for a complete analysis, it is necessary to perform event-specific hazard rate analyses for MRSA infection, discharge and death as well as a summary analysis for the cumulative risk of MRSA infection [ 19 ]. The major aim of this paper is to find an appropriate model to study the incidence of MRSA infections by accounting for multiple time scales, competing risks and the hierarchical nature of the data.
To do this, we explore, compare and combine the aforementioned time scales in a real ICU data setting. We calculate hazard rates with respect to the corresponding time scale and perform analyses based on the stratified Cox proportional hazards model to study patient-individual risk factors in a competing-risk framework.
We included ICUs which contributed to the registry between January and December and we included only patients who stayed at least two days in an ICU due to the definition of hospital-acquired infections.
We excluded ICUs which contributed fewer than patient admissions to the cohort to ensure a sufficient amount of patient time at risk for each ICU.
The study population contains 81 intensive care units with 84, admissions , admission-days.
Statistical methods In the Additional file 1 is a Lexis diagram [ 21 ] of individual patient data from one selected ICU over days in calendar time.
It demonstrates how the data depend on the two time scales. In the following, we compare the two time scales in several steps. For the ICU time scale, the time origin is the time of admission. For the calendar time scale, patient admissions entered the model with staggered or delayed entry with left-truncation occurring at the time of admission.
The overall hazard rates depend both on ICU or calendar time.
The variation of the overall hazards due to different ICUs was accounted by using a shared frailty model [ 22 ]. More formally, let c represent the calendar time and c0 the truncation time, i.
The assumption of proportional hazards was checked via the inspection of the Schoenfeld residuals [ 24 ]; note that proportionality due to the rate metric does not lead to proportionality due to the risk metric but even if proportionality is not fulfilled the hazard ratio has the meaningful interpretation of an time-averaged effect [ 25 ]. We then model both times together by including the second time scale as a covariate.
We stratified for ICU in order to allow the hazard to be different across ICUs, and hence we did not use the frailty terms. In simple words, the formula above is the product of the time-dependent probability of staying alive at-risk on ICU and the conditional probability of acquiring a MRSA infection. Thus, the risk sets for the subdistribution hazard are unnatural discharged and died patients remain technically at-risk. However, unlike the event-specific hazard, the subdistribution hazard is directly linked to the corresponding cumulative incidence function of MRSA infection.
The resulting subdistribution hazard ratios of an exposure can be interpreted as effects which can be seen when plotting cumulative incidence functions, grouped by exposure categories.
If necessary, other more detailed functions which, for instance, includes also the calendar month of admission can be chosen. If necessary, other categorizations can be chosen. Model 3b: model 3a plus year of admission as covariate. Results Overall hazards The overall hazard rates are displayed in Fig. The bottom row is clearly showing what is happening with respect to event risk over a long time period perhaps reflecting more what is going on at the ICU level whereas the top row is showing what is happening at the patient level in the short term since admission to an ICU.
After 15 days, the MRSA hazard slightly decreases. This hazard has to be interpreted jointly with the corresponding hazards of the competing events since the cumulative risk of MRSA infection depends also on the discharge and death hazards. The hazards of death or discharge without MRSA are also increasing within the first week after admission see Fig. After days, the hazard of death without MRSA is about 0. Calculated values are given in table 2.
Half of the rats in each group were killed on 14 , the significance of differences among mean values was calculated [Duncan's mul d 20 and half on d Soft tissues liver, kid ney, spleen and duodenum and femurs tiple-range test 20, 21 ] on a within-study were removed; the duodena were flushed basis only.
Portions of all diets and tissues were Composition of diets. Results of analysis weighed and were wet digested in mixtures of of diets for nine elements are shown in nitric-perchloric or nitric-perchloric-sulfuric table 4. The results of the analysis of diets acids and analyzed by inductively coupled AB and AF agreed with those for diets A argon plasma-atomic emission spectrometry and ABF, and these data are not shown.
The methods and procedures have studies for diets A and ABF, except that been described in detail The levels Statistical methods. Means and standard of phosphorus, iron, zinc and copper in diet errors were calculated for levels of nine AIN reflect contributions from casein as elements in rat tissues and diets. Because well as from the mineral mix.
Mineral com significant differences in concentrations of position can be precisely controlled to be major and trace elements in liver, kidney, highly reproducible in these purified diets.
Responses to diets. Rats fed diet NIH r grew significantly better than all groups fed purified diets in study 1 fig. Lower weight gains were obtained with the O LU younger animals used in study 2. Differences in food consumption were consistent with 2 observed differences in growth rates. Downloaded from jn. Femur percent ash was also significantly higher in this group.
Tissue minerals. Concentrations of major and trace elements in tissues of Long-Evans Fig. Rats rats for studies 1 and 2 are shown in tables were 26 d old on d 0 and were fed the diets for 3 wk. Concentrations of potassium, phos phorus and magnesium in liver tissue were similar for the basal groups in both studies.
Rats fed diet NIH had appears that rats fed the purified diets significantly higher levels of iron and lower would not have reached the same maximum levels of manganese in liver, kidneys, duode size attainable by rats fed diet NIH Sig num and femur than did rats fed the other nificant differences in tissue mineral levels diets in study 1 table 9.
When rats were were observed among groups in study 1. Differences in sodium were ob and the other purified diets. For example, served in liver, spleen and femur; differences rats fed diet NIH had higher levels of iron in potassium were observed in spleen and and lower levels of manganese in four of the femur. Levels of sodium were significantly five tissues examined.
In the tion for the rat, and this may have contrib femur, decreases in potassium vs. In addition, competi diet ABF table Fewer of these changes tive interactions in intestinal transport of between diets A and ABF occurred in study manganese, calcium, phosphorus and zinc 1 tables 7 and 9. Levels of major and trace 26, 27 , as well as iron, have been de minerals in kidney and duodena were not scribed.
In duodenal tissue, the major sig significantly affected by the variations in nificant effects were higher iron and lower diet composition used in study 2 tables 8 manganese in rats fed diet NIH compared and Rats fed the non- tissue manganese levels. This was especially port and excretion can be expected to be true in tissues of rats fed diet NIH When highly sensitive to diet composition.
Fibrous components may lulose also have been involved. Such factors as Development of a nutritionally adequate competition between elements for binding purified diet for weanling rats. AIN rodent diet, but lacks cellulose and and biotin are added, however, growth is biotin. Although there appears to be no ab equivalent to that supported by diet AIN Similarly, biotin is thought diets. Although growth is significantly im not to be required by rats under standard proved, efficiency of food utilization is not laboratory conditions due to its synthesis by affected by this level of cellulose.
Effects of the intestinal flora The induction of a fiber on the intestine are complex and vary biotin deficiency generally requires the with the physical and chemical properties feeding of diets containing raw egg white.
When both cellulose flora of rats. Weights of tissues are given in table 6. Utilization of volatile fatty acids Synthesis of biotin by the intestinal flora is produced by fermentation of cellulose may thought to be adequate to provide for the contribute small but significant net energy needs of young rats. However, Bitsch et al. Other mech those fed egg white-containing diets or anisms by which cellulose might improve biotin-free diets, reported that enterai micro- growth include alterations in synthesis or bial synthesis is not adequate to cover the release of trophic hormones and effects on biotin requirement of rats.
In our studies, morphology of the intestinal mucosa that addition of biotin improved growth of wean may alter intrinsic absorptive activities. Weights of tissues are given in table 7.
Evelyn Bonnin in these studies. Rader, J. L, Gaston, C. O'Dell, B. NY Acad. Fox, M. Health Perspect. Long-Evans rats.
L, Celesk, E. W, Wolnik, K. Tissue Int. National Research Council Nutrient Re and toxic elements. Cereal Chem. Bremner, I. Nielsen, F. Factors Influencing Metabolism and Toxicity of Duncan, D.