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RespOnse Shift ALgorithm in Item response theory (ROSALI) for response shift detection with missing data in longitudinal patient-reported outcome studies



Some IRT models have the advantage of being robust to missing data and thus can be used with complete data as well as different patterns of missing data (informative or not). The purpose of this paper was to develop an algorithm for response shift (RS) detection using IRT models allowing for non-uniform and uniform recalibration, reprioritization RS recognition and true change estimation with these forms of RS taken into consideration if appropriate.


The algorithm is described, and its implementation is shown and compared to Oort’s structural equation modeling (SEM) procedure using data from a clinical study assessing health-related quality of life in 669 hospitalized patients with chronic conditions.


The results were quite different for the two methods. Both showed that some items of the SF-36 General Health subscale were affected by response shift, but those items usually differed between IRT and SEM. The IRT algorithm found evidence of small recalibration and reprioritization effects, whereas SEM mostly found evidence of small recalibration effects.


An algorithm has been developed for response shift analyses using IRT models and allows the investigation of non-uniform and uniform recalibration as well as reprioritization. Differences in RS detection between IRT and SEM may be due to differences between the two methods in handling missing data. However, one cannot conclude on the differences between IRT and SEM based on a single application on a dataset since the underlying truth is unknown. A next step would be to implement a simulation study to investigate those differences.

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  1. Oort, F. J. (2005). Using structural equation modeling to detect response shifts and true change. Quality of Life Research: An International Journal of Quality of Life Aspects of Treatment, Care and Rehabilitation, 14(3), 587–598.

    Article  Google Scholar 

  2. Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data. Hoboken: Wiley.

    Book  Google Scholar 

  3. Swartz, R. J., Schwartz, C., Basch, E., Cai, L., Fairclough, D. L., McLeod, L., et al. (2011). The king’s foot of patient-reported outcomes: Current practices and new developments for the measurement of change. Quality of Life Research, 20(8), 1159–1167.

    Article  PubMed Central  PubMed  Google Scholar 

  4. Fischer, G. H., & Molenaar, I. W. (1995). Rasch models: Foundations, recent developments, and applications. New York: Springer.

    Book  Google Scholar 

  5. Wang, W.-C., & Chyi-In, W. (2004). Gain score in item response theory as an effect size measure. Educational and Psychological Measurement, 64(5), 758–780.

    Article  Google Scholar 

  6. Andrich, D. (2011). Rating scales and rasch measurement. Expert Review of Pharmacoeconomics & Outcomes Research, 11, 571–585.

    Article  Google Scholar 

  7. De Bock, E., Hardouin, J. -B., Blanchin, M., Le Neel, T., Kubis, G., Bonnaud-Antignac, A., et al. (2013). Rasch-family models are more valuable than score-based approaches for analysing longitudinal patient-reported outcomes with missing data. Statistical Methods in Medical Research (in press).

  8. Sébille, V., Hardouin, J.-B., & Mesbah, M. (2007). Sequential analysis of latent variables using mixed-effect latent variable models: Impact of non-informative and informative missing data. Statistics in Medicine, 26(27), 4889–4904.

    Article  PubMed  Google Scholar 

  9. Hardouin, J.-B., Conroy, R., & Sébille, V. (2011). Imputation by the mean score should be avoided when validating a Patient Reported Outcomes questionnaire by a Rasch model in presence of informative missing data. BMC Medical Research Methodology, 11(1), 105.

    Article  PubMed Central  PubMed  Google Scholar 

  10. De Bock, É. de, Hardouin, J. -B., Blanchin, M., Neel, T. L., Kubis, G., & Sébille, V. (2014). Assessment of score- and Rasch-based methods for group comparison of longitudinal patient-reported outcomes with intermittent missing data (informative and non-informative). Quality of Life Research, 1–11.

  11. Hamel J. F., Sébille V., Le Neel T., Kubis G., & Hardouin J. B. (2012) Study of different methods for comparing groups by analysis of patients reported outcomes: Item response theory based methods seem more efficient than classical test theory based methods when data is missing. Under review.

  12. Schwartz, C. E., & Sprangers, M. A. (1999). Methodological approaches for assessing response shift in longitudinal health-related quality-of-life research. Social Science & Medicine, 48(11), 1531–1548.

  13. Glas, C. A. W. (1988). The derivation of some tests for the Rasch model from the multinomial distribution. Psychometrika, 53, 525–546.

    Article  Google Scholar 

  14. Glas, C. A. W. (2010).

  15. Satorra, A., & Bentler, P. M. (1994). Corrections to test statistics and standard errors in covariance structure analysis. In A. von & C. C. Clogg (Eds.), Latent variables analysis: Applications for developmental research (pp. 399–419). Thousand Oaks, CA, US: Sage Publications, Inc.

  16. Rosseel, Y. (2012). Lavaan: An R package for structural equation modeling. Journal of Statistical Software, 48(2), 1–36.

    Google Scholar 

  17. R Development Core Team. (n.d.). R Development Core Team. (2013). R: A language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing.

  18. Schermelleh-Engel, K., Moosbrugger, H., & Müller, H. (2003). Evaluating the fit of structural equation models: Tests of significance and descriptive goodness-of-fit measures. Methods of Psychological Research-Online, 8, 23–74.

    Google Scholar 

  19. Bryant, F. B., & Satorra, A. (2012). Principles and practice of scaled difference Chi Square testing. Structural Equation Modeling: A Multidisciplinary Journal, 19(3), 372–398.

    Article  Google Scholar 

  20. Enders, C. K. (2013). Analyzing structural equation models with missing data. In Structural Equation (Ed.), Modeling : a second course (pp. 493–519). Charlotte, NC: IAP, Information Age Publ.

    Google Scholar 

  21. Enders, C. K., & Bandalos, D. L. (2001). The relative performance of full information maximum likelihood estimation for missing data in structural equation models. Structural Equation Modeling, 8(3), 430–457.

    Article  Google Scholar 

  22. Kepka, S., Baumann, C., Anota, A., Buron, G., Spitz, E., Auquier, P., Guillemin, F., Mercier, M. (2013). The relationship between traits optimism and anxiety and health-related quality of life in patients hospitalized for chronic diseases: data from the SATISQOL study. Health and Quality of Life Outcomes, 11(1), 134.

  23. Ware, J. E., & Sherbourne, C. D. (1992). The MOS 36-item short-form health survey (SF-36). I. Conceptual framework and item selection. Medical Care, 30(6), 473–483.

    Article  PubMed  Google Scholar 

  24. Leplège, A., Ecosse, E., Verdier, A., & Perneger, T. V. (1998). The French SF-36 Health Survey: translation, cultural adaptation and preliminary psychometric evaluation. Journal of Clinical Epidemiology, 51(11), 1013–1023.

    Article  PubMed  Google Scholar 

  25. Leplège, A. (2001). Le questionnaire MOS SF-36: manuel de l’utilisateur et guide d’interprétation des scores. Paris: Editions ESTEM.

    Google Scholar 

  26. Fairclough, D. L. (2002). Design and analysis of quality of life studies in clinical trials: Interdisciplinary statistics. London: Chapman & Hall/Crc.

    Google Scholar 

  27. Hamel, J.-F., Hardouin, J.-B., Le Neel, T., Kubis, G., Roquelaure, Y., & Sébille, V. (2012). Biases and power for groups comparison on subjective health measurements. PLoS ONE, 7(10), e44695.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

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This study was supported by the Institut National du Cancer, under reference “INCA_6931.” The SatisQoL cohort project (investigators: P. Auquier, F. Guillemin (PI), M. Mercier) was supported by an IRESP (Institut de recherche en santé publique) Grant from Inserm, and a PHRC (Programme Hospitalier de Recherche Clinique) National Grant from French Ministry of Health, France.

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Correspondence to Véronique Sébille.



The category probability curves (Fig. 6) represent the responses’ probabilities for an individual to endorse each response category for an item as a function of his latent trait level. δ j1 can be interpreted as the value of the latent trait for which the probability to respond negatively to item j is equal to the probability to answer positively to the first positive category (coded 1) for item j. The item characteristic curves (Fig. 7) are a representation of the expected score to an item as a function of the latent trait level. For example, for item j at time t, the slope of the curve is linked to the value of the discriminating power α (t) j .

Fig. 6
figure 6

Category probability curves of item j. The parameter δ jp corresponds to the item difficulty for each positive category p (p = 1, …, 3) of item j

Fig. 7
figure 7

Item characteristic curves for item j at time t. The parameter \(\alpha_{j}^{t}\) is the discriminating power at time t (t = 1, 2) for item j

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Guilleux, A., Blanchin, M., Vanier, A. et al. RespOnse Shift ALgorithm in Item response theory (ROSALI) for response shift detection with missing data in longitudinal patient-reported outcome studies. Qual Life Res 24, 553–564 (2015).

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  • Item response theory
  • Response shift
  • Missing data
  • Attrition
  • Bias
  • Quality of life