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Eur J Cardiothorac Surg 2003;23:1023-1027
© 2003 Elsevier Science NL
Department of Cardiothoracic and Vascular Surgery, University of Texas Health Science Center at Houston, Medical School, Houston, TX 77030, USA
Received 12 September 2002; received in revised form 3 March 2003; accepted 6 March 2003.
* Corresponding author. Tel.: +1-713-500-5420 fax: +1-713-500-0656
e-mail: charles.c.miller{at}uth.tmc.edu
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Abstract |
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 Top Abstract 1. Introduction2. Methods3. Results4. DiscussionAppendix A. Conference...References |
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Key Words: Competing risks • Logistic regression • Multivariate model • Surgical outcome • Aortic aneurysm • Risk factors
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1. Introduction |
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TopAbstract1. Introduction2. Methods3. Results4. DiscussionAppendix A. Conference...References |
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Overall success is often cast as a competing risks problem. Traditional competing risks studies use failure-time statistics to look at long-term results, and draw a contrast between ‘actual’ and ‘actuarial’ analysis for describing the way outcomes are distributed over time [2,3]. Multivariate competing-risks analyses involving multiple predictor variables and multiple conditional failure-time distributions are a complex topic and are not the subject of this paper. Methods for modeling several outcomes simultaneously over the short term, such as the period of hospitalization, have received less attention in the literature. In this paper, we focus only on competing risks that are described by a short-term period prevalence endpoint.
One simple approach to estimating overall success might involve creation of a composite variable that is true when a good outcome occurs and false when any bad outcome occurs [4]. It would be termed a composite variable because several bad-outcome variables have to be false for ‘good outcome’ to be true. Accurate prediction of good outcome means predicting the absence of a range of undesirable events. However, these events may have entirely different risk factors, or may have common risk factors that nonetheless have dissimilar effects on outcome. This means that mathematical models attempting to predict a composite outcome with variables that are weighted differentially could suppress important predictor variables if their differential effects cancel or overpower one another. Consequently, we need a method to evaluate the possibility that a variety of risk factors imposing differential effects may form individual components or ‘layers’ of the composite outcome variable.
A composite endpoint is attractive for purposes of computing summary probability, but to evaluate global probability it is desirable to understand the multivariate effects of the risk factors on the component outcomes. We describe a simplified method for studying simultaneously the effects of predictor variables on multiple potential outcomes, following surgical repair of thoracoabdominal aortic aneurysm.
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2. Methods |
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TopAbstract1. Introduction2. Methods3. Results4. DiscussionAppendix A. Conference...References |
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2.1. Surgical methods
The adjuncts cerebrospinal fluid (CSF) drainage and distal aortic perfusion play a critical role in our surgical technique, having been found to lower the incidence of paraplegia and paraparesis [5,6]. Briefly, the highlights of our techniques are as follows. For CSF drainage and for monitoring CSF pressure a catheter is placed in the third or fourth lumbar space. Pressure is maintained at less than 10 mmHg throughout the procedure and for 72 h postoperatively. Following the thoracoabdominal incision, the diaphragm is preserved, exposing only the aortic hiatus. The patient is anticoagulated with heparin. The left atrium is cannulated via the left pulmonary vein or the left atrial appendage. A BioMedicus (Minneapolis, MN) pump with an in-line heat exchanger is attached to this cannula and the arterial inflow is established through the left common femoral artery, or the descending thoracic aorta, if the femoral artery is not accessible. For extensive aneurysms, sequential clamping is used. Reattachment of patent lower intercostal arteries (T8–T12) is performed routinely. The celiac, superior mesenteric, and renal arteries are perfused with cold perfusate (blood at 4 °C). Renal temperature is maintained at approximately 15 °C, but core body temperature is kept between 32 and 33 °C to avoid hypothermia.
2.2. Statistical methods
Data were collected prospectively on a wide variety of demographic, physiologic and operative data by a trained Master's level research nurse and entered into our specially designed Microsoft Access database. Database queries were exported to SAS version 8.02 for analysis (SAS Institute Inc., Cary, NC, USA). Preoperative renal dysfunction was defined as a serum creatinine greater than 2 mg/dl, or a recent history of renal failure or hemodialysis. Postoperative renal dysfunction was defined by a rise in serum creatinine of 1 mg/dl per day for 2 consecutive days after surgery or a requirement for hemodialysis. Pulmonary complications were defined as any event leading to mechanical ventilation of greater than 72 h postoperatively. Postoperative neurologic deficit was defined as paraplegia or paraparesis, observed as the patient awoke from anesthesia, and regardless of severity or postoperative recovery. Postoperative stroke was defined as a focal neurologic deficit due to cerebral infarction, as identified by a neurologist following patient computed tomography scan or magnetic resonance imaging. Mortality rate was based on patient deaths occurring within 30 days of surgery.
Because we cast this as a competing risks problem, a censoring hierarchy was required. Ideally, the censoring event would always be identified as the first event to occur. But because our database is not designed to capture time-to-event for postoperative complications other than death, death was the only event subject to time censoring. Non-fatal events that occurred prior to death censored death in order of severity. The order of severity for non-fatal events, from least to most severe, was renal failure, paraplegia/paraparesis, and stroke. The most severe non-fatal event censored all other events that occurred in any individual and was the censoring event for the analysis – the event that made the complication variable true. Death within 30 days was the censoring event if not preceded by a non-fatal event. The study followed the historical cohort design, with a 30-day period prevalence endpoint.
We evaluated outcome in two ways. First, we used a polytomous outcome model. Each of the four undesirable outcomes were modeled on predictor variables individually but simultaneously, to highlight differences in the multivariate effects. Second, we used an aggregate-endpoint analysis that utilized a single composite outcome variable to model the overall probability of a good patient outcome. The outcomes considered were renal failure, stroke, paraplegia/paraparesis, or death within 30 days of surgery. Patients without any of these complications were considered to have had a good short-term outcome after surgery.
Although the ultimate goal of the aggregate analysis was to determine the probability of a good outcome, we actually defined the response variable as ‘poor outcome’ so that the regression coefficients for the aggregate-variable analysis would run in the same direction as the coefficients for the polytomous categorical model. The polytomous model described the relationship between risk factors and presence (rather than absence) of specific complications. The variable ‘poor outcome’ was true if any censoring variable was true. Variables considered as predictor variable candidates are shown in Table 2. Variables that were significant in at least one dimension of the polytomous model were retained in the multiple logistic analysis as well. For the aggregate-outcome analysis, we used multiple logistic regression, with a single outcome variable defined as described above. Continuous predictor variables such as age were kept in their native distribution for multivariable analysis. Indicator variables were created for dichotomous predictor variables such as preoperative renal dysfunction, extent II thoracoabdominal aneurysm, etc. Computations were performed using the SAS LOGISTIC procedure [7].
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3. Results |
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TopAbstract1. Introduction2. Methods3. Results4. DiscussionAppendix A. Conference...References |
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In the polytomous model, where all of the complications were modeled individually but simultaneously, preoperative renal dysfunction was a significant predictor for every outcome (Table 3). Age and extent II aneurysm were significant for all outcomes but stroke. Acute dissection and adjunct were significant only for paraplegia/paraparesis. In the logistic model of the aggregate outcome, preoperative renal dysfunction, age and extent II aneurysm were highly significant predictors, but adjunct and acute dissection were not significant (Table 4).
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4. Discussion |
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TopAbstract1. Introduction2. Methods3. Results4. DiscussionAppendix A. Conference...References |
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Disparity among outcome prevalences in the multiple components of a polytomous endpoint – which, as we have noted, causes major problems for composite endpoint analysis – is not completely without consequences for polytomous models. In general, one risk factor can be identified reliably without overdetermination for about every 10 events. In the polytomous case, this means ten events per outcome class. Therefore, model selection should consider the number of events in each outcome variable category, and this should be balanced against biological plausibility and what is generally known about the risk factors, in addition to statistical significance criteria.
The traditional approach of examining multiple endpoints with multiple separate analyses can be another informative way to investigate the relationships between risk factors and individual outcomes, if several conditions are met. It is possible to use individual single dependent-variable logistic regression equations in combination to arrive at combined outcome probabilities that accumulate to 100%. This was described by Blackstone and reported by Kirklin and Barratt-Boyes in their classic text on cardiac surgery [10]. Hosmer and Lemeshow demonstrate the computations [11]. These segmental ordinary logistic models can be made to provide identical results to those obtained by polytomous analysis under appropriate conditions. Interested readers are referred to the excellent chapters in Refs. [10] and [11] for a thorough discussion. Our general feeling is that this formulation is a bit more cumbersome than the polytomous approach, but as we have said, the two methods can be made to be equivalent. As a straightforward addition to composite endpoint analysis, in any event, polytomous multivariate analysis is a useful addition to the outcome analysis tool kit.
In our view, it makes sense to do things in several stages – univariate, multivariate, aggregate – so that small effects can be scrutinized and a clearer view of the story contained in the underlying data can be had.
The major finding of this study is that preoperative renal dysfunction is an important risk factor for all the components of a poor outcome following thoracoabdominal aortic aneurysm repair, and that this is best observed after adjustments for effects of multiple risk factors and multiple outcomes have been made. This finding has helped to formalize our clinical impressions, and provides the rationale for further study of this important risk factor and for future development of strategies for management of renal dysfunction.
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Footnotes |
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Appendix A. Conference discussion |
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TopAbstract1. Introduction2. Methods3. Results4. DiscussionAppendix A. Conference...References |
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Dr Miller: Preoperatively it is a history of hemodialysis or a preoperative serum creatinine greater than 2.
Dr Roquette: Do you think this polytomous outcome should be used instead of another type of evaluation in this setting?
Dr Miller: I think polytomous analysis is another useful tool in the tool kit. The composite-endpoint analysis is useful, but I think that the polytomous analysis should be done in addition, because it allows us to see how the outcomes separate from one another and how they interact.
Dr F. Schmid (Regensburg, Germany): This is a huge number of patients you have analyzed, and I assume that the technical procedure evolved over the years. Is there an impact of the period of operation on that model?
Dr Miller: Practice has indeed changed over time, and period effect does exist for this reason. The polytomous categorical model is a generalization of the linear model, and as such, adjustments for period effect can be made if necessary.
Dr R. Mazhar (Doha, Qatar): You identified adjunct as a negative factor for poor outcome. Is this not the use of CSF tapping and distal cooling?
Dr Miller: It is beneficial, yes.
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References |
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TopAbstract1. Introduction2. Methods3. Results4. DiscussionAppendix A. Conference...References |
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