Health status and the cost of intensive care unit treatment

The study of resource allocation at an intensive care unit (ICU) represents a fascinating topic for the economic analysis of the provision of medical care. For patients facing high mortality risks, ICU treatment offers the chance of saving their lives and even providing recovery from very severe health problems. This requires a high utilization of medical care as is witnessed by the fact, for example, that ICU per diem rates typically exceed the rates of other hospital units by far. In brief, at a cost that is both high and certain, ICU treatment may produce potentially large health benefits.

In retrospect, these two facts imply that a substantial part of resources will be spent on patients who are going to die during or immediately after receiving treatment. Thus, ex post decedents have consumed high amounts of medical care but enjoyed no health benefit. It is tempting to interpret this observation as evidence of inefficiency because a cost is incurred without reaping any benefit in return.

However, such a conclusion would be premature as it is based on information that is not available at the time when treatment decisions need to be taken. Hence, it fails to account for the uncertainty that prevails with respect to health outcomes. While uncertainty constitutes a general feature of medical decision making [1], it is particularly important at the ICU. At the time treatment is provided, it is often not clear whether the patient will die or survive [2,3]. Indeed, this may be true even on the day before death occurs [4]. Since the provision of medical care must be evaluated ex ante, it is at least possible that the health benefits accruing to survivors justify the high cost of ICU treatment.

Turning to survivors and decedents of ICU treatment, respectively, a study undertaken by Detsky et al. found the correlation between the survival prognosis and the utilization of medical care to be very different [5]. For survivors, a higher initial chance of living was associated with a lower cost of treatment while the converse was true for decedents. Put differently, the cost of ICU treatment turned out to be high for individuals with an unexpected health outcome. A recent study undertaken at a German hospital corroborates these findings [6].

These empirical findings are puzzling. As argued before, treatment decisions need to be taken at a time where survival or death of the patient is still uncertain. In this sense, utilization of medical care at the ICU cannot differ between survivors and decedents. Why then should the relationship between initial survival prognosis and the average cost of treatment depend on the final outcome of treatment?

Newhouse, in a brief note, judged these results to be consistent with Bayesian learning but offered no detailed explanation [7]. In this editorial, we will argue that the aforementioned results can be explained by a process of rational decision-making at the ICU. Conditional upon current health status, treatment decisions are taken sequentially. Upon receiving treatment at a given stage, a patient may leave the process owing to either death or a substantial improvement in health status. As a result, the length of treatment and, thus, the utilization of medical care will be uncertain.

Sequential decision-making at the intensive care unit

Empirical analyses have focused on the survival probability of an individual. As part of the health outcome, however, this information will not be available at the time where a treatment decision must be taken. On the other hand, since survival constitutes the prime outcome of interest at the ICU, the survival probability of an individual will indicate his/her health status and vice versa. Hence, in a theoretical analysis that attempts to explain the choice of treatment, it seems preferable to consider health status directly.

In line with Michael Grossman’s seminal contribution, suppose that individuals inherit a stock of health capital H, with death occurring as soon as the stock no longer exceeds some positive minimum level (i.e., for H ≤ H_min) [8,9]. For an individual who is alive, his/her health status improves if, and only if, his/her stock of health capital rises. Therefore, as long as H > H_min holds, H also indicates current health status.

At the ICU, medical care is provided in stages. A stage denotes a short interval of time such that a treatment decision, taken at the start, may affect health status at the end of the stage. At each stage I, treatment involves a distribution over final health status H_i which depends on initial health status H_i-1. With respect to final health status, three broad outcomes are possible. For a health status no higher than the minimum level H_min, the patient dies at the end of the stage. If health status exceeds an upper bound (with > H_min), ICU treatment ends and the patient will be referred to another hospital unit. As initial health status H_i-1 rises, the probability of death is taken to decline whereas the probability of the best outcome (i.e., H_i > ) will either increase or remain equal to zero. Lastly, if final health status H_i satisfies H_min < H_i ≤ , ICU treatment will be applied again at another stage.

For a better understanding of the treatment process, two remarks are in order. First, the critical value is taken to be determined by a comparison of ICU treatment with the best alternative treatment that can be provided elsewhere in the hospital. Second, since our analysis is confined to ICU treatment, the provision of medical care at other hospital units is excluded. Thus, for patients who leave the ICU to receive further treatment at some other hospital unit, we consider only part of the treatment episode. While it is possible to cover the entire episode, this would only add complexity without offering additional insight.

As a result, medical care at the ICU is provided by means of a process whose length is uncertain. At the first stage, initial health status H₀ is taken to be low enough for the individual to warrant ICU treatment. Clearly, this implies H₀ < . After receiving treatment at stage I, the process ends if the patient either dies or is referred to another hospital unit. In any other case, final health status H₁ satisfies H_min < H₁ ≤ and the process continues.

Decedents & survivors

Consider now a treatment process such that, conditional upon reaching a stage, both survival and death may occur with positive probability. While the notion of a decedent involves no ambiguity, it is necessary to be more explicit about survivors. More specifically, a survivor is defined as an individual whose health is restored such that she no longer needs ICU treatment. Thus, for a survivor of stage I, final health status H_i must be above . Therefore, a patient whose health status satisfies H_min < H₁ ≤ will neither be a decedent nor a survivor of stage I: at the end of that stage, it is not clear whether he/she will eventually leave the ICU for the graveyard or for further treatment at another hospital unit.

Turning to survivors and decedents, it is useful to begin with identical patients and to look at the various probabilities of dying and surviving, respectively, over the treatment process. At the end of stage I, survivors and decedents obviously started out from the same initial health status H₀. At the second stage, however, initial health status H₁ is uncertain and satisfies H_min < H₁ ≤ . Moreover, with respect to H₁, the composition of decedents and survivors of that stage turns out to be different. In order to see this, consider the impact of a change from a low value H₁⁽¹⁾ to a higher value H₁⁽²⁾ > H₁⁽¹⁾ on health outcomes at that stage. By assumption, the probability of dying will decline whereas the probability of definite survival (i.e., the probability that H₂ > holds) will either remain zero or increase. Thus, for decedents of stage II, the probability of a low initial health status will be high, whereas survivors very likely had a high health status initially.

Applying the same line of argument to later stages, it is straightforward to reach similar conclusions. In sum, for any stage I ≥ 2, decedents are more likely to exhibit a low health status H_i-1 at the beginning of their last ICU treatment while the converse is true for survivors. Putting these results together, the health status of decedents on average will be lower than for survivors throughout the entire treatment process. Note that this statement refers to the two subgroups as a whole. For a decedent of some later stage I ≥ 2, it is possible that his/her health status may have been higher than for a survivor of the same stage at the end of each prior stage. However, such events would be rather unlikely.

Since the same treatment is provided to every ICU patient at each stage of the treatment process, the average cost of treatment for a patient with initial health status H₀ will be determined by the average number of stages. More generally, treatment of a heterogeneous population of patients with average initial health status H₀ requires the same utilization of medical care on average. Returning to the case of identical patients, no general statement can be made with respect to the average treatment costs of decedents and survivors, respectively. More specifically, these depend upon health status at the outset and on the impact of ICU treatment on health status.

The difference in the composition of the two subgroups provides the key to understanding why a higher initial health status H₀ may affect the cost of treatment for decedents and survivors in opposite ways. First, a rise in H₀ will increase the total probability of definite survival due to treatment. Hence, the probability of death will decline and the same holds true for the probability of death after the first stage. If the relative decline in the latter probability turns out to be higher, the probability of dying after the first stage for decedents will decline following a rise in H₀. More generally, if a higher initial health status leads to a shift in the probabilities of dying after each stage such that the reductions at later stages become relatively smaller, decedents will then exhibit a lower probability of dying at early stages and a higher probability of dying later. Obviously, this implies a higher average length of treatment and, thus, a rise in average treatment costs as well.

Turning to survivors, the probability of definite survival after the first stage may rise such that the relative increase exceeds the relative increase in the total probability of survival. In this case, a higher H₀ will increase the probability of survival after the first stage among survivors. More generally, if the rise in H₀ involves a shift such that, for survivors, early survival becomes more likely at the expense of survival at later stages, it will bring about a reduction in average length of treatment. Thus, the average cost of treatment for survivors will decline.

To be sure, this line of reasoning only indicates the possibility that a rise in initial health status may have totally different effects on the average cost of ICU treatment for survivors and decedents. While these relationships do not necessarily arise, it is possible to provide further justification. As argued earlier, both depend on a strong effect of the probabilities of dying and definite survival, respectively, at early stages of the treatment process relative to the effect on the corresponding total probabilities. At the end of the first stage, the impact upon final health status is the result of the rise in H₀ and the provision of ICU treatment. At the end of stage I ≥ 2, final health status will also be affected by ICU treatment provided at subsequent stages. Thus, at later stages, the effect of a higher health status at the outset of the process will be mitigated by a greater number of ICU treatments. In this sense, it is at least plausible that the associated impact on the probabilities of death or survival turns out to be smaller.

For the purpose of illustration, we present a simple example. For the sake of simplicity, we consider only the first two stages of the treatment process. While this precludes a complete analysis of survivors and decedents, it is sufficient to clarify the intuition underlying the line of reasoning exposed above. Let a₁ and a₃ denote the probabilities of death and definite survival at the first stage, respectively, with b₁ and b₃ as the corresponding probabilities for the second stage. In addition, let a₂ indicate the probability for the first stage that another stage of ICU treatment is necessary, with b₂ as the corresponding probability for the second stage. For an initial health status H₀⁽¹⁾ = 20, these probabilities are as follows:

At the first stage, initial health status is low such that ICU treatment involves a very substantial mortality risk and a zero probability of definite survival (i.e., the patient will never leave the ICU after the first stage for some other hospital unit). Nevertheless, there is a positive probability that the patient will receive further treatment at the second stage. At the second stage, both the probability of dying and the probability of definite survival are positive. Thus, decedents may turn up at both stages while definite survival is only possible at the second stage. Leaving out subsequent treatment stages, average length of treatment is equal to two stages for survivors while it must be lower for decedents.

For a higher initial health status H_n⁽²⁾ = 25, let the probabilities be given by:

Now ICU treatment at the first stage involves a lower mortality risk while the probability of definite survival is positive. Moreover, the probability of another stage of ICU treatment has also increased. Conditional upon reaching the second stage, the probability of dying is substantially lower than before whereas the probability of definite survival has gone up. In this sense, the rise in H₀ on average improves initial health status at stage II.

In this example, the change in initial health status affects the average cost of treatment in a very different manner for decedents and survivors. For survivors, average length of treatment declines because, with an initial health status equal to H₀⁽²⁾, definite survival may already occur after the first stage. Turning to decedents, for H₀ = H₀⁽¹⁾ the probability of dying after the first stage is given by (0.7/0.88) ≈ 0.8 while the corresponding probability for the second stage equals (0.18/0.88) ≈ 0.2. Following the rise in initial health status, these probabilities shift to (0.5/0.66) ≈ 0.76 for the first and (0.16/0.66) ≈ 0.24 for the second stage. Thus, for decedents the probability of dying after the second stage has increased. Clearly, this implies that average length and average cost of treatment will also rise.

Explaining medical care utilization at the ICU

Rather than Bayesian learning, the approach sketched earlier stresses the importance of treatment effects that arise from sequential decision-making at the ICU. Owing to the different composition of decedents and survivors with respect to the evolution of health status over the treatment process, a rise in initial health status, or, equivalently, a rise in the initial probability of survival, may plausibly affect the average treatment cost for each subgroup in opposite directions.

It is important to understand that neither of these relationships necessarily indicates a waste of resources from a societal perspective. In particular, this is true for the increase in the average treatment cost of decedents due to a higher initial health status. If the critical value for health status has been determined in a socially optimal manner, these changes precisely reflect rational decision-making at the hospital (i.e., they are consistent with an efficient utilization of medical care).

It is also instructive to consider the impact of a higher initial health status H₀ on the average cost of ICU treatment overall. By definition, this cost represents a weighted sum of the average treatment cost for decedents and survivors, with the weights being given by the probabilities of dying and surviving relating to the entire treatment process at the ICU. As argued earlier, a rise in H₀ implies a higher probability of survival. Suppose that, in addition, average treatment cost declines for survivors but increases for decedents. While the latter effect acts to increase the average cost of ICU treatment overall, the former effects work in the other direction. Hence, the total impact remains ambiguous in general.

In fact, the above example also indicates that a higher initial health status H₀ may well increase the average cost of ICU treatment. More precisely, it exhibits a case that implies the probability of a patient receiving ICU treatment for at least two stages to rise. At the first stage, the reduction in the probability of death exceeds the increase in the probability of definite survival. More generally, the impact on average length of treatment over the entire process will be positive if, conditional upon reaching a stage, the probability of receiving ICU treatment at the next stage is likely to increase.

Our analysis is also relevant for the ‘costs of dying’ approach which has received considerable attention recently [10–12]. This is true even though the approach relates to a somewhat different subject. Relying on the observation that, for a given age, average utilization of medical care for decedents is much higher than for survivors, a reduction in age-specific mortality is hypothesized to imply a reduction in per capita healthcare expenditure. This is based on the assumption that average expenditure for survivors and for decedents, respectively, will not be affected by the change in mortality. Applying a similar line of reasoning to ICU treatment, a rise in initial health status H₀, since it reduces mortality, can be expected to reduce the overall treatment cost on average.

However, as demonstrated previously, a reduction in mortality due to a higher initial health status may have a rather different impact on the average cost of ICU treatment. Moreover, in contrast to the assumption of the ‘costs of dying’ approach, the change in mortality will also affect average treatment cost for survivors and decedents. It is rather easy to explain these differences. Our analysis builds on what might be called the ‘costs of treatment’ approach that takes the utilization of medical care to depend directly on current health status but not on the outcome of treatment. This is in line with an early critique of the ‘costs of dying’ approach [13]. It is also consistent because, applying a basic principle of decision theory, treatment decisions at the ICU are taken to be based only on information that is available at the time when decisions have to be taken.

Financial & competing interests disclosure

The authors have no relevant affiliations or financial involvement with any organization or entity with a financial interest in or financial conflict with the subject matter or materials discussed in the manuscript. This includes employment, consultancies, honoraria, stock ownership or options, expert testimony, grants or patents received or pending, or royalties.

No writing assistance was utilized in the production of this manuscript.