Introduction
A substantial portion of gastrointestinal endoscopy is devoted to diagnosis and treatment
of various potential bleeding sites in the intestinal tract [1]
[2]. Occasionally, even an extensive search using different types of endoscopic and
radiographic procedures fails to identify an unequivocal bleeding source [3]. There is also a subgroup of patients in whom multiple attempts at hemostasis fail
to achieve a lasting resolution. For instance, patients with arteriovenous malformations
(AVMs) spread throughout the gastrointestinal tract, gastric arteriovenous ectasia
(GAVE or watermelon stomach), and radiation proctitis frequently continue to bleed
even after multiple sessions of thermo-ablation. Other patients who bleed secondary
to chronic use of medical anticoagulation, cannot be taken off their medication because
of their continued risk for thromboembolism. An excessive number of futile endoscopic
procedures may be spent on trying to resolve the gastrointestinal bleeding and achieve
lasting hemostasis [4]. If bleeding only occurs at a small rate and patients present with chronic anemia
rather than life-threatening episodes of acute and massive blood loss, expectant follow-up
represents a management option that is an alternative to continued endoscopic intervention.
Such patients can have their blood count monitored on a regular basis and receive
occasional blood transfusions as needed. The current decision analysis was designed
to answer the question of when to continue or abandon the quest to find and treat
an elusive gastrointestinal bleeding source.
Materials and methods
A decision tree was used to model the choice between a continued endoscopic search
versus expectant management with repeat transfusions in patients with gastrointestinal
bleeding from an unknown or untreatable source [5]
[6]. In the decision tree, the initial decision node between continued endoscopy and
expectant management was represented by a small square on the left ([Fig. 1]). All subsequent outcomes were governed by chance. Each branch following a chance
node was assigned a probability value, with all probability values of branches originating
from the same chance node adding up to 100 %. The outcomes of decisions or chance
events were represented by blue rectangles. Each outcome was associated with costs.
The outcome of a chance node was calculated by multiplying the individual costs with
their respective probability of occurrence and then adding them up at the corresponding
branching point. Ultimately, those decisions were favored that resulted in the least
costs. Instead of calculating the overall costs, in a threshold analysis one can also
calculate the probability values for the possible outcomes that would shift the decision-making
against or in favor of one of the two initial decisional options. In general, a low
threshold probability was associated with a preferred management option [7]
[8].
Fig. 1 Decision tree comparing the outcome of continued endoscopic search versus expectant
management with repeat transfusions in a patient with gastrointestinal bleeding from
an unknown source.
Results
The decision tree in [Fig. 1] illustrates the decision in favor of continued endoscopy or continued transfusions.
Each endoscopy can be successful and stop the bleeding or be unsuccessful and lead
to yet another subsequent endoscopy. The respective probabilities for each set of
successful and unsuccessful endoscopy are pse
and pe
, respectively, where pse + pe = 1. A successful outcome with no bleeding is assumed to cost nothing. The cost of the
first endoscopy is E. The expected cost of the second endoscopy is pe · E, the expected cost of the third endoscopy is pe
2 · E, the expected cost of the fourth endoscopy is pe
3 · E, and so forth. The overall expected costs of the decision in favor of endoscopy are:
A simple rule of analysis was used for the transition from the geometric progression
on the left and its summary by the Σ-sign to the subsequent fraction on the right
[9].
The respective probabilities of a successful and unsuccessful transfusion are pst
and pt
, respectively, where again pst + pt = 1. With T representing the cost associated with each individual transfusion, the overall
expected costs of the decision in favor of expectant management with continued transfusions
are:
For a decision in favor of continued endoscopy as opposed to continued transfusions,
the expected costs of the former should be less than those of the latter:
The last expression yields a threshold for the success rate of endoscopy to render
continued endoscopy the preferred management strategy. For instance, if each endoscopy
costs on average five to 10 times more than each transfusion, its associated probability
of success (without further bleeding or need for any future endoscopy) also needs
to be at least five to 10 times higher than the probability of success associated
with expectant management using repeat transfusions.
Assuming, for instance, that endoscopic therapy costs $ 1200 per session and transfusion
therapy $ 200, the ratio between the two cost items equals E/T = 6. Moreover, assuming a probability for successful transfusion therapy of pst
= 5 %, endoscopy would need to be associated with an expected success probability
of pse
≥ 6 · 5 % = 30 % to become the preferred management strategy. [Fig. 2] shows how the threshold for the expected success rate of continued endoscopy varies
with the assumption of success probability for transfusion therapy, as well as different
cost ratios for endoscopy over transfusion. The probability for successful transfusion
therapy increases the expectation for successful endoscopy. Similarly, increasing
costs of endoscopy compared to transfusion also leads to increasing expectation for
successful endoscopy.
Fig. 2 Threshold probability for success rate of endoscopy (pse
) as function of varying success probability for transfusion therapy (pst
), as well as varying cost ratio for endoscopy over transfusion (E/T).
As a rule, the sequence of continued endoscopies should be abandoned when the expected
probability for lasting success associated with the next endoscopy no longer exceeds
its threshold probability. In clinical practice, however, one would not necessarily
need to engage in such calculation. As indicated by the equation from above, the clinician
could simply compare the estimated cost ratio (of continued endoscopy to transfusion
therapy) with the expected probability ratio (of the two management options) and abandon
endoscopy if the cost ratio exceeds the probability ratio.
Discussion
A decision tree with a threshold analysis has been used to model when to discontinue
a sequence of repeated attempts to diagnose and treat an elusive gastrointestinal
bleeding source. The decision in favor or against a continued endoscopic sequence
depends on the costs of the two competing management options and their associated
chances of success. The analysis reveals that for a positive decision in favor of
continued endoscopy, its probability of success in achieving lasting hemostasis needs
to exceed the success probability of expectant management by a greater amount than
the costs of endoscopy exceed those of expectant management. This outcome of the decision
analysis largely confirms what one would expect based on clinical intuition. The underlying
principle is readily applicable as a rule of thumb for many situations in management
of patients with ongoing chronic gastrointestinal bleeding.
How would the proposed rule of thumb be applied in clinical routine? A low chance
of endoscopic hemostasis would argue in favor of expectant management. A high cost
of endoscopy and low cost of expectant management would raise the threshold for endoscopic
intervention and also speak in favor of expectant management. Old age and serious
comorbid conditions would render endoscopy riskier and thus costlier. A low rate of
gastrointestinal bleeding and infrequent utilization of transfusion in instances of
a shortened life expectancy would reduce overall costs of expectant management and
again raise the threshold for endoscopic intervention.
Like any mathematical model of a complex clinical problem, the current analysis had
to rely on several simplifying assumptions. For instance, it is assumed that the probability
for success or failure stays the same over time, when in reality these probability
values may vary among consecutive bleeding episodes. The probability for success is
likely to be highest at the beginning and drop after multiple prior attempts that
failed at localizing the bleeding source or achieving hemostasis. The analysis does
not consider the influence of time and the length of time intervals between consecutive
medical interventions. All endoscopic procedures are assumed to cost the same, but
different types of endoscopic interventions, such as esophagogastroduodenoscopy, colonoscopy,
double balloon enteroscopy, or video capsule endoscopy, with different costs are frequently
applied in sequence. Instances of repeat gastrointestinal bleeding could be associated
with additional costs resulting from physician visits, laboratory testing or other
diagnostics, hospital admission, and potential adverse events of medical intervention.
A similar argument would also apply to expectant management with its use of repeat
blood transfusions in instances of low blood count. The costs of endoscopy and expectant
management used in the current analysis should, therefore, be considered more reflective
of average costs associated with individual bleeding episodes leading to repeat endoscopy
or transfusion rather than just the costs of the procedure itself or the blood transfusion
alone.
Conclusion
In conclusion, the present decision analysis provides a framework for deciding on
when to continue or abandon the endoscopic search for an elusive gastrointestinal
bleeding site. On the one hand, the search should be discontinued if the expected
costs of additional endoscopic procedures are high compared with expectant management.
On the other hand, the search should be continued if the probability for achieving
lasting hemostasis is high. This framework may provide useful guidance in managing
this common clinical conundrum.
