Applying Rasch analysis to evaluate measurement equivalence of different administration formats of the Activity Limitation scale of the Cambridge Pulmonary Hypertension Outcome Review (CAMPHOR)
© Twiss et al. 2016
Received: 22 September 2015
Accepted: 31 March 2016
Published: 9 April 2016
Electronic formats of patient-reported outcome (PRO) measures are now routinely used in clinical research studies. When changing from a validated paper and pen to electronic administration it is necessary to establish their equivalence. This study reports on the value of Rasch analysis in this process.
Three groups of US pulmonary hypertension (PH) patients participated. The first completed an electronic version of the CAMPHOR Activity Limitation scale (e-sample) and this was compared with two pen and paper administrated samples (pp1 and pp2). The three databases were combined and analysed for fit to the Rasch model. Equivalence was evaluated by differential item functioning (DIF) analyses.
The three datasets were matched randomly in terms of sample size (n = 147). Mean age (years) and percentage of male respondents were as follows: e-sample (51.7, 16.0 %); pp1 (50.0, 14.0 %); pp2 (55.5, 40.4 %). The combined dataset achieved fit to the Rasch model. Two items showed evidence of borderline DIF. Further analyses showed the inclusion of these items had little impact on Rasch estimates indicating the DIF identified was unimportant.
Differences between the performance of the electronic and pen and paper administrations of the CAMPHOR Activity Limitation scale were minor. The results were successful in showing how the Rasch model can be used to determine the equivalence of alternative formats of PRO measures.
Patient reported outcomes (PROs) provide a crucial means of assessing the impact of a condition and its treatment from the patients’ perspective. It has become increasingly common for PROs to be used as secondary (and even primary) endpoints in clinical trials . In such studies electronic formats are generally employed. These may offer a range of benefits such as improving access to patients, increasing compliance, reducing missing data and avoiding errors associated with manual data entry [2–4]. Adapting pen and paper measures for use electronically requires a number of format changes. These may include changes to item presentation, instructions and/or response format. Various electronic devices are used including personal computers, tablets, cell phones and handheld devices. Smaller devices often entail major formatting changes as they require the PRO to be broken into small sections to fit the screen. The way in which participants are required to respond on these devices can differ; for example, by using a standard mouse or a touch screen monitor. An important question is whether or not changes in format affect data generated from the measure. In order to investigate this it is necessary for the new format to undergo formal equivalence testing.
A recent literature review showed that several studies have attempted to assess equivalence between different formats of PROs . However, the way in which equivalence is tested varies from study to study. These methods usually involve comparing sample means and/or assessing the level of agreement between the different formats using correlational techniques. Such studies have design limitations and only assess a small aspect of true ‘measurement equivalence’. For example, the statistic most widely used for assessing association is the intraclass correlation coefficient (ICC). However, the ICC requires interval/ratio level data, making its use inappropriate with most PROs currently available that produce data at the ordinal level .
Studies of association usually use a cross-over design in which participants are randomized to complete either a paper and pen version or an electronic version of the same PRO and then the other mode on a second administration. Generally, the time between administrations is short, with patients completing both formats at the same visit [7–9]. This is likely to lead to recall bias and inflated levels of agreement.
An alternative design employed is a parallel groups design in which participants are randomized to complete either a paper and pen version or an electronic version of the PRO. Mean scores on the measures are then compared and differences in these either considered in relation to minimal important difference values (if available) or effect sizes. Unfortunately, this approach gives markedly less information about measurement equivalence and is liable to bias if the samples are not closely matched on clinical characteristics.
A guidance document produced by the International Society for Pharmacoeconomics and Outcomes Research ePRO Good Research Practices Task Force  provides recommendations on the steps necessary to establish equivalence. The document suggests that respondent usability should always be assessed and that measurement equivalence should be tested quantitatively when ‘moderate’ changes are made to the format. The document follows common practice by recommending use of one of the two designs described above.
One of the major advances in PRO development and application in recent years has been the adoption of Item Response Theory (IRT) and, in particular, Rasch analysis . Unlike Classical Test Theory (CTT), IRT gives greater emphasis to item-level rather than test-level information and provides superior detail on the measurement properties of scales [12–14]. Although IRT has been identified as a potentially useful method for evaluating measurement equivalence  a review of the literature identified just two studies applying this approach [15, 16].
The Rasch model allows a series of detailed properties to be evaluated that can be applied to the assessment of measurement equivalence. These include individual item fit statistics, overall fit statistics, item severity ordering and the functioning of response options. In addition, it allows measurement bias at the item level to be assessed using differential item functioning (DIF). This is of particular relevance to measurement equivalence as DIF by mode of administration (paper and pen versus electronic) can be tested.
The aim of the present study was to compare the measurement equivalence of pen and paper and electronic formats of the Activity Limitation scale of the Cambridge Pulmonary Hypertension Outcome Review (CAMPHOR)  using Rasch analysis.
CAMPHOR Activity Limitation
The CAMPHOR Activity Limitation scale employs the World Health Organization’s Classification of Functioning, Disability and Health  and consists of 15 items with three response options (Able to do on own without difficulty/Able to do on own with difficulty/Unable to do on own). Rasch analysis was used in the development of this scale to ensure unidimensionality and good measurement properties.
An electronic version of the scale was designed to resemble the original paper and pen version as closely as possible. The items were presented on whole pages in the same way as the original. A minor change to the response format was made with participants asked to ‘click’ the relevant response option using the cursor. In addition, the instructions were changed with patients asked to ‘click’ their response rather than to ‘check a box’. All other instructions were identical to the paper and pen version.
Three separate samples of PH patients were included in the study. One sample completed an electronic version of the CAMPHOR and the other samples filled in a paper and pen version. All samples consisted of US patients with PH. Subscribers to listservs of the Pulmonary Hypertension Association, recruited by the Mayo Clinic, Rochester, completed an electronic version of the CAMPHOR (e-sample) . A second sample, drawn from the Adelphi Real World Pulmonary Arterial Hypertension Disease Specific Programme , completed the paper and pen CAMPHOR at outpatient clinics and specialist PH centres (pp1-sample). The second paper and pen sample (pp2-sample) was recruited by the University of Chicago from a tertiary referral centre . The original e-sample and pp1 samples consisted of 276 and 151 participants respectively. Random samples (generated via SPSS 19 random sample selection generator) of 147 patients were chosen from each of these clinical samples to match the size of the pp2 sample.
For the e-sample, ethics approval was provided by the Mayo Clinic Institutional Review Board. The pp-1 sample dataset was collected through a market research survey and accordingly ethics approval was not sought. For the pp-2 sample, ethics approval was provided by the University of Chicago Institutional Review Board. Informed consent was given by participants in all studies.
The samples were not matched for disease severity and the CAMPHOR was administered in different locations (clinic or home).
Data generated from the three samples of PH patients were compared. The design allowed any lack of equivalence between the functioning of electronic and pen and paper formats to be considered in the context of two different pen and paper administrations.
Assessment of fit to the Rasch model: In order to assess equivalence, it was first necessary to re-establish that the combined scales were unidimensional with good fit to the Rasch model. Therefore, the analyses assessed the PRO scales’ standard fit statistics . If fit statistics are adequate it is possible to assess measurement equivalence.
Measurement equivalence was assessed by investigating DIF  by method of administration. DIF occurs when sub-groups of a sample respond in different ways to a particular item, despite having the same level of the underlying trait being measured. This provides a way of assessing whether different formats of a measure produce bias at the item level. If there is no evidence of DIF then the measure exhibits equivalence. If DIF is shown it is necessary to assess its importance. If it is non-significant then equivalence is assumed.
Fit to the Rasch model
The Rasch model
The Rasch model is a simple logistic latent trait IRT model . Based on a probabilistic form of Guttman scaling, it states that items and persons can be located on the same linear scale. The probability of a given respondent affirming an item is defined as the relative distance between the item location (difficulty) and the respondent location (ability) on that scale. In relation to health outcome, it is a logistic function of the difference between a person’s severity level and the severity level of the item. In order to assess the measurement properties of a questionnaire formally, the response pattern created by the items is compared to that expected by the Rasch model. If the observed data do not deviate significantly from the expected responses the items fit the Rasch model.
The Rasch Unidimensional Measurement Model (RUMM) 2030  program was employed.
Before analyses were conducted it was necessary to determine whether the rating scale  or partial credit model  was most appropriate. Both of these approaches use the Rasch model but differ slightly in their mathematics. The rating scale model is more stringent in its requirements as the distance between response thresholds has to be uniform across all items. The likelihood ratio test is used to identify the most appropriate model.
Overall fit to the Rasch model
Fit to the Rasch model was examined by looking at the overall item-trait interaction Chi2 fit value. A non-significant Chi2 statistic (p > 0.05) indicates that the scale fits the Rasch model. Bonferroni corrections were applied to the statistical p-values throughout the analyses due to the large number of tests conducted (Bonferroni adjusted p value > 0.003).
Individual item fit
Individual item fit statistics were also used to investigate overall fit to the Rasch model. A significant Chi2 fit statistic (p < 0.05 (Bonferroni adjusted)) indicates misfit to the model. Fit residuals also provide a valuable source of information. These should fall within ±2.5. High negative residuals suggest that an item may be redundant, whereas high positive residuals suggest multi-dimensionality. In both cases they are indicative of misfit. Person fit residual and item fit residual statistics are transformed by RUMM to approximate z-scores. These z-scores, the residual mean values of person and item fit, can also be used to assess overall fit to the Rasch model. Perfect fit is represented by a mean anchored at 0 and a standard deviation of 1.
Internal Reliability – Person Separation Index (PSI)
The Person Separation Index (PSI) was employed to analyse internal reliability. This indicates the power of the items to distinguish between respondents. A PSI score of 0.8 is considered the minimum acceptable level.
Functioning of response options
Response thresholds are investigated to determine the adequacy of the response format. Thresholds represent locations on the latent continuum at which it will be equally likely that adjacent response options will be selected. Thresholds should be logically ordered. If response options are disordered they do not work as intended. This is an important area for the present study as the method of responding could influence the thresholds.
As noted above, evidence of unidimensionality is first investigated by looking at the item fit residuals. Evidence of unidimensionality was also investigated using t-tests to compare estimates derived from two separate subsets of items (loading most differently on the first factor of the Residual Principal Component Analysis) . If a scale is unidimensional these two subsets of items should give the same estimate of person ability. Generally, if more than 5 % of these t-tests are statistically significantly different, it is indicative of a multidimensional scale. A 95 % binomial confidence interval (using a normal approximation) is provided to indicate the interval within which the true value lies in repeated testing.
Assessment of equivalence
DIF was employed to test for equivalence between the different formats of the Activity Limitation scale. Analyses of variance (ANOVA) were employed to identify DIF by administration mode (e-sample versus pp1 versus pp2). Significant p-values (p < 0.05) indicate the presence of DIF.
Assessing the impact of DIF
If DIF is identified it is necessary to assess the extent to which it influences the calculation of the Rasch estimates. If DIF is minor, its influence on estimates may be only slight. The importance of any identified DIF was tested using a method outlined by Tenant and Pallant . Rasch estimates are first calculated using a ‘pure’ dataset where items exhibiting DIF are removed. These estimates are then saved to an anchor file. The whole dataset, including items exhibiting DIF, are anchored to this dataset so that the estimates are defined by the measurement framework of the ‘pure’ items. The resulting estimates (pure vs. full anchored dataset) are then compared. The proportion of estimates that differ by 0.5 logits is calculated to assess for the proportion of non-trivial DIF. Distribution of the estimates (including mean, standard deviation, median and interquartile range), correlation (intraclass correlation coefficient) between estimates and differences between the estimates (t-test) were also calculated.
e-sample (n = 147)
pp1 (n = 147)
pp2 (n = 147)
PH duration (years)
WHO classification (%)
PH type (%)
Idiopathic PH/Familial PH
PH due to left heart disease
PH due to lung conditions
PH due to other conditions
Reasons for PH unknown
CAMPHOR Activity limitation raw score
Further investigation was conducted using DIF analysis to assess whether differences in severity could have impacted on the equivalence testing results. There was no evidence of DIF by WHO classification (pp1 vs. pp2) after Bonferroni corrections were applied.
Fit to the Rasch model
The initial Likelihood Ratio test, used to determine the most appropriate Rasch model, was statistically significant supporting the use of the partial credit model for the analyses (p < .001).
Overall fit statistics for the combined dataset
Item-person fit residuals
Unidimensionality (95 % Confidence Interval)
Item fit residual
Person fit residual
Individual Item Fit
Walk around house
Walk short level distances
Walk longer level distance
Walk up incline
Climb a flight of stairs
Bend to pick up objects
Stand for short time
Stand for long time
Lift heavy objects
Carry heavy items
Do light house work
Do heavy housework
Assessment of equivalence
None of the items showed DIF by administration after application of Bonferroni corrections. However, one item (item 5, p = 0.003) showed borderline non-uniform DIF and another showed borderline uniform DIF (item 12, p = 0.002). These items were investigated in more detail.
In order to assess the level of bias exhibited by items 5 and 12, Rasch estimates were compared between a pure dataset excluding these items and an anchored dataset including them. There were only minor differences between the two estimates (with DIF items mean (SD) = −2.17 (2.38), without DIF items mean (SD) = −2.19 (2.41), t-test p = 0.224). Only 3.4 % of person estimates differed by more than 0.5 logits. In addition, a correlation between the two sets of estimates was very high (intraclass correlation coefficient = .998). Overall, the results indicate that the DIF identified was unimportant.
The study shows that it is feasible to use the Rasch model to assess measurement equivalence of the CAMPHOR Activity Limitation scale. The study has provided a clear methodological framework for using the Rasch model in this process. A three-step approach was used where fit to the Rasch model was first established, measurement equivalence was assessed using DIF analyses and the importance of the identified DIF investigated.
Adequate fit to the Rasch model was achieved in the first step. Overall and item level fit statistics showed the scale had good fit to the Rasch model. Results also showed support for the functioning of the response format. Problems with the functioning of the response options have been identified frequently when Rasch analysis is applied to existing scales [29–31]. The method of responding to items differs between modes of administration, underlining the importance of assessing response option functioning. In the present study, the functioning of the response options was good with no disordered response thresholds identified. This is likely to be due to the response options for the CAMPHOR Activity Limitation scale being carefully designed using Rasch-based evidence.
Only minor evidence of DIF by type of administration was found. This was investigated in more detailed using a systematic approach outlined previously by Tennant and Pallant . This determined whether the minor DIF identified had an important influence on estimates generated from the scale. This step is essential when DIF is identified in order to assess the degree of bias that items produce at the test level. The fact that two paper and pen versions were available allowed the electronic format to be compared carefully in relation to normal sample to sample variation. The results suggested that the electronic format did not differ more than the two paper and pen formats differed from each other. The results of these analyses supported the measurement equivalence of electronic and pen and paper versions of the CAMPHOR scales.
The success of the equivalence testing in this study should be considered in relation to the extent of changes in format that were made to the electronic version of the questionnaire. The new format was designed to resemble the original measure as closely as possible, having the same layout and with only minor necessary changes to the instructions. More extensive changes could well affect the Rasch fit statistics.
Two previous studies were identified that have applied IRT to assess measurement equivalence [15, 16]. One of these studies applied Rasch analysis . The results of this latter study were limited to an analysis of DIF by mode of administration and no formal investigation of the impact of the DIF on overall scores was performed. The present study has provided a more detailed approach to assessing equivalence using Rasch analysis and provides a foundation for future studies.
The use of Rasch analysis to test equivalence is likely to increase in the future as it has a number of advantages over CTT approaches. Its use gives considerably more detailed information on the measurement properties of scales allowing true ‘measurement’ equivalence to be determined. Analyses based only on association or comparisons of means have limited ability to detect lack of equivalence. The study design is simpler than randomized cross over designs as only one sample for each format is required. Although two paper and pen versions were used in the present study, this would not be necessary in standard equivalence testing. There is also no need to match samples in terms of disease severity or location at which they were completed.
A potential limitation of the Rasch approach is that relatively large sample sizes are needed (approximately 150) for each format. However, similar sample sizes would provide more accurate estimates when applying CTT approaches and it is crucial to know whether different formats are equivalent in many situations. A major limitation of this approach is that relatively few PRO measures fit the Rasch model due to their age and/or the lack of a coherent measurement model. This is actually a weakness of the PRO measures as in such cases it will remain difficult to establish the equivalence of different formats of the measures.
Differences between the performance of the electronic and pen and paper administrations of the CAMPHOR were minor. The results showed how the Rasch model can be used to determine the equivalence of alternative formats of PRO measures.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
- Scoggins JF, Patrick DL. The use of patient-reported outcomes instruments in registered clinical trials: evidence from ClinicalTrials.gov. Contemp Clin Trials. 2009;30(4):289–92.View ArticlePubMedPubMed CentralGoogle Scholar
- Hufford MR, Sheilds AL. Electronic subject diaries: an examination of applications and what works in the field. Appl Clin Trials. 2002;11(1):46–56.Google Scholar
- Stone AA, Shiffman S, Schwartz JE, Broderick JE, Hufford MR. Patient non-compliance with paper diaries. BMJ. 2002;324(7347):1193–4.View ArticlePubMedPubMed CentralGoogle Scholar
- Bloom DE. Technology, experimentation, and the quality of survey data. Science. 1998;280(5365):847–8.View ArticlePubMedGoogle Scholar
- Gwaltney CJ, Shields AL, Shiffman S. Equivalence of electronic and paper-and-pencil administration of patient-reported outcome measures: a meta-analytic review. Value Health. 2008;11(2):322–33.View ArticlePubMedGoogle Scholar
- Sheskin DJ. Handbook of parametric and nonparametric statistical procedures. 3rd ed. Florida: CRC Press; 2003.View ArticleGoogle Scholar
- Ring AE, Cheong KA, Watkins CL, Meddis D, Cella D, Harper PG. A Randomized study of electronic diary versus paper and pencil collection of patient-reported outcomes in patients with non-small cell lung cancer. Patient. 2008;1(2):105–13.View ArticlePubMedGoogle Scholar
- Abernethy AP, Ahmad A, Zafar SY, Wheeler JL, Reese JB, Lyerly HK. Electronic patient-reported data capture as a foundation of rapid learning cancer care. Med Care. 2010;48(6):S32–38.View ArticlePubMedGoogle Scholar
- Bishop FL, Lewis G, Harris S, McKay N, Prentice P, Theil H, Lweith GT. A within-subjects trial to test the equivalence of online and paper outcome measures: the Rolad Morris Disability Questionnaire. BMC Musculoskelet Disord. 2010;11(113):1–7.Google Scholar
- Coons SJ, Gwaltney CJ, Hays RD, Lundy JJ, Sloan JA, Revicki DA, Lenderking WR, Cella D, Basch E. Recommendations on evidence needed to support measurement equivalence between electronic and paper-based patient-reported outcome (PRO) measures: ISPOR ePRO Good Research Practices Task Force report. Value Health. 2009;12(4):419–29.View ArticlePubMedGoogle Scholar
- Rasch G. Probabilistic models for some intelligence and attainment tests. Chicago: University of Chicago Press; 1980.Google Scholar
- Bond TG, Fox CM. Applying the Rasch Model: Fundamental measurement for the human sciences. New Jersey: Lawrence Erlbaum Associates, Inc; 2001.Google Scholar
- Smith Jr EV. Evidence for the reliability of measures and validity of measure interpretation: a Rasch measurement perspective. J Appl Meas. 2001;2:281–311.PubMedGoogle Scholar
- Prieto L, Alonso J, Lamarca R. Classical test theory versus Rasch analysis for quality of life questionnaire reduction. Health Qual Life Outcomes. 2003;1(27):1–13.Google Scholar
- Bjorner JB, Rose M, Gandek B, Stone AA, Junghaenel DU, Ware Jr JE. Difference in method of administration did not significantly impact item response: an IRT-based analysis from the Patient-Reported Outcomes Measurement Information System (PROMIS) initiative. Qual Life Res. 2014;23(1):217–27.View ArticlePubMedPubMed CentralGoogle Scholar
- Chang YJ, Chang CH, Peng CL, Wu HC, Lin HC, Wang JY, Li TC, Yeh YC, Liang WM. Measurement equivalence and feasibility of the EORTC QLQ-PR25: paper-and-pencil versus touch-screen administration. Health Qual Life Outcomes. 2014;12:1–10.View ArticleGoogle Scholar
- McKenna SP, Doughty N, Meads DM, Doward LC, Pepke-Zaba J. The Cambridge Pulmonary Hypertension Outcome Review (CAMPHOR): A measure of health-related quality of life and quality of life for patients with pulmonary hypertension. Qual Life Res. 2006;15(1):103–15.View ArticlePubMedGoogle Scholar
- World Health Organization. International classification of functioning, disability and health. Geneva: World Health Organization; 2001.Google Scholar
- Swetz KM, Shanafelt TD, Drozdowicz LB, Sloan JA, Novotny PJ, Durst LA, Frantz RP, McGoon MD. Symptom burden, quality of life, and attitudes toward palliative care in patients with pulmonary arterial hypertension: Results from a cross-sectional patient survey. J Heart Lung Transplant. 2012;31(10):1102–8.View ArticlePubMedGoogle Scholar
- Anderson P, Benford M, Harris N, Karavali M, Piercy J. Real-world physician and patient behaviour across countries: Disease-Specific Programmes – a means to understand. Curr Med Res Opin. 2008;24(11):3063–72.View ArticlePubMedGoogle Scholar
- Gomberg-Maitland M, Thenappan T, Rizvi K, Chandra S, Meads DM, McKenna SP. United States validation of the Cambridge Pulmonary Hypertension Outcome Review (CAMPHOR). J Heart Lung Transplant. 2008;27(1):124–30.View ArticlePubMedGoogle Scholar
- Tennant A, Gonaghan PG. The Rasch measurement model in rheumatology: what is it and why use it? When should it be applied, and what should one should one look for in a Rasch paper? Arthritis Rheum. 2007;57:1358–62.View ArticlePubMedGoogle Scholar
- Hambleton RK. Good practices for identifying differential item functioning. Med Care. 2006;44:S182–8.View ArticlePubMedGoogle Scholar
- Andrich D, Sheridan B, Luo G. RUMM2030: a Windows program for the Rasch unidimensional measurement model. Perth: RUMM Laboratory; 2010.Google Scholar
- Andrich D. Rating formulation for ordered response catagories. Psychometrika. 1978;43:561–73.View ArticleGoogle Scholar
- Masters G. A Rasch model for partial credit scoring. Psychometrika. 1982;47:149–74.View ArticleGoogle Scholar
- Smith EV. Detecting and evaluating the impact of multidimensionality using item fit statistics and principal component analysis of residuals. J Appl Meas. 2002;3(2):205–31.PubMedGoogle Scholar
- Tennant A, Pallant JF. DIF matters: A practical approach to test if differential item functioning makes a difference. Rasch Measurement Transactions. 2007;20(4):1082–84.Google Scholar
- Twiss J, Meads DM, Preston EP, Crawford SR, McKenna SP. Can we rely on the Dermatology Life Quality Index (DLQI) as a measure of the impact of psoriasis or atopic dermatitis? J Invest Dermatol. 2012;132(1):76–84.View ArticlePubMedGoogle Scholar
- Leske DA, Hatt SR, Liebermann L, Holmes JM. Evaluation of the Adult Strabismus-20 (AS-20) questionnaire using Rasch analysis. Invest Ophthalmol Vis Sci. 2012;53(6):2630–9.View ArticlePubMedPubMed CentralGoogle Scholar
- Algurén B, Bostan C, Christensson L, Fridlund B, Cieza A. A multidisciplinary cross-cultural measurement of functioning after stroke: Rasch analysis of the brief ICF core set for stroke. Top Stroke Rehabil. 2011;18(1):573–86.View ArticlePubMedGoogle Scholar