of investigative scrutiny in such studies becomes more fine-grained, center-level ... Patient outcomes depend on more than doing the right things for our patients ...
Journal of Perinatology (2006) 26, 243–245 r 2006 Nature Publishing Group All rights reserved. 0743-8346/06 $30 www.nature.com/jp
COMMENTARY
Studying determinants of length of hospital stay J Schulman1,2 1
Department of Pediatrics, Albany Medical College, Albany, New York and 2Clinical Informatics and Outcomes Research, Children’s Hospital at Albany Medical Center, Albany, New York
Clinicians are accustomed to focusing on individual patients. However, when studying how long their patients stay in the hospital, the focus must widen. Length of stay summarizes the performance of the entire, exceedingly complex, NICU system. Ordinary statistical methods for modeling patient outcomes assume that what happens to one patient is unrelated to what happens to another. However, patients in the same NICU are exposed to similar hospital practices, so patient outcomes may be correlated. Length of stay data must be analyzed by methods that account for possibly correlated outcomes. In addition, to improve patient care and outcomes, predictive models must include determinants clinicians can influence. Such variables describe care process exposures, available beds, demand for beds, and staffing levels. Journal of Perinatology (2006) 26, 243–245. doi:10.1038/sj.jp.7211478
Recently in this journal, Cotten et al.,1 for the NICHD Neonatal Research Network, described their study of predictors of prolonged hospital stay (PHS) for extremely premature infants. PHS is a variable derived from length of hospital stay (LOS) in the NICU. LOS summarizes the combined effects of an immense array of patient characteristics and exposures, including diverse processes of care. To reflect critically on LOS studies, the reader must appreciate why these bundled effects must be disentangled and be aware of special analytical methods appropriate for such complicated inquiry. The effort is repaid with practical insight to determinants of neonatal morbidity and resource use. The present article examines several essential considerations that may be unfamiliar to clinicians, but that are central to understanding and improving NICU LOS.
Independent vs correlated outcomes The NICHD investigators predicted the probability for an infant with various characteristics to experience a PHS – defined as an infant born at 42 weeks postmenstrual age (PHS) or of an infant dying was independent of any other such event. Experienced clinicians know that such events in the same hospital may indeed be correlated, or clustered. Within a particular hospital, those hospital practices that predispose one infant to develop a condition such as chronic lung disease or >two episodes of late-onset sepsis (each, a variable found to contribute to PHS1) may also predispose another infant to develop that condition.
Methods for analyzing correlated data To determine whether individual outcomes are independent or correlated (clustered), one compares the variance of the data – a measure of the variability among values – within a cluster
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(hospital) with the variance of the data between clusters. If the observations appear correlated, then it is appropriate to explore the determinants of the outcome using multilevel techniques, also known as hierarchical techniques.2 Ordinary logistic modeling assumes that the effects of adjustment factors (covariates; examples from Cotten et al.1 include gestational age, SGA, NEC requiring surgery, and >2 episodes late onset sepsis) are the same between and within clusters (hospitals) – but sometimes covariate effects differ between and within clusters. For example, the effect on PHS of NEC requiring surgery might be different in different hospitals; perhaps surgical management is different. Multilevel modeling enables simultaneous examination of individual- and group-level factors and their interactions. Multilevel modeling answers the question: when individual cluster (hospital)-specific PHS logistic models differ among each other, how does one accurately represent this situation via a single logistic model? The point is: before combining observations from multiple sites, check that it is appropriate to pool data. When observations are indeed clustered, multi-level methods tend to shrink the standard errors, improving the precision of the effect estimates. Interestingly, many confidence intervals in the NICHD PHS model were rather wide (indicating relatively imprecise effect estimates) despite a large number of observations: 6410 infants from 12 centers.1 Clustered data may be a signal Covariates that vary at each level of aggregation (patient-level and hospital-level) may signal omitted patient-level explanatory variables. In PHS article, the authors indicate that ‘other unmeasured factors could have contributed to the variability.’1 Examples of such variables might include maternal ureoplasma infection, duration of exposure to FIO2 ¼ 1.0 during newborn stabilization, or severe neonatal neutropenia. Drawing inference from multiple levels of data aggregation Another caveat: when working with data representing multiple levels of aggregation, one must beware of drawing inferences about individuals from data about a higher-level aggregate. For example, it is unwarranted to associate an individual woman’s high fat intake with an increased risk of dying of breast cancer solely on the basis of higher breast cancer death rates in countries where the proportion of dietary intake as fat is elevated. The NICHD analysis of PHS included ‘center y factors,’1 but the investigators did not report finding significant center-level PHS predictors. As the degree of investigative scrutiny in such studies becomes more fine-grained, center-level factors doubtless will emerge; so readers should be mindful of this caveat when they draw inference from such Journal of Perinatology
findings. Interpretations that do not include these considerations may result in the ecological fallacy: effect estimates derived from a higher-, ecologic-level (in the present context, hospital-level), are thought to apply equally at the individual-level when in fact, heterogeneous exposures and covariate values among study subjects result in quite different effects at the individual level.3 Choice of variables The choice of variables to include in a predictive model must reflect a meticulously crafted conceptual framework that accurately reflects the roles of the known important factors.4 And if the model is to improve patient care and outcomes, it must include predictor variables subject to clinical influence: variables describing clinical care processes. That is, the model must enable actionable answers to flow from posing the question, ‘What would we do differently if we knew this thing?’ When an outcome variable is derived from another directly measured variable, as PHS is from LOS, the derived variable should make sense clinically. If a cut-point is involved, it should be informative and grounded in a clinically meaningful distinction. For an outcome as PHS, critical readers would want to be assured that inference does not change substantially if the cutpoint were shifted a few days up or down from 42 weeks PMA. When observations are not correlated, considering LOS as a time variable in a time to event (survival) analysis might yield even more helpful models. So-called ‘hazard’ models could inform clinicians and parents of the expected LOS in light of patient characteristics, exposures, and care processes up to a particular date.5 One reason such methods provide greater insight to determinants of length of stay over a logistic model is because survival analysis uses more information about the outcome. The PHS outcome variable in the logistic regression model of Cotten et al.1 collapses all the information contained in the actual time to discharge – LOS, into one of two categories, PHS or not. In contrast, time to event (survival) analysis works with the actual value of LOS and can provide a more nuanced understanding of predictor–outcome relationships. Partnering with engineering: queueing theory Another set of possible determinants of LOS may be explored using queueing methods, techniques for understanding patterns of highway traffic, airline arrivals and departures, and supermarket checkout.6,7 At first thought, patient flow through an intensive care unit may seem to have nothing in common with such phenomena. But in each, a ‘customer,’ waits to be served by a ‘server.’ When the server cannot process each customer upon arrival, then a queue forms – a group of customers that have indicated they want service but have not yet received it. The time it takes to serve a customer is called the service time. LOS thus equals service time.
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Queueing methods can produce cumulative arrival and departure diagrams that describe at a glance the flow of patients through an ICU: desirable NICU management tools, but not commonly available. Queueing theory formulates system performance as a function of demand (patient arrival rate), numbers of servers (bed and staff numbers), and service time (LOS).8 Patient arrivals appear to be well modeled by the Poisson process.8,9 Readers’ experience of patient arrivals to a NICU, as well as of NICU census, likely resonates with the characteristics of this probability distribution: s.d. equal to the mean and therefore, a process that tends to have a wide range in outcome values. NICU managers may mistakenly interpret this wide range to indicate unpredictability. However, queueing methods make patient throughput predictable, and therefore more manageable.9,10 Service times may be modeled as an exponential function,8,9 although often an empirical distribution may be best.6 These insights suggest a role for specialized techniques such as parametric survival analysis models of LOS. The main point is that queueing theory suggests including in predictive models for LOS, variables not often considered in publications to date, such as NICU admission rates, operational capacity, and staffing patterns. Conclusion Patient outcomes depend on more than doing the right things for our patients. We must also do the right things the right way. No doubt, we must change current processes of care. To do so for the better, we must understand the fine structure of our care processes and how specific upstream care process steps connect to the way things turn out for our patients.4,11 Those connections may occur at multiple levels, may interact, and may include aspects of NICU operation heretofore considered mainly by administrators. Although, for many clinicians, understanding those connections entails new ways of thinking, as Albert Einstein observed, ‘We
cannot solve our problems with the same thinking we used when we created them.’
References 1 Cotten CM, Oh W, McDonald S, Carlo W, Fanaroff AA, Duara S et al. Prolonged hospital stay for extremely premature infants: risk factors, center differemces, and the impact of mortality on selecting a best-performing center. J Perinatol 2005; 25: 650–655. 2 Normand S-LT, Glickman ME, Gatsonis CA. Statistical methods for profiling providers of medical care: issues and applications. J Am Statist Assoc 1997; 92: 803–814. 3 Rothman KJ, Greenland S. Modern Epidemiology. 2nd edn. Lippincott Williams & Wilkins: Philadelphia, 1998. 4 Schulman J. Managing Your Patients’ Data in the Neonatal and Pediatric ICU: an Introduction to Databases and Statistical Analysis. Blackwell: Oxford, UK, 2006. 5 Schulman J. Prediction of length of hospital stay in neonatal units for very low birth weight infants (letter). J Perinatol 1999; 19: 613. 6 Hall RW. Queueing Methods For Services and Manufacturing. Prentice Hall: Upper Saddle River, NJ, 1991. 7 Reid PP, Compton WD, Grossman JH, Fanjiang G (eds), Committee on Engineering and the Health Care System, National Academy of Engineering, Institute of Medicine. Building a Better Delivery System: A New Engineering/Health Care Partnership. The National Academies Press: Washington, DC, 2005. 8 Ozcan YA. Quantitative Methods in Health Care Management. Jossey-Bass: San Francisco, 2005. 9 McManus ML, Long MC, Cooper A, Litvak E. Queuing theory accurately models the need for critical care resources. Anesthesiology 2004; 100: 1271–1276. 10 Nguyen JM, Six P, Antonioli D, Glemain P, Potel G, Lombrail P et al. A simple method to optimize hospital beds capacity. Int J Med Inform 2005; 74: 39–49. 11 Schulman J. Evaluating the Processes of Neonatal Intensive Care. BMJ Books: London, 2004.
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