Management of Radial Nerve Palsy Associated With Humeral Shaft Fracture: A Decision Analysis Model
When managing radial nerve palsy associated with a humerus fracture, both surgeon and patient must balance the risks and benefits of performing an invasive surgical procedure to address a functional deficit that is likely, but not certain, to recover with nonsurgical management. The purpose of this study was to better understand the determinants of optimal management strategy using expected-value decision analysis. Probabilities for the occurrences of the potential outcomes after initial observation or early surgery were determined from a systematic review of the literature. Scores for these outcomes were obtained from a questionnaire on patient preferences completed by 82 subjects without a history of humerus fracture and radial nerve palsy and used in the model as a measure of utility. A decision tree was constructed, fold-back analysis was performed to determine optimal treatment, and sensitivity analyses were used to determine the effect on decision making of varying outcome probabilities and utilities. Observation was associated with a value of 8.4 and early surgery a value of 6.7 given the outcome probabilities and utilities studied in this model, making observation the optimal management strategy. When parameters were varied in sensitivity analysis, it was noted that when the rate of recovery after initial observation falls below 40% or when the utility value for successful early surgery rises above 9.4, early surgery is the preferred management strategy. Initial observation was the preferred strategy. In clinical settings in which the likelihood of spontaneous recovery of nerve function is low or when an informed patient has a strong preference for surgery, early surgery may optimize outcome. Economic and Decision Analysis II.
Management of Radial Nerve Palsy Associated With
Humeral Shaft Fracture: A Decision Analysis Model
Julius Bishop, MD, David Ring, MD, PhD
Purpose When managing radial nerve palsy associated with a humerus fracture, both surgeon
and patient must balance the risks and beneﬁts of performing an invasive surgical procedure
to address a functional deﬁcit that is likely, but not certain, to recover with nonsurgical
management. The purpose of this study was to better understand the determinants of optimal
management strategy using expected-value decision analysis.
Methods Probabilities for the occurrences of the potential outcomes after initial observation
or early surgery were determined from a systematic review of the literature. Scores for these
outcomes were obtained from a questionnaire on patient preferences completed by 82
subjects without a history of humerus fracture and radial nerve palsy and used in the model
as a measure of utility. A decision tree was constructed, fold-back analysis was performed
to determine optimal treatment, and sensitivity analyses were used to determine the effect on
decision making of varying outcome probabilities and utilities.
Results Observation was associated with a value of 8.4 and early surgery a value of 6.7 given the
outcome probabilities and utilities studied in this model, making observation the optimal man-
agement strategy. When parameters were varied in sensitivity analysis, it was noted that when the
rate of recovery after initial observation falls below 40% or when the utility value for successful
early surgery rises above 9.4, early surgery is the preferred management strategy.
Conclusions Initial observation was the preferred strategy. In clinical settings in which the likelihood
of spontaneous recovery of nerve function is low or when an informed patient has a strong preference
for surgery, early surgery may optimize outcome. (J Hand Surg 2009;34A:991–996. © 2009
Published by Elsevier Inc. on behalf of the American Society for Surgery of the Hand.)
Type of study/level of evidence Economic and Decision Analysis II.
Key words Decision analysis, fracture, humerus, nerve palsy, radial nerve.
HE OPTIMAL MANAGEMENT strategy for radial
nerve palsy in the setting of a humeral shaft
fracture remains controversial.
early surgical exploration of the nerve cite a technically
easier procedure, the ability to immediately classify the
nerve injury, and a chance to stabilize the fracture and
soft tissues as important advantages.
observation herald the high rate of spontaneous recov-
ery and caution against the morbidity of surgical treat-
ment of an injury that would have recovered with ex-
Deﬁnitive high-quality data
are lacking, resulting in substantial variation in opinion
regarding the optimal management strategy.
Expected-value decision analysis is a methodologi-
cal tool that is based in gaming theory and allows for
the quantitative analysis of decision making under con-
ditions of uncertainty.
The process of expected-
value decision analysis involves the creation of a deci-
From the Department of Orthopaedic Surgery, Massachusetts General Hospital, Boston, MA.
Received for publication July 20, 2008; accepted in revised form December 24, 2008.
Support was received from Small Bone Innovations, Smith and Nephew, Wright Medical, Tornier,
Corresponding author: David Ring, MD, PhD, Department of Orthopaedic Surgery, Massachu-
setts General Hospital, Yawkey Center, Suite 2100, 55 Fruit Street, Boston, MA 02114; e-mail:
© Published by Elsevier, Inc. on behalf of the ASSH. 䉬 991
sion tree to structure the decision problem, the
determination of outcome probabilities and utilities,
fold-back analysis to determine the optimal decision-
making strategy, and sensitivity analysis to determine
the effect of varying outcome probabilities and utilities
on decision making. In this way, decision analysis may
allow the clinician and the patient to optimize decision
making based on best-available evidence and patient
preferences. It also helps to determine the most impor-
tant factors affecting management strategies and the
decision-making process, which may not always be
intuitive and can help determine the best questions to
address in future research.
Decision analysis requires simpliﬁcation of a com-
plex clinical situation into a simple model. It also re-
quires that the clinical scenarios represented in the
model can be communicated to the general public with
sufﬁcient clarity that they can assign utilities to various
outcomes. Our approach was based on an interpretation
of the existing literature that concludes that nearly all
intact nerves recover, thereby reserving nerve grafting
for lacerated nerves and tendon transfers for any nerve
that does not recover no matter the prior treatment.
The purpose of this study was to use expected-value
decision analysis to determine the optimal management
strategy—initial observation or early surgical explora-
tion—for a humerus fracture with an associated radial
nerve palsy according to the best available data and
patient preferences based on survey results while also
determining the factors with greatest inﬂuence on the
MATERIALS AND METHODS
Institutional review board approval was obtained for this
study. Analysis was performed using statistical software
(the Treeage Pro software package; Treeage Software,
Outcome probabilities were determined by review of
the literature for articles regarding humeral shaft frac-
ture and radial nerve palsy. This body of literature was
recently summarized in a review by Shao et al.
authors systematically searched the literature and iden-
tiﬁed 391 citations relevant to humerus fracture and
radial nerve palsy. Of these, 35 studies involving 1045
patients met inclusion criteria and were used to deter-
mine the likelihood of recovery of radial nerve function
after initial observation, early surgery, and late surgery
for failed initial observation. These authors synthesized
data published as early as 1967 and as recently as 2004.
We updated this search using the same inclusion criteria
and identiﬁed no additional studies meeting inclusion
criteria. It was assumed that the probability of bony
union was the same in the surgical and nonsurgical
Utilities represent patient preferences for various dis-
ease states. Outcome utility values were obtained from
82 adult subjects at a major orthopedic clinic. These
were not patients but rather healthy escorts accompa-
nying patients at the time of a clinic visit. Subject ages
ranged in age from 18 to 82 years, and any subject with
a history of “arm fracture” was excluded. The same
survey was also collected from 20 orthopedic residents
who served as an “expert panel” of people knowledge-
able about the various outcomes. The questionnaire
posed scenarios for the different outcomes and asked
subjects to rate these outcomes on a scale from 0 to 10,
where 0 represented the worst possible outcome and 10
represented the best possible outcome (Appendix; this
appendix can be viewed at the Journal’s web site at
www.jhandsurg.org). The scale was anchored at 0 by
the outcome of late surgical intervention followed by no
recovery of nerve function and was anchored at 10 by
the outcome of nonsurgical treatment followed by re-
covery of nerve function.
Decision tree and fold-back analysis
A decision tree was constructed with 1 decision node, 3
chance nodes, and 5 terminal nodes (Fig. 1). The deci-
sion tree demonstrates 2 differing management strate-
gies for radial nerve palsy in the setting of ipsilateral
humeral shaft fracture. The decision node divides into 2
branches: initial observation and early surgical explo-
ration. Both branches are followed by various chance
nodes, each one terminating in a discrete clinical out-
come. Per convention, utility data were placed to the
right of the terminal nodes, and probability data were
placed under the terminal nodes.
Fold-back analysis was performed to identify the
optimal strategy. This involves multiplying each out-
come utility by its associated probability, providing an
“expected value” for each clinical end point. The ex-
pected values for each end point can then be summed
for a given management strategy and the ultimate ex-
pected values of the different strategies compared. The
management strategy associated with the highest ex-
pected value is optimal for the given outcome utilities
992 HUMERUS FRACTURE AND RADIAL NERVE DECISION ANALYSIS
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One-way sensitivity analysis was performed to model
the effect on decision making of varying the utility of
recovery after early surgery (Fig. 2) and the probability
of recovery after initial observation (Fig. 3). These were
the 2 variables found to affect the decision-making
strategy within their clinically plausible ranges.
Two-way sensitivity analysis was performed to model
the effect on decision making of simultaneously
varying both the utility of recovery after early sur-
gery and the probability of recovery after watchful
waiting (Fig. 4).
Finally, 1-way sensitivity analysis was also performed
to model the prospect of early tendon transfer surgery
after failed initial observation. This was done by
setting the probability of “recovery” at 100% and
then varying the utility of this outcome (Fig. 5).
Outcome probabilities and utilities
For initial nonsurgical treatment, the probability of
recovery after observation was 72% (315 of 435).
For patients who failed to recover after initial
observation, there was a 69% (72 of 104) like-
lihood of recovery with late nerve surgery, leaving
a 31% (32 of 104) probability of no recovery at the
end of treatment. After early surgery, the proba-
bility of recovery was 85% (188 of 222), leaving a
15% (34 of 222) probability of no recovery at the
end of treatment.
Recovery after late nerve surgery was found to
have a mean patient-derived utility of 6.4 (SD 2.5).
Recovery after early nerve surgery had a mean
utility of 7.4 (SD 2.3), and failure to recover after
early nerve surgery had a mean utility value of 2.7
FIGURE 1: The decision tree for observation versus early surgery for humerus fracture associated with radial nerve palsy.
Decision nodes are represented by a square, chance nodes are represented by a circle, and terminal nodes are represented by a
triangle. Mean outcome utilities (0 –10) are listed to the right of the terminal node. Outcome probabilities (0 –1) are listed under
the terminal node title.
FIGURE 2: One-way sensitivity analysis for the utility of successful
early surgery (“uSuccessfulEarlySurgery”). The probability of suc-
cessful early surgery is varied on the x axis. The lines represent the
expected value (EV) for the decision to manage with observation and
the decision to perform early surgery. Above the threshold value (a
utility of early surgery of 9.4), early surgery is favored.
FIGURE 3: One-way sensitivity analysis for the probability of
recovery with initial observation. The probability of recovery
is varied on the x axis. The lines represent the expected value
(EV) for the decision to manage with observation and the
decision to perform early surgery. Below the threshold value
(a probability of recovery of with observation of 40%), early
surgery is favored.
HUMERUS FRACTURE AND RADIAL NERVE DECISION ANALYSIS 993
Vol A, July–August
(SD 2.6) (Fig. 1). These utilities were not signiﬁ-
cantly different (p ⬎ .05) from the values derived
from the survey of orthopedic residents.
Fold-back analysis identiﬁed initial observation as the
optimal decision strategy. The expected value for ob-
servation was 8.4, and the expected value of early
surgery was 6.7 (Fig. 1).
One-way sensitivity analysis was performed to
model the effect on decision making of varying the
utility of recovery after early surgery (Fig. 2) and the
probability of recovery after observation (Fig. 3). Early
surgery was favored when the utility of recovery after
early surgery was greater than 9.4 or when the proba-
bility of recovery after initial observation was less than
Two-way sensitivity analysis was performed to
model the effect on decision making of simultaneously
varying both the utility of recovery after early surgery
and the probability of recovery after observation. The
preferred decision path for the range of values of both
“utility of recovery after early surgery” and “probability
of no recovery after initial observation” is demonstrated
graphically by the shaded areas in Figure 4.
The model exploring early tendon transfer after
failed initial observation showed that when utility for
tendon transfer is greater than 4.4, this becomes the
preferred strategy compared with that of late nerve
surgery (Fig. 5).
The management of radial nerve injury associated with a
closed fracture of the humeral diaphysis is debated.
The decision between initial surgical or nonsurgical
treatment of the radial nerve injury lends itself well
to expected-value decision analysis because of well-
deﬁned treatment options and relatively discrete out-
comes. The principal advantage of observation is the
fact that most nerves are intact and recover, and the
principal advantage of early surgery is that it may
provide the best opportunity for nerve recovery when
a nerve laceration is identiﬁed and grafted in a timely
Our decision analysis determined that initial obser-
vation is the optimal decision path, given the outcome
probabilities derived from the literature and the utilities
obtained from surveys. This ﬁnding is in accordance
with a number of previous studies addressing this issue.
Perhaps more importantly, our analysis identiﬁed the
important variables in the decision-making process.
Sensitivity analysis determined that early exploration
FIGURE 5: A The decision tree for nerve surgery versus
tendon transfer for persistent radial nerve palsy after initial
observation. Decision nodes are represented by a square,
chance nodes are represented by a circle, and terminal
nodes are represented by a triangle. Mean outcome utilities
(0 –10) are listed to the right of the terminal node. Outcome
probabilities (0–1) are listed under the terminal node title.
B One-way sensitivity analysis for the utility of tendon
transfer (“uTendonTransfer”) for persistent radial nerve palsy
after initial observation. The utility of tendon transfer is varied
on the x axis. The lines represent the expected value (EV) for
the decision to perform nerve surgery and the decision to
perform tendon transfer. Above the threshold value (a utility
for tendon transfer of 4.4), tendon transfer surgery is favored.
FIGURE 4: Two-way sensitivity analysis for the probability of
recovery after initial observation (x axis) versus the utility of
successful early surgery (“uSuccessfulEarlySurgery”; y axis).
The labeled areas on the plot represent the preferred decision
path for the range of values of both the probability of recovery
with observation (x axis) and the utility of successful early
surgery (y axis).
994 HUMERUS FRACTURE AND RADIAL NERVE DECISION ANALYSIS
Vol A, July–August
was favored when the probability of recovery after
initial observation was less than 40%. In certain scenar-
ios, such as open humerus fracture, the probability of
nerve laceration exceeds 40%, and early exploration
would be the optimal decision path.
other scenarios that fall outside the purview of this
decision analysis might favor early exploration of the
radial nerve: for instance, when surgical treatment of
the humerus fracture is elected for other reasons (eg,
concomitant forearm injury or “ﬂoating elbow”), then
advantage should be taken of this opportunity to exam-
ine the dysfunctional radial nerve.
Sensitivity analysis also determined that early explo-
ration was favored when the utility for recovery after
early surgery was greater than 9.4. There are certainly
some “risk-taking” patients in clinical practice who opt
for plate ﬁxation over closed treatment of uncompli-
cated humerus fractures, and these same patients would
likely favor exploration in the setting of radial nerve
Finally, we also used our model to explore the role of
tendon transfers rather than nerve surgery in cases
where radial nerve function fails to recover after obser-
vation. Tendon transfers for radial nerve dysfunction
provide rapid and reliable return of hand opening but
cannot restore sophisticated extensor tendon func-
Sensitivity analysis in this case indicated that
assuming a 100% recovery rate, tendon transfer is the
preferred management strategy when utility for tendon
transfer type function is greater than 4.3. A strategy of
initial observation followed by tendon transfer if nerve
function fails to return may be particularly appealing to
lower-demand patients who value a rapid and reliable
recovery and do not need sophisticated extensor func-
tion for their daily activities. Appropriate patient coun-
seling is critical to ensure that tendon transfer is seen as
a treatment alternative rather than a failure in this set-
The limitations of decision analysis involve the
methods by which probabilities and utilities were ob-
tained. In general, the most accurate, stable, and robust
estimates of outcome probabilities are derived from a
meta-analytic synthesis of randomized clinical trials,
the highest level of clinical evidence. In this analysis,
we obtained outcome probabilities from a quantitative
review of the literature. No randomized trials or even
comparative studies were available for analysis. Some
studies were more than 40 years old and probably do
not reﬂect modern management strategies.
Determination of outcome utility also has limita-
tions. Utility is a subjective value that an individual
places on the speciﬁc outcome. This can be very difﬁ-
cult to operationalize and to quantify. In general, the
most robust estimates of patient-derived utilities are
derived from complex qualitative methods, such as the
standard reference gamble or time trade-offs, in which
patients are asked to gamble or choose between health
states usually referenced to death. In this study, we
determined patient-derived utility values from a direct
scaling method using a Likert scale because of the
complexity of the standard reference gamble and the
difﬁculty of referencing to death for humerus fracture
with radial nerve palsy. Although use of a direct
scale for the determination of utility values is less
rigorous than the standard reference gamble, this
technique has been corroborated methodologically
and has distinct advantages in terms of feasibility and
Adult escorts of patients attending an
outpatient clinic are a sample of convenience that is
probably a good representation of the general public,
but this is debatable. Although speciﬁc scenarios
were posed, the individuals completing the question-
naires may not have had deep insight into the sub-
tleties and implications of the various disease states
and treatments. Recognizing this, we also distributed
the utility survey to 20 orthopedic residents. There
were no signiﬁcant differences (p ⬎ .05) between the
responses of the residents and those of the subjects,
suggesting that our scenarios provided adequate in-
sight into the various described clinical conditions.
Regardless of how outcome probabilities and utilities
are determined, they are considered point estimates
in decision analysis, and sensitivity analyses are
therefore performed to assess how decision making
changes over a range of these values, and our ap-
proach is reasonable.
The results of this study may help us to better un-
derstand the decision between initial observation and
early surgical exploration that is faced by a patient with
a humerus fracture and associated radial nerve palsy.
For a given individual patient, the optimal strategy
depends not only on the probabilities of the various
outcomes but also on personal preference. Thus, there
may not be one right answer for all patients. Risk-taking
patients with a high utility for successful early surgery
would likely choose early exploration, whereas risk-
averse patients with a lower utility even for successful
surgery would not. Some low-demand patients who
value quick and reliable recovery at the expense of
sophisticated hand function may even favor tendon
transfer when there is no recovery after a period of
initial observation. We therefore advocate a model of
shared decision making in which the physician and the
patient are jointly involved in the medical decision-
HUMERUS FRACTURE AND RADIAL NERVE DECISION ANALYSIS 995
Vol A, July–August
making process, considering both outcome probabilities
and patient preferences.
Ongoing research efforts should focus on methods of
making an early distinction between nerves that will
recover spontaneously and those that will not in this
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Patient Utility Questionnaire: Humerus Fracture/
Radial Nerve Injury
Date: __________ Age: ____ Gender (M/F): ____
With your help, this survey will deﬁne the relative
desirability of various results of treatment of a
fracture of the upper arm (broken humerus bone)
combined with an injury to the radial nerve. For the
purposes of this survey, you should imagine that you
have this injury.
The humerus bone usually heals in about 2 to 3
months without surgery and also does well if surgery
is indicated. For the purposes of this survey, please
assume that the fracture heals and causes you no
The radial nerve controls the muscles that open
your hand and lift your wrist. If your radial nerve
was injured, you would develop a “wrist drop,”
meaning that you would not be able to lift your wrist
or open your hand. There would also be a numb area
on the back of your hand and wrist, but your
ﬁngertips would all feel normal.
The nerve usually recovers on its own over 6 to 12
months, but sometimes surgery is needed. Surgery
leaves a long scar on your arm, and there is a small
risk of infection, medical problems from anesthesia,
and additional nerve injury. Two types of surgery are
1. Nerve surgery. The surgeon looks at the nerve to
see if it is damaged. When the surgeon ﬁnds nerve
damage, it is repaired by taking another nerve
from your lower leg, which leaves you perma-
nently numb on the side of your foot. You can
walk and play sports ﬁne, it just feels a little
strange. The radial nerve usually takes a year or
more to recover after this surgery.
2. Tendon transfer surgery. Surgery can make your
hand and wrist open again by moving some of
your arm muscles to different positions. While the
hand will open and close after this surgery, it
won’t allow you to play piano and do other so-
phisticated hand functions. Typing will be possi-
ble, but slower.
For each possibility/scenario, please choose a
number on the scale from 0, representing the worst
possible result or outcome of treatment of the nerve
injury, to 10, representing the best possible result of
treatment of the nerve injury. Please make all of your
ratings with respect to the best and worst possible
results as we have deﬁned them in items 1 and 5.
1. Your nerve recovers completely on its own
within 6 to 12 months of the injury, without any
treatment or surgery.
2. Four weeks after the injury, the nerve has not
recovered. You have nerve surgery. The nerve
recovers over the next year.
3. Four weeks after the injury, the nerve has not
recovered. You have nerve surgery. Over a
year later there is no recovery and you have a
second, tendon transfer surgery.
4. Six months after the injury, the nerve has not
recovered. You have nerve surgery. The nerve
recovers over the next year.
5. Six months after the injury, the nerve has not
recovered. You have nerve surgery. Over a
year later there is still no nerve recovery and
you have a second, tendon transfer surgery.
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