This is the pre-peer-review version of the following article: Wilkinson, D. The window of opportunity: decision theory and the timing of prognostic tests for newborn infants. Bioethics (2009) vol. 23 (9) pp. 503-14 which has been published in final form at http://dx.doi.org/ 10.1111/j.1467-8519.2009.01762.x
    
    The Window Of Opportunity: Decision Theory And The Timing Of Prognostic Tests For Newborn Infants
    Dominic Wilkinson
    The Ethox Centre, Department of Public Health and Primary Health Care, The University of Oxford, Oxford Uehiro Centre for Practical Ethics, The University of Oxford, Address for correspondence:: The Ethox Centre, Department of Public Health and Primary Health Care, The University of Oxford, Badenoch Building, Headington, OX3 7LF email: dominic.wilkinson@ethox.ox.ac.uk Tel: +44 (0) 1865 287 887 Fax: +44 (0) 1865 287 884
    
    ABSTRACT In many forms of severe acute brain injury there is an early phase when prognosis is uncertain followed later by physiological recovery and the possibility of more certain predictions of future impairment. There may be a Window of Opportunity for withdrawal of life support, but if decisions are delayed there is the risk that the patient will survive with severe impairment. In this paper I focus on the example of neonatal encephalopathy and the question of the timing of prognostic tests and decisions to continue or withdraw life-sustaining treatment. How should parents decide what to do given the conflicting values at stake? I apply decision theory to the problem, using sensitivity analysis to assess how different features of the tests or different values would affect a decision to perform early or late prognostic testing. I will draw some general conclusions from this model for decisions about the timing of testing in neonatal encephalopathy. Finally I consider possible solutions to the problem posed by the Window of Opportunity. Decision theory highlights the costs of uncertainty. This may prompt further research into improving prognostic tests. But it may also prompt us to reconsider our current attitudes towards the palliative care of newborn infants predicted to be severely impaired.
    
    INTRODUCTION Case: A mother goes into labour with her first child. She is eagerly anticipating a healthy newborn, but late in labour something goes horribly wrong. The baby is born pale, floppy and apparently lifeless. The infant (Shaun) is resuscitated and transferred to the neonatal intensive care unit, where he is critically ill in the first days of life. He is comatose, dependent on life support, and it appears that his brain and other organs have been deprived of oxygen and blood supply during the birth process. The doctors and Shaun’s parents worry about the risk of him having permanent brain damage if he survives. They wonder whether continuing to keep him alive is the right thing to do. Shaun’s doctors consider performing further tests of his brain to help predict the chance and severity of long term impairment. But there is a problem. If the tests are performed now they are imperfect, the results associated with significant uncertainty. If the tests are delayed, they will be more accurate, but there is the risk that Shaun will no longer be dependent on life support machines. He may then survive, but with severe impairment.1
    
    1
    
    This case and the name used are fictitious. When I use the term ‘severe impairment’ in this paper I have in mind impairments likely to make a child highly dependent on caregivers, including for example severe cerebral palsy and/or severe learning disability. Nuffield Council on Bioethics. 2006. Critical care decisions in fetal and neonatal medicine : ethical issues. London: Nuffield Council on Bioethics: 71. I wish to set aside the question
    
    In critically ill patients there are a range of ethical dilemmas. One dilemma relates to the timing of prognostic testing and decisions to continue or withdraw life-sustaining treatment (LST). As illustrated in the case above, there can be conflicting values at stake. There may be a Window of Opportunity for early withdrawal, but at the cost of greater uncertainty in prognosis. Such dilemmas are often seen, for example, in adults or children with head injury or in extremely premature infants. In what follows I will focus on the example of neonatal encephalopathy(NE) (Box 1). There are different questions that we might ask about the Window of Opportunity. Should the window influence treatment decisions? Is it permissible to withdraw life support from patients who have a risk of severe impairment, but who could survive to be unimpaired? If it is permissible to withdraw or to continue life support how should caregivers decide what to do given opposing and potentially incompossible values? In this paper I will focus on the last of these questions.2 I will briefly summarise the natural history of NE and outline some of the features that relate to the timing of prognostic testing and the timing of withdrawal of LST. I apply decision theory to the problem, using sensitivity analysis to assess how different features of the tests or different values would affect a decision to perform early or late prognostic testing. I will draw some general conclusions from this model for decisions about the timing of testing in neonatal encephalopathy.
    
    Finally I consider possible solutions to the problem posed by the Window of Opportunity. Neonatal Encephalopathy (NE): an illness marked by abnormal neurological behaviour in the newborn period.3 Infants have often been born in poor condition and required active resuscitation. Other terms for this illness include ‘birth asphyxia’, or ‘hypoxic-ischemic encephalopathy’. Severe encephalopathy: infants with NE who are severely hypotonic, comatose, and have usually lost the drive to breath. They have at least an 80% chance of severe impairment if they survive. Moderate encephalopathy: infants with NE who have reduced tone and conscious state. They often have seizures. They have about a 30% chance of severe impairment if they survive. Box 1: Definitions THE WINDOW OF OPPORTUNITY Neonatal encephalopathy affects 1 in 1000 live births,4 and globally leads to almost 900,000 deaths per year.5 It is classified on the basis of the degree of abnormal neurological behaviour into mild, moderate and severe subtypes.6 The natural history is of acute critical illness that may worsen after the first 24 hours but then usually improves.7 The period of hypoxia and ischemia that is the most common cause of brain injury also causes
    3
    
    D. Ferriero. Neonatal brain injury. N Engl J Med 2004; 351: 1985-1995.
    4
    
    of impairment, and the best interests of such infants. D. Wilkinson. Is it in the best interests of an intellectually disabled infant to die? J Med Ethics 2006; 32: 454-459. For the sake of what follows I will assume that there is a level of predicted impairment that is so severe that it would justify allowing infants to die. While we may disagree about the level of this impairment most would agree with this underlying assumption.
    2
    
    V. Pierrat, et al. Prevalence, causes, and outcome at 2 years of age of newborn encephalopathy: population based study. Arch Dis Child Fetal Neonatal Ed 2005; 90: F257-261.
    5
    
    World Health Organisation. World Health Report: 2005: make every mother and child count. Geneva: World Health Organisation: 190.
    6
    
    I refer in this paper to ‘parents’, since they are often the most appropriate decision-makers. But the issues raised below could apply equally to other decision-makers (for example non-parent caregivers or doctors). Author’s Pre-print. 1/10/09
    
    G.M. Fenichel. Hypoxic-ischemic encephalopathy in the newborn. Arch Neurol 1983; 40: 261-266. H. Sarnat & M. Sarnat. Neonatal encephalopathy following fetal distress. A clinical and electroencephalographic study. Arch Neurol 1976; 33: 696-705.
    7
    
    J.J. Volpe. 2008. Neurology of the newborn. 5th edn. Philadelphia ; London: Saunders: 402-404. 2
    
    multi-organ illness, and infants often have significant cardiac depression, renal failure and coagulopathy.8 Modern neonatal intensive care is able to support most infants through this period of physiological instability. Within a few days of birth there are signs of organ recovery in all except the most profoundly affected infants. Encephalopathy starts to lessen, and one of the earliest signs is that the infant starts to breathe for himself. Yet despite outward evidence of improvement some infants have sustained severe and irreversible brain injury. Newborns, like Shaun, with severe NE have an 80% or greater chance of severe impairment if they survive, including spastic quadriplegic cerebral palsy, epilepsy and severe cognitive impairment.9 For infants with moderate encephalopathy, the chance of severe impairment is about 30%.10 Determining which infants will have significant brain damage is crucial, yet prognostication for newborn infants is always associated with uncertainty.11
    
    There are various tools that can assist with prognosis, for example clinical examination, electrophysiological investigations or imaging of the brain.12 All of these tools face the same problem – that early predictions are more fallible than late predictions. For example, in one study neurological examination performed in the first four days of life had a false positive rate of 45%, yet this fell to less than 1% when performed at the end of the third week.13 Magnetic resonance imaging of the brain is regarded by many as the most useful test for determining the extent and severity of brain injury.14 It too has greater predictive power if it is performed after the first week of life.15 Consequently there is some reason to delay prognostic testing. But there are also reasons not to delay. In the face of poor prognosis LST is sometimes withdrawn. The majority of deaths for newborns with NE in developed countries follow such decisions.16 What happens after this support is withdrawn is affected by the timing. During the first couple of days after birth infants are usually dependent upon medical interventions that are unambiguously intensive. The mechanical ventilator can be withdrawn, the endotracheal tube removed, medications to support blood
    12 13
    
    8
    
    P. Shah, et al. Multiorgan dysfunction in infants with post-asphyxial hypoxic-ischaemic encephalopathy. Arch Dis Child Fetal Neonatal Ed 2004; 89: F152-155.
    9
    
    It is often claimed that all infants with severe encephalopathy die or are severely impaired.Volpe. 441; M. Shevell. Ethical issues in pediatric critical care neurology. Seminars in pediatric neurology 2004; 11: 179-184. In a metaanalysis of published trials some infants with severe encephalopathy survived without disability.J.E. van de Riet, et al. Newborn assessment and long-term adverse outcome: a systematic review. American journal of obstetrics and gynecology 1999; 180: 1024-1029. The mortality rate in all such studies is affected by withdrawal of life support and the problem of the self-fulfilling prophecy. (Wilkinson D. The self-fulfilling prophecy in intensive care. 2009 Submitted) In a meta-analysis of trials of hypothermia for NE, 80% of infants classified as having severe encephalopathy died or were severely impaired.S. Jacobs, et al. Cooling for newborns with hypoxic ischaemic encephalopathy. Cochrane database of systematic reviews (Online) 2007: CD003311.
    10 11
    
    Volpe. 441; Shevell.
    
    E. Mercuri, et al. Neonatal neurological examination in infants with hypoxic ischaemic encephalopathy: correlation with MRI findings. Neuropediatrics 1999; 30: 83-89.
    14
    
    N.J. Robertson & J.S. Wyatt. The magnetic resonance revolution in brain imaging: impact on neonatal intensive care. Arch Dis Child Fetal Neonatal Ed 2004; 89: F193-197; M. Rutherford, et al. Magnetic resonance imaging in neonatal encephalopathy. Early Hum Dev 2005; 81: 13-25.
    15
    
    C. Kuenzle, et al. Prognostic value of early MR imaging in term infants with severe perinatal asphyxia. Neuropediatrics 1994; 25: 191-200; M.A. Rutherford, et al. Hypoxic ischaemic encephalopathy: early magnetic resonance imaging findings and their evolution. Neuropediatrics 1995; 26: 183-191.
    16
    
    Volpe. 441; Shevell. Shevell.
    
    D.J. Wilkinson, et al. Death in the neonatal intensive care unit: changing patterns of end of life care over two decades. Arch Dis Child Fetal Neonatal Ed 2006; 91: F268-271. 3
    
    Author’s Pre-print. 1/10/09
    
    pressure (inotropes) ceased, and in most instances the infant will die quickly. By contrast, if the decision is deferred by even a few days infants have often resumed breathing and no longer require inotropes. At this stage, if a decision is made to withdraw the ventilator infants are unlikely to die quickly and may not die at all. In this setting there is the possibility of withdrawal of other (less intensive) forms of treatment. In practice the main option is withdrawal of artificial nutrition. Withdrawal of artificial nutrition from newborn infants is highly contentious.17 It is an option in infants with NE because those most severely affected usually have impaired ability to coordinate sucking and swallowing. They are dependent on the provision of artificial feeding (usually by a nasogastric tube in the short to medium term) to survive. If artificial feeding is withdrawn infants usually die, but the dying process may be prolonged. It can take three weeks or longer for infants to die.18 Although withdrawal of artificial nutrition is supported by some professional guidelines19 many neonatal units do not support this practice. Some have argued that it is contrary to the interests of infants.20 To sum up, there are competing considerations in the timing of prognostic tests for infants with NE. Certainty favours later testing. Early tests
    17
    
    may miss infants who have in fact suffered severe brain injury (a false negative result). Alternatively they may falsely identify infants as having a poor prognosis who would not have been severely impaired had they survived (a false positive result). Parents also sometimes struggle to make decisions quickly and benefit from time to come to terms with prognosis. On the other hand, there is a Window of Opportunity for withdrawal of life support. If decisions are delayed there is the risk that the infant will no longer be dependent on mechanical ventilation. The infant may then survive with severe impairment. Withdrawal of artificial nutrition is permitted in some centres, but this has the potential to lead to a death that is prolonged and distressing for the infant, parent and carers. What should parents do when faced with this sort of choice? Is there a way of rationally appraising and reconciling these conflicting priorities? DECISION THEORY One approach to decision-making under uncertainty is to use decision theory. Von Neumann-Morganstern utility theory remains the most widely used form.21 It allows complicated decisions to be broken into constituent parts.22 The probability of different outcomes are combined with the value attached to different outcomes to determine which course of action will lead to the greatest expected utility. For example imagine that if an action A is taken, there are two possible outcomes a and b. Expected Utility23 (A) = Probability(a) x Value(a) + Probability(b) x Value(b)
    
    E.D. Miraie. Withholding nutrition from seriously ill newborn infants: a parent's perspective. J Pediatr 1988; 113: 262-265; B.H. Levi. Withdrawing nutrition and hydration from children: legal, ethical, and professional issues. Clin Pediatr (Phila) 2003; 42: 139-145; B.S. Carter & S.R. Leuthner. The ethics of withholding/withdrawing nutrition in the newborn. Semin Perinatol 2003; 27: 480-487; N. Porta & J. Frader. Withholding hydration and nutrition in newborns. Theoretical medicine and bioethics 2007; 28: 443-451.
    18 19
    
    21
    
    J.C. Sinclair & G.W. Torrance. 1995. The use of epidemiological data for prognostication and decision-making: from probability to preference. In Ethics and Perinatology. A. Goldworth, et al., eds. Oxford: Oxford University Press.
    22
    
    Carter & Leuthner.
    
    Royal College of Paediatrics and Child Health. 1997. Withholding and withdrawing life-saving treatment in children: a framework for practice. London: Royal College of Paediatrics and Child Health: 30.
    20
    
    J. Cohen, D. Asch & P. Ubel. 2000. Bioethics and decision making: what can they learn from each other? In Decision-making in health care. G.B. Chapman & F.A. Sonnenberg, eds. Cambridge: Cambridge University Press.
    23
    
    H. Kuhse. Death by non-feeding: not in the baby's best interests. J Med Humanit Bioeth 1986; 7: 79-90. Author’s Pre-print. 1/10/09
    
    Expected utility is sometimes distinguished from expected value. Outcomes with objective values (for example monetary values) may be more or less desirable to an individual depending 4
    
    If the expected utility of action A is greater than another alternative (B), it should rationally be preferred. Decision theory has been applied to many areas of medical decision making.24 There have been fewer studies applying decision theory to explicitly ethical problems,25 nevertheless it may be valuable in understanding the interplay between different variables and in revealing underlying assumptions.26 In one paper, a model of resuscitation decisions for a critically ill patient identified a number of important factors for such decisions including the chance of recovery to a good life, the estimated maximum quality of life and the length of life gained.27 In this section of the paper I will use decision theory to analyse the importance of different factors in decisions about the timing of prognostic testing in NE. The aim is to see if decision theory can enrich our understanding of the problem. I will first outline the characteristics of the decision-theoretic model, then look at the answers that it suggests for specific questions. In the final section of the paper I will return to the potential implications of decision theory for practice. Characteristics of model In the model I combine prognostic testing with decision making. Although prognostic tests are sometimes performed without a view to discontinuation of LST I take it that this does not upon the strength of their preference for that outcome. The use of the individual’s preference for different outcomes rather than an objective value gives rise to “expected utility” rather than expected value. In what follows there is no assumption of objective values for discrete outcomes.
    24
    
    give rise to any particular difficulty in decisionmaking. I compare Early prognostic testing and decision-making (Early Testing, ET) with Late Prognostic testing and decision-making (Late Testing, LT).28 I will assume that the results of tests are used to inform decisions about the withdrawal of LST, and that if the test results reveal a poor prognosis LST is withdrawn. This is clearly a simplification since test results are not purely dichotomous, and neither is impairment. The values that I use can be thought of as average values, representing a spectrum of outcomes.29 I have assumed that in the absence of treatment withdrawal all infants survive. Some infants with NE die of overwhelming organ failure in the first day or two of life despite maximal efforts to keep them
    
    28
    
    For the purposes of this analysis there is no need to specify exactly what is meant by ‘early’ and ‘late’ here. By way of illustration we could, for example, take ET to refer to testing in the first two to three days of life, and LT to refer to testing after one week.
    29
    
    R.J. Lilford, et al. Decision analysis and the implementation of research findings. BMJ 1998; 317: 405-409.
    25 26
    
    Cohen, Asch & Ubel.
    
    J. Savulescu. Treatment limitation decisions under uncertainty: the value of subsequent euthanasia. Bioethics 1994; 8: 49-73.
    27
    
    Ibid.
    
    Some forms of economic modelling attempt to put specific values on quality of life and calculate quality-adjusted life years. For these purposes, however, we do not need the specific value of outcomes; to determine whether one course of action would be better than another we only need relative value. D.G. Froberg & R.L. Kane. Methodology for measuring health-state preferences--II: Scaling methods. Journal of clinical epidemiology 1989; 42: 459-471. 5
    
    Author’s Pre-print. 1/10/09
    
    Figure 1 Decision tree for early versus late prognostic test and decision-making The square box on the left represents the decision. Circles represent chance nodes, and the rectangular boxes outcome states. Some infants who die following withdrawal of life support would have survived with severe impairment (poor outcome) if treatment had not been withdrawn. Others would have survived without severe impairment (good outcome). Following Late Testing, a proportion of infants who are predicted to be severely impaired survive. Some of these surviving infants are severely impaired, some are not.
    
    Author’s Pre-print. 1/10/09
    
    6
    
    alive.30 But of those infants who survive to two or three days of age, almost all can survive – if intensive care is provided. It will helpful to start with a decision-tree (Fig 1). The left side of the figure reflects the initial decision, with the boxes on the right showing the possible outcomes. There is a choice between performing no test, performing ET or LT. The outcomes include death, survival with severe impairment (poor outcome), or survival without severe impairment (good outcome). To calculate expected utility we need to know the probability of different outcomes (given each choice), and the values that parents assign to each outcome. Table 1 lists the assumptions used as a starting point for the model as well as plausible alternatives. I will shortly look at the effect of different values for these variables on decisions. For example I start by assuming that there is a high pre-test probability of poor outcome (80%).31 This would be the case in an infant like Shaun with severe encephalopathy. We will shortly see how decisions would be affected if the pre-test probability of poor outcome were as low as 20% or as high as 95%.
    
    Variables Pre-test probability of poor outcome ET - sensitivity ET - specificity LT - sensitivity LT - specificity Survival with good outcome Survival with poor outcome Death Disutility of late withdrawal Proportion of infants surviving late withdrawal
    
    Starting value 0.8 0.8 0.8 0.9 0.9 1 -0.5 0 -0.05 0.2
    
    Possible values 0.2-0.95 0.3-0.9 0.6-0.9 0.8-0.95 0.8-0.95
    
    -0.05 to -1.0
    
    0 to -0.5 0.1-1
    
    Table 1. Starting assumptions for modelling of prognostic decision-making, as well as the range of plausible alternative values for these variables. ET – Early testing LT – Late testing
    
    30 31
    
    Volpe. 403-404.
    
    The incorporation of pre-test probabilities into the model might seem vulnerable to a problem of infinite regress, since how are these probabilities to be determined? In practice there is always some initial prognostic information available (for example based upon condition and birth and response to resuscitation). The decision here is about further testing with a view to potential withdrawal of LST. Author’s Pre-print. 1/10/09 7
    
    The probability of different outcomes can be determined from the characteristics of the test and the pre-test probability.(see Appendix) The sensitivity of the test refers to the proportion of infants with poor outcome that are correctly identified. The test specificity is the proportion of infants with good outcome who are correctly identified. We will start by assuming fairly accurate testing early but more accurate testing later.(Table 1) In practice Early Testing may have lower sensitivity than this but higher specificity. Again, we will subsequently see how this would affect decisions.32 By convention in medical decision-making life in full-health is assigned a value of one, and death a value of zero. Outcomes that are judged to be worse than death are given negative values. There are difficult philosophical questions about whether life with severe impairment is worse than death. Some approaches to outcome assessment specifically exclude the possibility of outcomes that are worse than death.33 But it is not uncommon for individuals for think death preferable to certain possibilities (for example dementia or coma or cancer recurrence).34 It is possible to include such preferences by giving them a negative value,35 and this is consistent with expected value theory.36 When parents or clinicians are considering withdrawal of lifesustaining treatment, this is based upon a belief that continued treatment would be worse than allowing the patient to die. We can only make
    
    sense of such decisions by assigning certain outcomes a negative value. Note that there is a difference between the value that an individual would attach to their own existence (if able to do so), and the value that parents attach to their child surviving in such a condition. It might be the case that parents would choose to withdraw life support in the face of an impairment that (from the child’s own perspective) would not be worse than death. I wish to remain neutral here about the permissibility of withdrawal in such a case. Other parents would not assign a negative value to survival with severe impairment. They might assign it instead a reduced positive value. But for these parents it would not be rational to withdraw LST, and the problem of the timing of prognostic tests would not arise. We can factor in the specific features of Late Testing into the model by adding disutility to outcomes involving late withdrawal of LST and by factoring in survival after Late Testing.37 As highlighted above, a proportion of infants who are predicted on the basis of Late Testing to be severely impaired will nevertheless survive. Having set out the relevant characteristics of the model we can use it to examine the influence of different variables on decisions. I will divide this analysis into a series of focussed questions. Applying decision theory to the problem i. How does the pre-test probability of poor outcome affect decisions? Infants with severe encephalopathy have a high a priori risk of poor outcome, those with moderate encephalopathy have a lower risk. We can
    
    32
    
    The sensitivity and specificity of a test depend not only on the properties of a test, but also on the cut-off point chosen for diagnosis. In this case this is the specific test result taken to predict severe impairment. Choosing a higher cut-off point results in lower sensitivity but higher specificity, and vice versa.
    33
    
    D.M. Franic & D.S. Pathak. Effect of including (versus excluding) fates worse than death on utility measurement. International journal of technology assessment in health care 2003; 19: 347-361.
    34
    
    37
    
    D.L. Patrick, et al. Measuring preferences for health states worse than death. Med Decis Making 1994; 14: 9-18; Franic & Pathak.
    35 36
    
    Patrick, et al. Franic & Pathak.
    
    I have assigned a negative utility to deaths following late withdrawal. This accords with the general intuition that a death following early withdrawal of life support would be preferable to a death after late withdrawal. Although in some cases this might not be the case (for example if an infant were to remain ventilator dependent and die quickly following late withdrawal) this seems a reasonable assumption. (see also Appendix) 8
    
    Author’s Pre-print. 1/10/09
    
    Figure 2 One-way sensitivity analysis for the pre-test probability of poor outcome The dotted lines indicate the intersection of different alternatives ie if the pre-test probability is >0.6 Early Repeated Testing has the greatest expected utility. Expected Utility, in this and all subsequent figures, is multiplied by 100 for the sake of simplicity (this has no effect on comparisons).
    
    Author’s Pre-print. 1/10/09
    
    9
    
    perform a sensitivity analysis38 on the model of timing decisions to assess the effect of this variable on decisions. Figure 2 shows the results of this analysis, comparing ET with LT. When the pre-test probability of poor outcome is more than 0.6 (60%) the line corresponding to ET is higher (ie has greater expected utility) than the line corresponding to LT. It would be better to test early than to test later in infants with severe encephalopathy for example. Conversely when the pre-test probability is between 0.2 and 0.6 (20 to 60%) the line corresponding to Late Testing is uppermost and has greater expected utility. This would be a better strategy for infants with moderate encephalopathy. Apart from late or early testing there are two other strategies of testing we could consider. No testing would involve a strategy of performing no prognostic tests and continuing intensive care in all infants. Early Repeated testing (ERT) would involve performing early testing (with withdrawal of LST in those infants predicted to have severe impairment), then repeating tests at a later stage for surviving infants. This would have the advantage of detecting infants with poor outcome missed by early testing. Figure 2 shows these additional comparisons. Early repeated testing has the highest expected utility of any of the strategies when the pre-test probability of poor outcome is high. (It is consistently superior to Early Testing alone, and in subsequent analyses I will focus on the comparison between ERT and LT.) It might also be noted that if the pre-test probability of poor outcome is very low (less than 0.2 (20%)) the line for No Testing is highest; it becomes better not to perform any prognostic testing at all. ii. How does the value assigned to severe impairment affect decisions? Parents may vary in their views about severe impairment. They may be more or less averse to their infant surviving in such a state. The starting assumption was that survival with severe impairment had a value of ‘-0.5’. This compares with a value of +1 for survival with good outcome. But conceptually it can be difficult to interpret or explain this sort of negative utility.
    
    How would parents decide what value to place on this? The traditional way of arriving at such a value uses the standard gamble.39 Parents would be asked about the chance of severe impairment at which they would consider withdrawing life sustaining treatment. For example, imagine that there is a p chance of a good outcome, but a (1-p) chance of an infant surviving in a state of severe impairment. If we can determine the probability p at which parents are indifferent between withdrawing and continuing treatment (given the chance of severe impairment) we can calculate the value of this outcome state.40 The value of the state is given by –p/(1-p). A value of -0.5 for a state of severe impairment would correspond to p=0.33. In other words, if parents are willing to withdraw treatment when there is more than a 66% chance of severe impairment, that is equivalent to a value for this outcome of -0.5. We can use the model to determine the effect of this variable on decisions and its interaction with the pre-test probability of poor outcome. Figure 3 shows a two-way sensitivity analysis. The upper (shaded) region of the graph corresponds to those points where Early Repeated testing would be preferable to Late Testing. The lower region corresponds to the points where Late Testing has greater expected utility. For infants with moderate encephalopathy LT is always preferable.41 For
    
    39 40 41
    
    Froberg & Kane. Ibid.
    
    38
    
    The sensitivity analysis for the decision model should not be confused with the test sensitivity referred to earlier. Author’s Pre-print. 1/10/09
    
    The line corresponding to the intersection of Early Repeated and Late testing only falls below a pre-test probability of 30% if the value of severe impairment is <-1.8 (not shown). At this point Early Repeated testing would become preferable for infants with moderate encephalopathy. This value would correspond to a value of p of 0.9 in the standard gamble, or parents being prepared to withdraw life support if the chance of a good outcome (ie survival without severe impairment) were 90% or less. Although it is possible that some parents would give a value this negative to survival with severe impairment I have limited analysis to values up to -1.0 (corresponding to p of 0.5). In practice it is hard to believe that clinicians would acquiesce to parental withdrawal of life support if the chance of severe impairment were less than 50%. 10
    
    Figure 3 Two-way sensitivity analysis for the effect of pre-test probability and the value of severe impairment The shaded region of the graph indicates the points when Early Repeated Testing is preferred.
    
    Author’s Pre-print. 1/10/09
    
    11
    
    infants with severe encephalopathy ERT is better as long as there is even a small negative value assigned to survival with severe impairment. In the figure it can be seen that the line only rises above a pre-test probability of 0.8 when there is a value less than -0.1 for severe impairment. Along the lines of the reasoning outlined above this value would correspond to withdrawal of life support being acceptable to parents if there were a greater than 90% chance of severe impairment. One implication of this analysis, then, is that it may not be important for decisions to know how negatively parents view survival with severe impairment. It would be enough to know whether they view it negatively. iii. How do test characteristics affect decisions? We may wonder whether the characteristics of the prognostic test used affect decisions. For example we might be contemplating magnetic resonance imaging or electroencephalography. Early testing might be more specific but less sensitive, or vice versa. When the sensitivity or the specificity of the test falls it favours Late Testing.(Appendix Figure A1) In the former case this is because of the increased numbers of false negatives (infants with poor outcome missed by testing), in the latter case it reflects the increased false positive rate (infants with good outcome falsely predicted by the test to have poor outcome). But this effect is relatively minimal. It influences decisions mostly where there is intermediate pre-test probability of poor outcome.42 iv. How do the negative features of late withdrawal influence decisions? Whether or not parents opt for Early Testing may be influenced by their attitude towards late withdrawal. How is this reflected in the model? Appendix Figure A2 shows the interaction between the negative features of late withdrawal and decisions. For infants with severe
    
    encephalopathy Early Repeated testing is preferable to Late Testing unless late withdrawal is viewed neutrally (ie has no disvalue) and the chance of survival following Late Testing is close to zero. For infants with moderate encephalopathy Late Testing is always preferred.43 POTENTIAL IMPLICATIONS OF DECISION THEORY What conclusions can be drawn from the application of decision theory to the Window of Opportunity problem? What practical help can decision theory provide? i. Decision theory as a tool for specific cases One option would be to use decision theory to provide specific guidance to parents of infants like Shaun. It would be possible to enter into the model specific features relevant to Shaun (for example the estimated pre-test risk of poor outcome), as well as the values that his parents attribute to different outcomes. It has been suggested that the use of models for decisionmaking in the critically ill could enhance autonomy and help individuals make informed choices.44 Parents may be reluctant to use a mathematical model for a decision of this nature. Decisions about the withdrawal of life support from their newborn infant are among the most difficult choices that parents ever have to make. They involve deep-seated and strongly held values. On the other hand, it is precisely the importance of such decisions and the difficulty in resolving the conflict between values that motivates the use of decision theory. Although decision theory is explicitly normative, (it is a theory about how decisions ought to be made) the aim would not be to prescribe a particular course of action for parents. Instead it would aim to help them think through the alternatives, and the reasons that they have in favour of early or Late Testing. A more serious problem for decision theory in practice is the issue of metauncertainty.45
    
    42
    
    From figure A1 it can be seen that early testing only becomes preferable for infants with moderate encephalopathy (pre test probability <40%) when both the sensitivity and specificity of early testing are very high (both more than 95%). Early Repeated testing ceases to be of greater utility for infants with severe encephalopathy if both sensitivity and specificity of early testing are relatively low. Author’s Pre-print. 1/10/09
    
    43
    
    When the pre-test probability of poor outcome is intermediate (0.5) the decision is more sensitive to these factors.
    44 45
    
    Savulescu; Cohen, Asch & Ubel. Savulescu. 12
    
    Discussion thus far has largely been confined to first order uncertainty – i.e. uncertainty about which outcome will come about. But we may also be unsure of the likelihood of different outcomes (there could be a 60-90% chance of severe impairment for example).46 There may be doubt about the severity of different outcomes. Severe impairment might include permanent unconsciousness, or spastic quadriplegia with moderate intellectual impairment. Parents may also be deeply ambivalent about the value to place on those outcomes. More sophisticated models could be developed to incorporate a spectrum of outcomes. Tools could help parents assign value to different potential outcomes. Improvements in prognostic tests may yield more specific predictions. In the meantime empirical research could assess the acceptability of decision theoretic models for parents and clinicians. The process of applying decision theory may (even granted the uncertainties listed above) help parents to clarify values and options. ii. Generation of guidelines for decisionmaking Another possibility is that the results of analysis could be used to generate guidelines or heuristics for decision-making. Within the bounds of the assumptions outlined above the following conclusions could be drawn. 1. A strategy of Early Repeated Testing is preferable to Early Testing alone 2. The pre-test probability of poor outcome had a large effect on decisions. If the pretest probability of severe impairment is low prognostic testing and decisionmaking should be deferred. If the pre-test probability is high Early Testing would be preferable. 3. It is more important to know whether severe impairment is viewed negatively (ie whether withdrawal of LST would be contemplated if severe impairment were
    
    predicted) than to know the specific value assigned to this outcome. 4. Test characteristics do not change decisions unless the test is very accurate (high sensitivity and specificity, favours Early Testing), or very inaccurate (low sensitivity and specificity, favours Late Testing). 5. If Late Testing is associated with a risk of survival with severe impairment, or if late withdrawal is viewed negatively (ie has additional disutility) Early Testing is favoured. As an example of the way that decision theory could be applied to the practical problem, these conclusions are combined in the form of a guideline in Figure 4. Such a guideline would not require knowledge of the exact probabilities of outcomes nor the specific values attributed to different outcomes. iii. The costs of uncertainty Decision theory makes uncertainty explicit,47 and to that extent is able to highlight the consequences of imperfect knowledge. For example, in the model outlined above Early Repeated Testing had greater expected utility than Late Testing for infants with a high pre-test probability (0.8) of poor outcome. For every 100 infants with severe encephalopathy undergoing Early Repeated Testing there would be 5 false positive and 5 false negatives. The number of these is small, but it is still striking that for each infant who survives with severe impairment one infant dies who would have otherwise survived unimpaired.48 On the other hand a strategy of Late Testing was preferable for infants with moderate encephalopathy. If adopted for all such infants, Late Testing would yield 6 false positives and 8 false negatives per 100 infants. Although the specific numbers are only meaningful within the setting of the assumptions I have outlined, they highlight the costs of uncertainty. The implication of the Window of Opportunity is that some infants will survive with severe impairment,
    
    46
    
    Some of this uncertainty arises from problems in obtaining information about prognosis that is not influenced by treatment withdrawal. This is the epistemic problem of the self-fulfilling prophecy. Wilkinson D. The Self-fulfilling prophecy in Intensive Care. 2009 Submitted Author’s Pre-print. 1/10/09
    
    47 48
    
    Lilford, et al.
    
    Assuming that treatment is withdrawn in all infants with a test indicating poor prognosis. 13
    
    while some infants will die who would not have been impaired. SOLUTIONS TO THE WINDOW OF OPPORTUNITY Decision theory provides one way of attempting to resolve the competing considerations posed by the Window of Opportunity problem. But an alternative approach would be to attempt to change the factors that give rise to the problem in the first place. One obvious way to reduce the problem would be to improve prognostic tests. Advances in imaging or other technologies may allow early accurate detection of severe brain injury and predict infants who will be severely impaired. This would remove one important reason to delay testing and decision-making. It provides a strong incentive for further research. Nevertheless the problem wouldn’t be completely resolved, since families may still take some time to come to terms with prognosis and decide to withdraw LST. At present no such test exists. A second possible solution would be to address the features of late withdrawal of LST that motivate Early Testing. The problem arises because most infants are no longer dependent upon mechanical ventilatory support. The prospect of withdrawal of nasogastric-tube feeding raises concerns about infants suffering during the dying process, concerns for the wellbeing of parents, and disquiet amongst medical and nursing staff about whether this form of end-of-life care is ethical or legal. Most of these Figure are amenable to change. Although some factors 4 professional the timing of to the ethical Guideline forguidelines referprognostic tests and decision-making acceptability of withdrawal of artificial nutrition in certain circumstances in children (notably in persistent vegetative state),49 others suggest that it may be permissible only in exceptional circumstances.50 If there were professional guidelines clearly stipulating in which
    
    49 50
    
    Royal College of Paediatrics and Child Health.
    
    Nuffield Council on Bioethics.: 98-99. The Nuffield report suggests that artificial nutrition may be withheld only where there is failure of gastrointestinal function, and provision of feeds would be likely to lead to additional suffering. Author’s Pre-print. 1/10/09 14
    
    circumstances artificial nutrition could be withdrawn in newborn infants this would provide reassurance to staff and (to some degree at least) legal protection. The concerns about the infants themselves and families could be alleviated by the implementation of a concerted and coordinated palliative care model.51 A dedicated team of caregivers would look after the infant and support the parents – either in hospital, or (preferably) in the community. A team of this sort that regularly looked after dying infants would be able to assess and manage distress or discomfort experienced by the infant, and reduce the risk of suffering during the dying process. The other factor that drives Early Testing is the knowledge that some infants with poor outcome will survive if prognostic testing occurs late. Is this amenable to change? One option that has been proposed to manage uncertainty in treatment limitation decisions would be to defer decision-making until the outcome were clear, and then to offer euthanasia if the patient rationally wished to die, or would rationally choose death if he were competent.52 Euthanasia in newborn infants is even more controversial than in competent adults.53 It has been legally permitted only in the Netherlands, where a set of guidelines for its practice have been published and endorsed. The Groningen Protocol stipulates that “hopeless and unbearable suffering” that cannot be alleviated must be present.54 It is not clear that infants with NE and predicted severe impairment would fall into this category, and the only cases in which the protocol has been applied to date have been infants with severe spina bifida and hydrocephalus.55 Nevertheless in the Netherlands
    
    at least, one response to the Window of Opportunity would be to defer decision-making until greater certainty could be achieved, and then resort to euthanasia if a poor outcome were predicted. CONCLUSION The generic features of the Window of Opportunity are early critical illness with uncertain prognosis and later physiological recovery coinciding with more certain predictions of future impairment. Similar situations are seen in many forms of acute brain injury. In this paper I have focused on the example of NE. Decision theory provides one way to help caregivers manage the conflicting priorities and values at stake. It could be applied to individual patients, though the problem of meta-uncertainty makes it challenging to know what to put into the model. Alternatively decision theory could also be used to generate guidelines like the above flow-chart. In the case of the infant Shaun, described at the start of this paper, early prognostic testing should be seriously considered because of the high pretest probability of severe impairment if he survives. If the test is equivocal or reassuring his parents should consider repeating it subsequently. The analysis in this paper suggests that detailed knowledge of all variables is not necessary. Within a plausible range, the value assigned to different outcomes and the test characteristics do not greatly influence which strategy has the highest expected utility. The other benefit of decision theory is that it highlights the costs of uncertainty. This may prompt further research into improving prognostic tests. But it may also prompt us to reconsider our current attitudes towards the palliative care of newborn infants predicted to be severely impaired. It is the lack of palliative options for such patients that creates the problem of the Window of Opportunity.
    
    51
    
    A. Catlin & B. Carter. Creation of a neonatal end-of-life palliative care protocol. J Perinatol 2002; 22: 184-195.
    52 53
    
    Savulescu.
    
    K. Costeloe. Euthanasia in neonates. BMJ 2007; 334: 912-913.
    54
    
    E. Verhagen & P.J. Sauer. The Groningen protocol--euthanasia in severely ill newborns. N Engl J Med 2005; 352: 959-962.
    55
    
    22 cases were reported to the district attorney’s office in the Netherlands over 7 years (as required by law for any instances of euthanasia).Ibid. There is some reason to think that this is a substantial Author’s Pre-print. 1/10/09
    
    underestimate, and that other cases (that may have included infants with NE and poor predicted outcome) were not reported. A.A. Verhagen & P.J. Sauer. End-of-life decisions in newborns: an approach from The Netherlands. Pediatrics 2005; 116: 736-739. 15
    
    Dominic Wilkinson is supported by an Oxford Nuffield Medical Fellowship, Eric Burnard Fellowship, and Royal Australasian College of Physicians Astra-Zeneca Medical Fellowship. The funders had no involvement in this work. Acknowledgments: I am extremely grateful to Tony Hope and Julian Savulescu for helpful comments on previous versions of this paper. I have also benefited enormously from comments by Toby Ord, Tom Douglas and Angela McLean.
    
    APPENDIX FIGURES Figure A2 Two-way sensitivity analysis for the effect of the disvalue of Late Testing/withdrawal, and probability of survival following late poor prognosis The curves represent testing for infants with different pre-test probability. The area below the curves indicates the points where Early Repeated Testing is preferred. The curve for infants with moderate encephalopathy is not shown (pre test probability = 0.3), as Late Testing is always preferred – regardless of the disvalue of withdrawal, or the probability of survival after late prognosis.
    
    Figure A1 Two-way sensitivity analysis for the effect of pretest probability and early test sensitivity/specificity The lines represent testing with different specificity. The area on the graph above the curves represents the region where Early Repeated Testing is preferred. The area on the graph below the curves represents the points where Late Testing is preferred.
    
    Author’s Pre-print. 1/10/09
    
    16
    
    APPENDIX Modelling and sensitivity analysis for this paper used Excel (Microsoft, Redmond, Mass. USA) Abbreviations Pt = Pre test probability of poor outcome P(sw) = probability of survival after late withdrawal of life support SNe = Sensitivity of early testing SPe = Specificity of early testing SNl= Sensitivity of late testing SPl = Specificity of late testing P (FN)= Probability of False negative test result (survival with poor outcome ) P (TP) = Probability of True Positive test result (death of an infant who would have survived with poor outcome) P (TN) = Probability of True Negative test result (survival with good outcome) P (FP) = Probability of False positive test result (death of an infant who would have survived with a good outcome) V (D) = Value assigned to death = 0 V (POL) = Value assigned to survival with poor outcome V (L) = Value assigned to life with good outcome = 1 V (LW) = Value assigned to late withdrawal For Early testing: The probability of Death (of infant with poor outcome) P (TP) = Pt x SNe P (FN) = (1- SNe) x Pt P (TN) = SPe x (1-Pt) P (FP) = (1- SPe) x (1-Pt) Expected Utility = (P (TP) x V (D)) + (P (FN) x V (POL)) + (P (TN) x V (L)) + (P (FP) x V (D)) = 0 + (P (FN) x V (POL)) + P (TN) + 0 For Late testing: P (TN) = SPl x (1-Pt) P (FN) = (1- SNl) x Pt P (FP) = (1- SPl) x (1-Pt) P (TP) = Pt x SNl Survival after late withdrawal (good outcome) = P(sw) x P (FP) Death after late withdrawal (good outcome) = 1-P(sw) x P(FP) Survival after late withdrawal (poor outcome) = P(sw) x P (TP) Death after late withdrawal (poor outcome) = 1-P(sw) x P(TP) Expected Utility = P (TN) x 1 + (P (FN) x V (POL)) + (P(sw) x P (FP)) x 1 + ((1-P(sw)) x P(FP) x V(LW)) + (P(sw) x P (TP) x V (POL)) + ((1-P(sw)) x P(TP) x V(LW)) Author’s Pre-print. 1/10/09 17
    
    Disutility of late withdrawal is attached only to deaths Ie the value of death becomes V(LW) for those deaths rather than 0 For simplicity I have not discounted survival without impairment (following late testing), or changed the utility of survival with severe impairment (following late withdrawal) One-way sensitivity analysis: The Expected Utility is calculated for Early Testing, Late Testing, No Testing, and Early Repeated Testing with different values of the variable in question. Since the probabilities and values are independent, Expected Utility is represented by a straight line when plotted against any individual variable. The intersection of lines represents the points where testing strategies are equivalent Two-way sensitivity analysis The intersection points for Early Repeated and Late testing are calculated using simultaneous equations derived from calculated Expected Utility For example, using Pt as the dependent variable Expected Utility (Pt) = a + b x Pt Where a and b are constants a = EU (0) [Calculated expected utility for Pre-test probability of 0] b = (EU (0.1) – EU (0))/ 0.1 Intersection of ERT with LT corresponds to the value of Pt when the expected utility of ERT and LT are equal aET + bET x Pt = aLT + bLT x Pt Pt = aLT-aET / bET-bLT
    
    Author’s Pre-print. 1/10/09
    
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