Asymmetric Injury in Carpal Tunnel Syndrome. C. J. Zheng, MD, PhD. Department of Occupational and Environmental Medicine.

Transcription

1 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: Pager: 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 $ billion annually (Patterson and Simmons 00). The mechanistic pathways that underline the development of CTS are not clear and the importance of work-related risk factors remains contentious (Thurston 000). Some experts believe that preexisting medical conditions are more essential and work-related factors merely

2 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 996). 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.

3 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 ) CTS - No ) 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 ) No CTS ) Unilateral CTS right or left hand is affected

4 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 ) No CTS ) 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 ) No CTS ) 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

5 takes the numerical values ( 0,,,3,4, 5 ) and has the following relationship with the CTS outcome states: CTS outcome state No CTS RT only RT>LT RT=LT RT<LT LT only Random variable Y Second, the corresponding probability mass function is denotable by Pr[ Y = i x, x,..., x ], i = 0,,,3,4, 5. n i Here Pr[ Y = i x, x,..., x n ] =. Also the covariates, x, x,..., xn (or x j, j =,..., n ), are 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 ( x, x,..., x ) 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 x, x,..., x ] can also be viewed as a transitional probability defined over the study interval [ 0, T ]: n Pr[ Y = i x, x,..., x ] = Pr[ Y ( T ) = i Y (0) = 0; x, x,..., x ]. n n n Definition V: Continuous Outcomes ) RT CTS score right-hand examination score (e.g., nerve conduction velocity) ) 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.

6 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 x, x,..., x. The multinomial logistic regression model is a common n choice for structuring the functional dependence of a polytomous categorical variable Y on covariates x,...,, x xn : αi + βijx j j e Pr[ Y = i x, x,..., xn ] = α +. i βijx j j e i Here i = 0,,,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 x, x Pr[ Y = i x, x ( i ),..., x,..., x n n ] = r 4 ] = r [ fp i i ( p ) 5 i + ( f ) p 5 i ( p ) ] i

7 p = g x, x,..., x ), p = h x, x,..., x ) ( n ( n Here the model assumes that there exist two subsets of CTS patients: ) 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 p ; note that if the symmetrical-injury assumption is true, p should be equal or close to / ). ) The other set of patients (the proportion is f ) have a work-related etiology and tend to develop an asymmetrical injury (the injury probability is p which should be biased toward ; i.e., favoring the dominant hand). 3) The covariates ( x, x,..., xn ) are incorporated into the model by assuming that they affect the injury probabilities only ( p = g x, x,..., x ), p = h x, x,..., x ) ). A more generalized (more ( n ( n 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 r Overall risk for CTS f Proportion of CTS patients due to symmetrical injury p = g( x, x,..., xn ) Probability for symmetrical injury p = h x, x,..., x ) Probability for asymmetrical injury ( n 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 (000). 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 laterality symptoms (bold-face) listed in the table are associated with negative

8 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 Nocturnal awakening Morning symptoms Symptoms while driving Relief from shaking hand when awakened Distribution of symptoms Symptoms mainly in thumb, index, and middle fingers Symptoms mainly in little and ring fingers Symptoms mainly in middle and ring fingers Symptoms affecting all five fingers Ambidextrous Benefit from splinting Duration of symptoms > year 0.3 Laterality of symptoms Symptoms worse on right side Symptoms worse on left side Age (per year) Analysis of Reinstein s Data A dataset published by Reinstein (98) contains a multi-state data table and appears usable for analysis with a multi-state probability model. CTS Data Reported by Reinstein (98) RT only RT>LT RT=LT RT<LT LT only Sum Right-handed dominance Left-handed dominance 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:

9 Pr[ Y = i x] Pr[ Y * = i x] = 5, i =,,3,4, 5. Pr[ Y = i x ] i= Here x denotes the hand-dominance pattern ( x = for right-handedness; x = 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* = x = f p + f 4 ] ( ) ( ) p Pr[ Y* = x] = 4[ fp ( p) + ( f ) p ( p )] Pr[ Y* = 3 x ] = 6[ fp ( p ) + ( f ) p ( p 3 Pr[ Y* = 4 x] = 4[ fp ( p) + ( f ) p ( p ) ) 3 ] ] Pr[ Y* = 5 x = fp + f p 4 4 ] ( )( ) If a CTS patient is right-handed ( x = ): g ( x ) = p, h( x ) = p. If a CTS patient is left-handed ( x = ): g( x ) = p, h( x ) = p. The computational results are as follows: Data input: from Reinstein (98) Program: Outputs: Microsoft Excel Solver program 4-Hit Model for Reinstein s Data Parameter Estimate Explanation r N/A Overall risk for CTS f Proportion of CTS patients due to non-dominant-hand injury p.000 Asymmetrical probability for non-dominant-hand injury p 0.67 Asymmetrical probability for dominant-hand injury

10 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 Obs Left-handed Exp Obs Comments: ) The goodness-of-fit of the 4-hit model seems good ( χ = 5.54; d.f. = 5; p-value > 0.35). ) 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 ( p, p ) 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 ). The other larger subset (96.%) suffers the dominant-hand-based injury (the biased injury probability is 67.%). 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 000), 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.

11 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 (000) A neurophysiological grading scale for carpal tunnel syndrome. Muscle Nerve. 3(8):80-3 Greene WB (ed.) (000) Essentials of Musculoskeletal Care. American Academy of Orthopaedic Surgeons, Rosemont, Illinois Mackenzie K, Peters M (000) Handedness, hand roles, and hand injuries at work. J Safety Res 3(4): -7 Patterson JD, Simmons BP (00) Outcomes assessment in carpal tunnel syndrome. Hand Clin 8(): Reinstein L (98) Hand dominance in carpal tunnel syndrome. Arch Phys Med Rehabil May;6(5):0-3 Rosenbaum RB and Ochoa JL (00) Carpal Tunnel Syndrome and Other Disorders of the Median Nerve, nd edition. Butterworth-Heinemann, Boston Stanek EJ 3rd, Pransky G (996) Unilateral vs. bilateral carpal tunnel: challenges and approaches. Am J Ind Med 996 9(6): Thurston A (000) Aetiology of the so-called idiopathic carpal tunnel syndrome. Curr Orthopaed 4 (6):