Generalizability of grip strength measurements in patients with tennis elbow.

Generalizability of Grip Strength Measurements in Patients with Tennis Elbow Maximum grip strength [1,2] and pain-free grip strength [3,4] have been used as outcome measures in patients with lateral epicondylitis at the elbow. Although both measures appear to be reliable, little information has been offered on the measurement properties and rationale associated with the coefficients used to summarize these data. The literature has not examined reliability for repeated measurements obtained at the same test session (interrepetition reliability) or for measurements obtained on different days (interoccasion reliability). The paucity of literature on maximum grip strength and pain-free grip strength pertaining to lateral epicondylitis is paralleled by the scarcity of methodologically sound literature reviewing the reliability of grip strength in other patient populations and in healthy subjects.

Mathiowetz and colleagues in a study of maximum grip strength on a series of 27 healthy female volunteers demonstrated that the reliability based on the mean score of three tests was greater than that of the mean score of two tests or a single test. [5] They reported that a reliability coefficient based on the highest value on two occasions was slightly more reliable than the estimated coefficient for a single measurement (.79 and .82 for the right hand and .86 and .92 for the left hand). No formal statistical tests were used to determine whether these differences were statistically significant.

Reliability Coefficients

A variety of coefficients have been used to indicate reliability. Such coefficients include the Pearson product-moment correlation coefficient (PPMCC), the intraclass correlation coefficient (ICC), [6] and, in our study, a set of ICCs known as generalizability coefficients. [7] The use of the PPMCC as a reliability index has been questioned because it measures an association and not agreement; thus, when one measurement is biased with respect to another measurement, this coefficient will lead to an inflated estimate of the reliability. [8] Such an inflated estimate of reliability would occur if the first of two measurements on a group of subjects consistently differed from (ie, was 50% of) the second measurement. In this example, the PPMCC would be 1.00 (a perfect correlation); however, in no instance would the two measurements have agreed with each other.

Given that the mathematical foundation for the ICC is based on a repeated-measures analysis of variance (ANOVA), this coefficient is suitable for repeated measurements of the same attribute. Also, systematic error (bias), as described in the example above, is treated as error, and the magnitude of the ICC is thus lowered. The difference between classical test theory, on which the reliability coefficient is based, and generalizability theory is a conceptual one because mathematically the coefficients represent ICCs. Classical test theory proposes that any observed score can be broken down into a true score (which no one truly knows) and a singular random error term. Furthermore, classical test theory implies that the true score belongs to only one family of parallel tests and consequently has only one reliability coefficient. [7] The reliability coefficient is defined as the true variance divided by the total (true plus error) variance. Often, the researcher is interested in generalizing over a variety of conditions, or "universes," and classical test theory does not provide for this requirement.

To illustrate this notion, consider the situation where the researcher is interested in determining the reliability of a particular strength measurement. Reliability coefficients could be calculated based on repeated measurements taken at 1) one occasion; 2) two occasions on the same day; 3) two occasions on different days; 4) two occasions as performed by different clinicians, and so on. The strength test, therefore, would simultaneously have different reliability coefficients. Generalizability theory acknowledges that different conditions of observation exist (eg, repetitions, occasions, observers, devices, clinics) that the researcher may wish to generalize over, and it challenges the researcher to define the universe of conditions of interest. A second advantage of generalizability theory is that it acknowledges that in many instances the error term in the reliability equation actually contains distinct sources of error and allows for the relative magnitude of these sources of error to be identified.

The purpose of this study was to determine the interrepetition and interoccasion (tests performed on different test dates) generalizability of maximum grip strength and pain-free grip strength measurements in the involved limb and maximum grip strength measurements in the uninvolved limb of patients with the diagnosis of proximal extensor carpi radialis brevis tendinitis. We elected to measure the maximum grip strength on the uninvolved limb because clinical decisions are often based on between-limb comparisons. [4] Our null hypotheses were 1) there would be no difference in the mean values among repetitions; 2) there would be no difference in the mean values between occasions; and 3) there would be no significant variance associated with individual patients generating their maximum force on different occasions (patient-occasion interaction), different repetitions (patient-repetition interaction), and different repetitions on different occasions (occasion-repetition interaction).

Method

Subjects

This study was conducted in a community sports injuries clinic. The subjects consisted of 35 consecutive patients (17 men, 18 women) with extensor carpi radialis brevis tendinitis. Six cases of tendinitis involved the teno-periosteal junction, 19 cases involved the tendon body, and 10 cases spanned both the teno-periosteal junction and the tendon body. Thirty-three cases involved the dominant limb. The average age of the patients was 44.5 years (s = 8.6 years), and the mean duration of symptoms was 3.9 months (s = 3.5 months).

Patients were eligible for this study if they provided informed consent and met the following diagnostic criteria based on those described by Cyriax. [9] Briefly, they must have complained of discomfort at or about the lateral epicondyle and have tenderness on palpation over one of the following areas: 1) the origin of the extensor carpi rdialis brevis tendon; 2) the tendon body of the extensor carpi radialis brevis; or 3) the extensor carpi radialis brevis tendon, with the tenderness extending from the origin to the tendon body. They also must have complained of pain at the lateral aspect of the elbow when performing resisted wrist extension exercises combined with radial deviation while the elbow was completely extended. Patients were excluded from the study for any of the following reasons: 1) combined lesions (eg, cervical and elbow problems, multiple lesions about the elbow) 2) bilateral elbow problems during initial assessment, 3) history of prior surgery to the elbow, and 4) history of an injection to the elbow within the past six months.

Design

To be able to examine the variability both among repetitions and between days, a repeated-measures study design was adopted that provided three measurements during the same test session and three additional strength measurements at a second test session within seven days of the initial measurement. During this time frame, each patient received two ultrasound treatments (1 W/[cm.sup.2] pulsed for six minutes). No clinically important change in the patient status was expected to occur during this time period.

Device

The testing device used in this study was a Smedley hand-held dynamometer. (*1) Indexes of test-retest reliability and validity for the dynamometer were determined by loading the device with a set of calibration weights on repeated occasions. The loads varied from 10 to 60 kg. The reliability coefficient (ICC[1,1]) was calculated to be .999. The validity index can be expressed by the following regression equation: Actual force (in kilograms) = 1.36 X measured force (in kilograms) - 1.6. The PPMCC for this expression was determined to be .998.

Protocol

The handle of the dynamometer was positioned with a 5-cm space between the hand-contact surfaces. This spacing appeared to be appropriate for all patients in this study. The handgrip was not padded. The testing procedure consisted of positioning the patient standing with the elbow in complete extension and the shoulder and radioulnar joints in neutral rotation.

(Figure). Pain-free grip strength measurements of the involved limb were conducted first. The patient was instructed to slowly squeeze the dynamometer and to stop the instant discomfort was first felt. At the time of this study, the testing procedure in the clinic where the study was conducted consisted of obtaining three repetitions separated by a 20-second rest interval, and it was this protocol that was evaluated in our study. Using a similar procedure, three maximum grip strength measurements were then performed on the uninvolved limb, followed by three maximum grip strength measurements on the involved limb. No warm-up exercises were allowed because we believed they might add to the discomfort of the involved limb. The patients were tested each day between 1 PM and 6 PM, although each patient was not tested at exactly the same time each day.

Data Analysis

The data analysis consisted of first reviewing the mean values of the 35 patients for each of the six measurements. A three-way ANOVA table was generated with occasion (two levels) and repetition (three levels) as the two trial factors. Variance components were then calculated and used to construct various sets of generalizability coefficients (Appendix). [10] The standard error of measurement and the corresponding 95% confidence limits were also calculated. [8]

Results

A review of the mean values in Table 1 does not support the existence of a trend for days or repeated measurements within day. The three-way ANOVA demonstrated that no statistically significant differences existed among repetitions, between occasions, or for the patient-repetition and occasion-repetition interactions for each of the three measures (p [is greater than] .05). Statistically significant differences (p [is less than] .001) did exist for the patient-occasion interaction for each of the three measures. Table 2 provides the variance components derived from the three-way ANOVA. The generalizability coefficients derived from the variance components in Table 2 are presented in Table 3. Table 4 presents the 95% confidence range expressed in kilograms for a variety of repetition and occasion combinations. Thus, if the clinician were to average six repetitions (three per day X two days) for a given patient's pain-free grip strength, there would be a 95% chance that the value would be within 4.8 kg of the mean.

Discussion

An application of the methodology applied in our study to evaluate grip strength has not appeared previously in the literature. The interpretation of the variance components presented in Table 2 is as follows. First, the largest source of variation for each of the three measures is due to stable differences among patients. The variances attributable to repetitions and occasions were extremely small (zero for pain-free grip strength and maximum grip strength for the involved limb), indicating that no systematic differences existed among repetitions or between occasions. The finding of no difference between occasions supports our design premise that no clinically important change would take place in the patients over the seven-day time interval, and the finding of no difference among repetitions supports the notion that no fatigue or learning occurred during testing. Of additional interest is the finding that in each case the patient-occasion interaction accounted for a large portion of the nonpatient (overall error) variance. Our interpretation of this finding is that some patients demonstrated higher grip strengths on the first occasion, whereas others produced greater values on the second occasion.

Often, the clinician is unable to summarize a series of trials performed by a patient. According to Kroll, reliability theory dictates that "if the error variances are random and uncorrelated, then the proper procedure is to use the mean of all available trials." [11] Error variances are considered to be random when no systematic differences exist among repetitions or between occasions, and uncorrelated when the magnitude of the measurement does not influence the magnitude of the error term. Because we found no systematic differences either among repetitions or between occasions, we believe that the best strategy to achieve a representative estimate of the patient's strength is to average the repetitions rather than to opt for the highest or lowest value.

In addition to averaging repetitions, the results of this study also suggest that an optimal data-collection strategy exists. To illustrate this point, consider the following question: Will a clinician achieve a more generalizable estimate of pain-free grip strength by averaging nine measurements taken on one occasion or by averaging nine measurements taken over three occasions (three measurements per occasion)? The variance components for pain-free grip strength in Table 2 demonstrate that the variation attributable to the patient-occasion interaction (7.43) is greater than the variation attributable to the patient-repetition interaction (2.35). This finding suggests that increasing the number of test occasions will have a greater impact on increasing the generalizability than will increasing the number of repetitions. Substituting these values into the equation in Case 3 of the Appendix produces a coefficient of .948 when nine measurements are averaged at a single test occasion compared with a coefficient of .974 when three measurements per occasion are averaged over three test occasions. In clinical terms, these coefficients represent an error of [+ or -] 5.8 and 4.0 kg, respectively.

The generalizability coefficients for maximum grip strength for the uninvolved extremity in this study are slightly higher than the test-retest reliability coefficients reported by Mathiowetz et [al.sup.5] (.79 for the right hand and .86 for the left hand). One potential reason for this minor difference is that Mathiowetz et al's sample consisted of 27 healthy female students, whereas our sample consisted of 17 male and 18 female patients. We would expect that the grip strengths for Mathiowetz et al's subjects would be more homogeneous than the grip strengths for our heterogeneous sample. Accordingly, as the difference in the sample's grip strength increases, so will the variance. Thus, because both the reliability and generalizability coefficients have the variance term attributable to subjects in the numerator, it is to be expected that the study with the larger intersubject variance term would also produce the greater reliability coefficient (assuming a similar error term in both studies). Because Mathiowetz et al do not state the units of force reported in their study (presumably they were pounds), we are not able to directly compare variances; therefore, we calculated the coefficient of variation (ie, the standard deviation divided by the mean) to be .17 for Mathiowetz et al's sample and .30 for our sample, using the data for maximum grip strength for the uninvolved limb (Tab. 1). The magnitude of these coefficients supports the notion of a greater intersubject variability in our study compared with that of Mathiowetz et al.

Conclusion

Our study examined the interrepetition and interoccasion generalizability of pain-free grip strength and maximum grip strength for the involved and uninvolved limbs of a sample of patients with lateral epicondylitis. The results demonstrated high generalizability coefficients for both interrepetition and interoccasion measurements. The results did not demonstrate systematic differences either among repetitions or between occasions. Because bias did not exist, the best estimate of the patient's grip strength is achieved by averaging all measurements. Finally, our study demonstrated that patients perform less consistently when tested on different days as compared with when repeated measurements are taken at the same test session. This finding suggests that for a clinician to obtain a meaningful estimate of within-patient variability (that is, meaningful in the sense that clinicians follow patients over time and therefore to detect true change over time, they must first know the extent of the normal day-to-day variability), repeated measurements on different occasions nwhen no true change is anticipated) should be obtained.

(*1) Therapeutic Instruments, Div of J A Preston Corp, 60 Page Rd, Clifton, NJ 07012.

References

[1] Binder AI, Parr G, Page P, et al: A clinical and thermographic study of lateral epicondylitis. Br J Rheumatol 22:77-81, 1983

[2] Thurtle OA, Tyler AK, Cawley MID: Grip strength as a measure of response to treatment for lateral epicondylitis. Br J Rheumatol 23:154-156, 1984

[3] Burton K: Grip strength in tennis elbow. Br J Rheumatol 23:310, 1984

[4] Stratford PW, Levy DR, Gauldie S, et al: Extensor carpi radialis tendonitis: A validation of selected outcome measures. Physiotherapy Canada 39:250-255, 1987

[5] Mathiowetz V, Weber K, Volland G, et al: Reliability and validity of grip and pinch strength evaluations. J Hand Surg [Am] 9:222-226, 1984

[6] Winer BJ: Statistical Principles in Experimental Design, ed 2. New York, NY, McGraw-Hill Book Co, 1971, p 286

[7] Cronbach LJ, rajaratnam N, Gleser CG: Theory of generalizability: A liberalization of reliability theory. British Journal of Statistical Psychology 16:137-163, 1963

[8] Kramer MS, Feinstein AR: Clinical biostatistics: LIV. The biostatistics of concordance. Clin Pharmacol Ther 29:111-123, 1981

[9] Cyriax J: Textbook of Orthopaedic Medicine: Diagnosis of Soft Tissue Lesions, ed 8. London, England, Bailliere Tindall, 1982, vol 1

[10] Brennan RL: Elements of Generalizability Theory. Iowa City, IA, American College Testing Program, 1983

[11] Kroll W: Reliability theory and research decision in selection of a criterion score. Research Quarterly 38:412-419, 1967

P Stratford, MSc, is a part-time assistant professor, Department of Medicine, McMaster University, Hamilton, Ontario, Canada, and Teaching Master, Department of Physiotherapy, Mohawk College, Chedoke Campus, Health Sciences Education Centre, PO Box 2034, Sanatorium Rd, Hamilton, Ontario, Canada L8N 3T2. Address correspondence to Department of Physiotherapy, Mohawk College, Chedoke Campus, Health Sciences Education Centre, PO box 2034, Sanatorium Rd, Hamilton, Ontario, Canada L8N 3T2.

G Norman, PhD, is Professor, Department of Clinical Epidemology and Biostatistics, McMaster University.

J McIntosh, MSc, is Assistant Clinical Professor, Department of Clinical Epidemology and Biostatistics, McMaster University, and Clinical Specialist, McMaster Division of Chedoke-McMaster Hospitals, Hamilton, Ontario, Canada L9H 2K9.

This article was submitted January 29, 1988; was with the authors for revision for 11 weeks; and was accepted September 16, 1988.