Abstract
In this paper, we aim at ranking a set of nursing homes based on their ability in maintaining their residents’ physical conditions as good as possible. In this respect, we propose a nursing home performance indicator, which is essentially a probability to avoid resident health status worsening. Specifically, latent Markov models with covariates and normally distributed continuous random effects are fitted to produce standardised 180-day ahead transition matrices, upon which the aforementioned index is based. Nursing home effects on these transition matrices are modelled through fixed as well as random effects. The performance index is used to build two distinct rankings, one of which also accounts for the variability induced by the estimation process. In this framework, several rankings can be obtained by combining the model specification (fixed vs. random effects), the kind of ranking and the number of latent states, which is the typical sensitivity parameter of latent Markov models. Our methodological approach is applied to a dataset which was gathered from a health protocol implemented in Umbria (Italy). Results for this data show a rather high degree of robustness, in the sense that the obtained rankings are almost the same.
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References
Afshartous, D., & Preston, R. A. (2010). Confidence intervals for dependent data: Equating non-overlap with statistical significance. Computational Statistics & Data Analysis, 54(10), 2296–2305.
Altman, R. M. (2007). Mixed hidden Markov models: An extension of the hidden Markov model to the longitudinal data setting. Journal of the American Statistical Association, 102(477), 201–210.
Arling, G., Kane, R. L., Lewis, T., & Mueller, C. (2005). Future development of nursing home quality indicators. The Gerontologist, 45(2), 147–156.
Arling, G., Lewis, T., Kane, R. L., Mueller, C., & Flood, S. (2007). Improving quality assessment through multilevel modeling: The case of nursing home compare. Health Services Research, 42(31), 1177–1199.
Bacci, S., Pandolfi, S., & Pennoni, F. (2014). A comparison of some criteria for states selection in the latent Markov model for longitudinal data. Advances in Data Analysis and Classification, 8, 125–145.
Bartolucci, F., Lupparelli, M., & Montanari, G. E. (2009). Latent Markov model for longitudinal binary data: An application to the performance evaluation of nursing homes. The Annals of Applied Statistics, 3(2), 611–636.
Bartolucci, F., Pennoni, F., & Vittadini, G. (2011). Assessment of school performance through a multilevel latent Markov Rasch model. Journal of Educational and Behavioral Statistics, 36(4), 491–522.
Bartolucci, F., Farcomeni, A., & Pennoni, F. (2013). Latent Markov models for longitudinal data. Statistics in the social and behavioural sciences. Boca Raton: Chapman & Hall.
Bartolucci, F., Bacci, S., & Pennoni, F. (2014). Longitudinal analysis of self-reported health status by mixture latent auto-regressive models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 63(2), 267–288.
Bartolucci, F., Pandolfi, S., & Pennoni, F. (2017). LMest: An R package for latent Markov models for longitudinal categorical data. Journal of Statistical Software, 81(4), 1–38.
Castle, N. G., & Ferguson, J. C. (2010). What is nursing home quality and how is it measured? The Gerontologist, 50(4), 426–442.
Colombi, R., Martini, G., & Vittadini, G. (2017). Determinants of transient and persistent hospital efficiency: The case of Italy. Health Economics, 26(S2), 5–22.
Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society, Series B, 39(1), 1–38.
Fletcher, R. (1987). Practical methods of optimization (2nd ed.). New York: Wiley.
Gnaldi M., Ranalli M. G. (2010) Composite indicators of scientific research: The robustness of university rankings based on composite measures. In Proceedings of the XLV scientific meeting of the Italian Statistical Society. June, 16–18, Padua.
Gnaldi, M., & Ranalli, M. G. (2016). Measuring university performance by means of composite indicators: A robustness analysis of the composite measure used for the benchmark of Italian universities. Social Indicators Research, 129, 659–675.
Goldstein, H., & Healy, M. J. R. (1995). The graphical presentation of a collection of means. Journal of the Royal Statistical Society, Series A, 158(1), 175–177.
Grilli, L., & Rampichini, C. (2009). Multilevel models for the evaluation of educational institutions: A review. In P. Monari, M. Bini, D. Piccolo, & L. Salmaso (Eds.), Statistical methods for the evaluation of educational services and quality of products (pp. 61–80). Heidelberg: Physica-Verlag HD.
Hirdes, J. P., Ljunggren, G., Morris, J. N., Frijters, D. H., Finne Soveri, H., Gray, L., Bjorkgren M., Gilgen R. (2008). Reliability of the interRAI suite of assessment instruments: A 12-country study of an integrated health information system. BMC Health Services Research, 8(1), 277.
Kim, H., Jung, Y. I., Sung, M., Lee, J. Y., Yoon, J. Y., & Yoon, J. L. (2015). Reliability of the interRAI Long Term Care Facilities (LTCF) and interRAI Home Care (HC). Geriatrics & Gerontology International, 15(2), 220–228.
Kitagawa, E. M. (1964). Standardized comparisons in population research. Demography, 1(1), 296–315.
Koukounari, A., Moustaki, I., Grassly, N. C., Blake, I. M., Basáñez, M. G., Gambhir, M., Mabey D. C., Bailey R. L., Burton M. J., Solomon A. W. (2013). Using a nonparametric multilevel latent Markov model to evaluate diagnostics for trachoma. American Journal of Epidemiology, 177(9), 913–922.
Makai, P., Brouwer, W. B., Koopmanschap, M. A., Stolk, E. A., & Nieboer, A. P. (2014). Quality of life instruments for economic evaluations in health and social care for older people: A systematic review. Social Science & Medicine, 102, 83–93.
Marozzi, M., & Bolzan, M. (2016a). An index of household accessibility to basic services: A study of Italian regions. Social Indicators Research, 136(3), 1237–1250.
Marozzi, M., & Bolzan, M. (2016b). Skills and training requirements of municipal directors: A statistical assessment. Quality and Quantity, 50, 1093–1115.
Maruotti, A. (2011). Mixed hidden Markov models for longitudinal data: An overview. International Statistical Review, 79(3), 427–454.
Maruotti, A., & Rocci, R. (2012). A mixed non-homogeneous hidden Markov model for categorical data, with application to alcohol consumption. Statistics in Medicine, 31(9), 871–886.
Montanari, G. E., & Pandolfi, S. (2018). Evaluation of long-term health care services through a latent Markov model with covariates. Statistical Methods & Applications, 27(1), 151–173.
Montanari, G. E., Doretti, M., & Bartolucci, F. (2017a). A multilevel latent Markov model for the evaluation of nursing homes’ performance, mPRA Working Paper. Available at http://mpra.ub.uni-muenchen.de/80691/.
Montanari, G. E., Doretti, M., & Bartolucci, F. (2017b). An ordinal latent Markov model for the evaluation of health care services. In Proceedings of SIS 2017 Statistical Conference on statistics and data science: New challenges, new generations (pp. 707–712).
Montanari, G. E., Doretti, M., & Bartolucci, F. (2017c). Statistical assessment of public health care services: A multilevel latent Markov model. In Proceedings of the 8th scientific conference on innovation and society, statistical methods for evaluation and quality. September, 6th–7th, 2017, Naples.
Oakes, D. (1999). Direct calculation of the information matrix via the EM algorithm. Journal of the Royal Statistical Society Series B (Methodological), 61, 479–482.
Pennoni, F., & Vittadini, G. (2013). Two competing models for ordinal longitudinal data with time-varying latent effects: an application to evaluate hospital efficiency. Journal of Methodological and Applied Statistics, 15, 53–68.
Phillips, C. D., Zimmerman, D., Bernabei, R., & Jonsson, P. V. (1997). Using the resident assessment instrument for quality enhancement in nursing homes. Age and Ageing, 26(S2), 77–81.
Pohle, J., Langrock, R., van Beest, F. M., & Schmidt, N. M. (2017). Selecting the number of states in hidden Markov models: Pragmatic solutions illustrated using animal movement. Journal of Agricultural, Biological and Environmental Statistics, 22(3), 270–293.
Rampichini, C., Grilli, L., & Petrucci, A. (2004). Analysis of university course evaluations: From descriptive measures to multilevel models. Statistical Methods and Applications, 13(3), 357–373.
Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464.
Vermunt, J. K., Langeheine, R., & Bockenholt, U. (1999). Discrete-time discrete-state latent Markov models with time-constant and time-varying covariates. Journal of Educational and Behavioral Statistics, 24(2), 179–207.
Vittadini, G., & Minotti, S. C. (2005). A methodology for measuring the relative effectiveness of healthcare services. IMA Journal of Management Mathematics, 16(3), 239–254.
Wiggins, L. M. (1973). Panel analysis: Latent probability models for attitude and behavior processes. San Francisco: Jossey-Bass.
Zucchini, W., & MacDonald, I. L. (2009). Hidden Markov models for time series (1st ed.). Boca Raton: Chapman & Hall.
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The authors would like to thank the referees for their useful and invaluable comments as well as Regione Umbria for sharing LTCF data and providing financial support.
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Montanari, G.E., Doretti, M. Ranking Nursing Homes’ Performances Through a Latent Markov Model with Fixed and Random Effects. Soc Indic Res 146, 307–326 (2019). https://doi.org/10.1007/s11205-018-1947-7
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DOI: https://doi.org/10.1007/s11205-018-1947-7