Asymmetric Injury in Carpal Tunnel Syndrome
C. J. Zheng, MD, PhD
Department of Occupational and Environmental Medicine
Regions Hospital
University of Minnesota
Saint Paul, Minnesota
Tel: 651-254-3443
Pager: 651-629-1672
Email: zhen0075@umn.edu
Introduction
Carpal tunnel syndrome (CTS) is a median-nerve-compression neuropathy at the wrist that
commonly affects middle-aged women. Early symptoms include intermittent hand paresthesias,
pain, nocturnal awakening and symptom aggravations while driving or reading. A number of
medical conditions (e.g., diabetes mellitus, pregnancy, rheumatoid arthritis, thyroid disorder) and
work-related factors (e.g., repetitive upper-extremity overuse) can increase the risk for CTS. The
estimated medical costs related to CTS are high and exceed $1 billion annually (Patterson and
Simmons 2002).
The mechanistic pathways that underline the development of CTS are not clear and the
importance of work-related risk factors remains contentious (Thurston 2000). Some experts
believe that preexisting medical conditions are more essential and work-related factors merely
enhance the manifestation of CTS. Others consider that work-related factors are more important
and proper implementation of ergonomic programs can prevent the occurrence of most CTS
cases. Many people would agree that more quality data collected with better research
methodology are needed to resolve the argument.
A brief review of the literature suggests that failure to distinguish between unilateral CTS versus
bilateral CTS is a common methodology weakness (Stanek and Pransky 1996). Most
investigators have regarded the laterality issue as an inconvenience and adopted an approach that
typically combines together unilateral CTS with bilateral CTS. This method, however, can be
very misleading. This is not only because it discards potentially useful information, but also
because unilateral CTS may not possess the same set of risk factors as bilateral CTS. Other
researchers have used an equally problematic approach that treats each affected hand separately
as the basic unit for outcome definition. This method ignores the fact that the paired hands from
a given patients are statistically correlated. If a CTS patient has her right hand affected already,
for example, her risk for left-hand neuropathy cannot be properly predicted by a populationbased model.
In this short communication, I plan to consider a few simple probability models that can be used
to describe the laterality patterns. Possible applications in CTS data analysis are also discussed,
though in a fairly rudimentary manner. My purpose is to illustrate that a new standard may be
needed to propel the advance of CTS etiologic research.
Study Design
Probability model construction and study design are interrelated. To begin my discussions,
however, I will assume that a cohort study design is always preferred. At-risk people who enter
into a CTS follow-up study are initially free of CTS. At the end of the study period, most of the
study subjects may remain free of CTS, but some of them are expected to develop CTS. Careful
examination of the covariates and the outcomes from the cohort study is expected to reveal a
pattern of correlations and possible etiologic clues.
Outcome Definition
Probability models are useful tools in epidemiological studies. They can be used to conceptualize
a study design, model the resultant data set and predict the outcomes. A proper definition of the
study outcome is, however, a prerequisite for good model construction.
Definition I: Dichotomous Outcomes
1) CTS - No
2) CTS - Yes
Comments: Dichotomous outcomes are very common in epidemiological studies of diseases
(healthy versus ill) or injuries (alive versus dead). Because this simple definition does not
distinguish unilateral versus bilateral CTS cases, it is probably problematic for CTS research.
Definition II: Trichotomous Outcomes
1) No CTS
2) Unilateral CTS
right or left hand is affected
3) Bilateral CTS
both hands are affected
Comments: This definition is considered an improvement over the dichotomous-outcome
definition. Notably, however, it fails to distinguish between unilateral left-hand CTS versus
unilateral right-hand CTS.
Definition III: Tetratomous Outcomes
1) No CTS
2) RT CTS
right hand is affected only
3) Bilateral CTS both hands are affected
4) LT CTS
left hand is affected only
Comments: A minimum requirement for CTS study?
Definition IV: Polytomous Outcomes
1) No CTS
2) RT only
right hand is affected only
3) RT>LT
right hand is more severely affected than left hand
4) RT=LT
right hand is equally affected than left hand
5) RT<LT
right hand is less severely affected than left hand
6) LT only
left hand is affected only.
Comments: The polytomous-outcome definition takes into account the severity of CTS and is
chosen as the basis for the ensuing discussions. A few mathematical notations are also worth
introducing here. First, let the random variable Y denote the outcome states of CTS. Here Y
takes the numerical values ( 0,1,2,3,4,5 ) and has the following relationship with the CTS outcome
states:
CTS outcome state
Random variable Y
No CTS RT only RT>LT RT=LT RT<LT LT only
0
1
2
3
4
5
Second, the corresponding probability mass function is denotable by
Pr[Y = i | x1 , x2 ,..., xn ] , i = 0,1,2,3,4,5 .
Here
∑ Pr[Y = i | x , x ,..., x
1
2
n
] = 1 . Also the covariates, x1 , x2 ,..., xn (or x j , j = 1,..., n ), are
i
assumed to be given. This is consistent with the presumed cohort study design. That is, all at-risk
subjects are initially free of CTS and a set of covariates ( x1 , x2 ,..., xn ) are available from the
baseline survey. The outcome states are re-assessed at the end of the follow-up study. Within this
context, Pr[Y = i | x1 , x2 ,..., xn ] can also be viewed as a transitional probability defined over the
study interval [ 0 , T ]:
Pr[Y = i | x1 , x2 ,..., xn ] = Pr[Y (T ) = i | Y (0) = 0; x1 , x2 ,..., xn ] .
Definition V: Continuous Outcomes
1) RT CTS score
right-hand examination score (e.g., nerve conduction velocity)
2) LT CTS score
left-hand examination score
Comments: Using paired continuous variables to characterize CTS status can be a good
alternative outcome definition. Although I will not consider this possibility in details, it should
be noted that the approach may significantly reduce the sample size required for a risk factor
study.
Multi-State Probability Model I: Multinomial Logistic Regression
In the next two sections, I will consider the issue of how to define the quantitative relationship
between Y and covariates x1 , x2 ,..., xn . The multinomial logistic regression model is a common
choice for structuring the functional dependence of a polytomous categorical variable Y on
covariates x1 , x2 ,..., xn :
Pr[Y = i | x1 , x2 ,..., xn ] =
e
αi +
∑e
∑ βij x j
j
αi +
∑ β ij x j
.
j
i
Here i = 0,1,2,3,4,5 . This model is a direct generalization of the traditional dichotomous logistic
regression analysis. It is familiar to many epidemiologists and also has the advantage that
modeling analysis can be easily done using available commercial software programs (e.g., SAS,
SYSTAT).
Multi-State Probability Model II: 4-Hit Regression
The above multi-state logistic regression model also has some disadvantages. First, it has too
many parameters to estimate and therefore requires a very large study sample. Second, it does
not have a symmetrical structure and treats potentially supporting information from left-sided
versus right-sided unilateral CTS incoherently. To overcome these problems, I have also
considered a 4-hit model (based on simple binomial trials; “4 hits” = “4 trials”):
Pr[Y = 0 | x1 , x2 ,..., xn ] = 1 − r
 4  i −1
[ fp1 (1 − p1 ) 5−i + (1 − f ) p 25−i (1 − p2 ) i −1 ]
Pr[Y = i | x1 , x2 ,..., xn ] = r 
 i − 1
(i ≥ 1)
p1 = g ( x1 , x2 ,..., xn ) , p2 = h( x1 , x2 ,..., xn )
Here the model assumes that there exist two subsets of CTS patients:
1) One set of patients (the proportion is f ) have a systemic medical conditions (e.g.,
hypothyroidism) and tend to develop a symmetrical type of symptoms (the injury probability
during each hit/trial is p1 ; note that if the symmetrical-injury assumption is true, p1 should be
equal or close to 1 / 2 ).
2) The other set of patients (the proportion is 1 − f ) have a work-related etiology and tend to
develop an asymmetrical injury (the injury probability is p 2 which should be biased toward 1;
i.e., favoring the dominant hand).
3) The covariates ( x1 , x 2 ,..., x n ) are incorporated into the model by assuming that they affect the
injury probabilities only ( p1 = g ( x1 , x2 ,..., xn ) , p2 = h( x1 , x2 ,..., xn ) ). A more generalized (more
complicated, too) approach is to allow f be dependent on the covariates.
Summary Definition of the Parameters Used in the 4-Hit Model
Parameter
Explanation
Overall risk for CTS
r
Proportion of CTS patients due to “symmetrical” injury
f
p1 = g ( x1 , x2 ,..., xn ) Probability for “symmetrical” injury
p2 = h( x1 , x2 ,..., xn ) Probability for asymmetrical injury
Possible Application: Bland’s Questionnaire
A possible application of the above multi-state models is a re-evaluation of the clinical-history
questionnaire published by Bland (2000). This questionnaire (reproduced below) is useful in
deriving an initial working diagnosis of CTS and reportedly has the sensitivity of 79%. The
weight scores estimated by Bland are mostly consistent with existing clinical experiences.
However, the 2 laterality symptoms (bold-face) listed in the table are associated with negative
weight scores. This is puzzling as the predicted lower probability for CTS diagnosis would
unlikely be applicable to unilateral CTS. A data re-analysis with a multi-state probability model
should be done and may provide some new insights about CTS diagnosis.
Subjective Symptoms and Weights Used in Bland’s Questionnaire
Feature
Weight
Constant term in regression equation
• 3.3817
Nocturnal awakening
0.5584
Morning symptoms
0.5135
Symptoms while driving
0.2709
Relief from shaking hand when awakened
0.4795
Distribution of symptoms
Symptoms mainly in thumb, index, and middle fingers
0.9165
Symptoms mainly in little and ring fingers
• 0.8625
Symptoms mainly in middle and ring fingers
0.8797
Symptoms affecting all five fingers
0.3751
Ambidextrous
• 0.6880
Benefit from splinting
0.4664
Duration of symptoms >1 year
0.2113
Laterality of symptoms
Symptoms worse on right side
• 0.3667
Symptoms worse on left side
• 0.3804
Age (per year)
0.0408
Analysis of Reinstein’s Data
A dataset published by Reinstein (1981) contains a multi-state data table and appears usable for
analysis with a multi-state probability model.
CTS Data Reported by Reinstein (1981)
RT only RT>LT RT=LT RT<LT LT only Sum
Right-handed dominance
28
59
51
9
8 155
Left-handed dominance
0
0
4
4
3
11
Multinomial Logistic Regression
Reinstein’s dataset is a case series study, not a cohort study. Assuming that the case
ascertainment is complete, we can write down a conditional polytomous logistic regression
model to fit the case series:
Pr[Y * = i | x1 ] =
Pr[Y = i | x1 ]
5
∑ Pr[Y = i | x ]
,
i = 1,2,3,4,5 .
1
i =1
Here x1 denotes the hand-dominance pattern ( x1 = 1 for right-handedness; x1 = 2 for lefthandedness) and Y * is the new random variable defined for the case-series study. The
computational process is, however, complicated and will not be pursued here.
4-Hit Regression
The 4-hit model can also be modified to fit Reinstein’s case series:
Pr[Y * = 1 | x1 ] = f (1 − p1 ) 4 + (1 − f ) p 24
Pr[Y * = 2 | x1 ] = 4[ fp1 (1 − p1 ) 3 + (1 − f ) p23 (1 − p 2 )]
Pr[Y * = 3 | x1 ] = 6[ fp12 (1 − p1 ) 2 + (1 − f ) p 22 (1 − p 2 ) 2 ]
Pr[Y * = 4 | x1 ] = 4[ fp13 (1 − p1 )1 + (1 − f ) p12 (1 − p2 ) 3 ]
Pr[Y * = 5 | x1 ] = fp14 + (1 − f )(1 − p 2 ) 4
If a CTS patient is right-handed ( x1 = 1 ): g ( x1 ) = p1 , h( x1 ) = p 2 .
If a CTS patient is left-handed ( x1 = 2 ): g ( x1 ) = 1 − p1 , h( x1 ) = 1 − p2 .
The computational results are as follows:
Data input:
from Reinstein (1981)
Program:
Microsoft Excel Solver program
Outputs:
Parameter
r
f
p1
p2
4-Hit Model for Reinstein’s Data
Estimate
N/A
0.038
1.000
0.671
Explanation
Overall risk for CTS
Proportion of CTS patients due to non-dominant-hand injury
Asymmetrical probability for non-dominant-hand injury
Asymmetrical probability for dominant-hand injury
Expected Number of Cases (4-hit model) versus Observed Number of Cases
RT only RT>LT RT=LT RT<LT LT only Sum
Right-handed Exp
30.3
59.3
43.6
14.2
7.6 155.0
Obs
28
59
51
9
8
155
Left-handed Exp
0.5
1.0
3.1
4.2
2.1 11.0
Obs
0
0
4
4
3
11
Comments:
1) The goodness-of-fit of the 4-hit model seems good ( χ 2 = 5.54; d.f. = 5; p-value > 0.35).
2) The 4-hit model offers the advantage of a “mechanistic interpretation ” . That is, the
number of “hit s” may be considered a measure of hand “trauma frequency”. The
probabilities ( p1 , p 2 ) may indicate how symmetrically the “ trauma hits’ are distributed.
3) The results from Reinstein’s data does not support my original speculation that there are
one subset of symmetrical CTS patients and the other asymmetrical. The model’s
estimates suggest instead that both subsets are asymmetrical. The smaller proportion
(3.8%) of CTS patients suffer non-dominant hand injury (the injury probability is 1). The
other larger subset (96.2%) suffers the dominant-hand-based injury (the biased injury
probability is 67.1%).
4) It is known that unilateral CTS more commonly affects the right hand. Given the fact that
majority of human population are also right-handed (about 90% in USA; Mackenzie and
Peters 2000), repetitive hand usage appears to be a risk factor for CTS. Unfortunately,
other covariates are not available from Reinstein’s data and their impacts on the lateral
asymmetry cannot be evaluated with the 4-hit model.
End Remarks
The multi-state probabilities models outlined above are rudimentary. Nevertheless, I hope that by
paying a careful attention to the lateral-asymmetry issue we may find a better way to design and
interpret future CTS research studies.
References
Bland JD (2000) A neurophysiological grading scale for carpal tunnel syndrome. Muscle Nerve.
23(8):1280-3
Greene WB (ed.) (2000) Essentials of Musculoskeletal Care. American Academy of Orthopaedic
Surgeons, Rosemont, Illinois
Mackenzie K, Peters M (2000) Handedness, hand roles, and hand injuries at work. J Safety Res
31(4): 221-227
Patterson JD, Simmons BP (2002) Outcomes assessment in carpal tunnel syndrome. Hand Clin
18(2):359-63
Reinstein L (1981) Hand dominance in carpal tunnel syndrome. Arch Phys Med Rehabil
May;62(5):202-3
Rosenbaum RB and Ochoa JL (2002) Carpal Tunnel Syndrome and Other Disorders of the
Median Nerve, 2nd edition. Butterworth-Heinemann, Boston
Stanek EJ 3rd, Pransky G (1996) Unilateral vs. bilateral carpal tunnel: challenges and approaches.
Am J Ind Med 1996 29(6):669-78
Thurston A (2000) Aetiology of the so-called ‘idiopathic’ carpal tunnel syndrome. Curr
Orthopaed 14 (6): 448-456