Skip to main content Accessibility help
×
Hostname: page-component-848d4c4894-5nwft Total loading time: 0 Render date: 2024-06-06T04:00:48.670Z Has data issue: false hasContentIssue false

Chapter 6 - Why Models Are Important in Healthcare

Published online by Cambridge University Press:  13 July 2023

Ramalingam Shanmugam
Affiliation:
Texas State University, San Marcos
Get access

Summary

A model is a description of the system that generates data. Box commented that some models are useful, but many are wrong. A reason exists for such a belief (Box, 2013). Nature functions in accordance with mysterious principles. Do such principles precisely fit the mathematical system humans have created? An example of such a mathematical system is the calendar. Over millennia, astronomers, scientists, and philosophers have struggled to redefine and refine the calendar. Different Tamil, Greek, Egyptian, and Sumerian calendars exist, but scholars realized an adjustment is necessary every four years to the number of days in the month of February. The current Gregorian calendar was introduced as an improvement on the Julian calendar in 1582. In a similar way to developing the calendar, modeling the chance-oriented healthcare system is a formidable task even for experts.

What is a model value? In general, values are depictions of a decision maker’s priorities. Model values are not unique to the healthcare field. Model values originated in finance. Swiss mathematician and physicist Daniel Bernoulli (1738) states money’s value decreases over time.

Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2023

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Selected References

Alemi, F., & Gustafson, D. H. (2007). Decision Analysis for Healthcare Managers. Chicago, IL: Health Administration Press.Google Scholar
Bartolucci, A., Shanmugam, R., & Singh, K. (2001). Development of the generalized geometric model with application to cardiovascular studies. Systems Analysis Modeling and Simulation, 41, 339349.Google Scholar
Bernoulli, D. (1738). Hydrodynamics. Dulsecker. Consultable enligne. http://imgbase-scd-ulp.ustrasbg.fr/displayimage.php.Google Scholar
Box, G. E. (2013). An Accidental Statistician: The Life and Memories of George E. P .Box. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
Chattamvelli, R., & Shanmugam, R. (2020). Discrete distributions in engineering and the applied sciences. Synthesis Lectures on Mathematics and Statistics, 12(2), 1227.Google Scholar
Chattamvelli, R., & Shanmugam, R. (2021). Continuous distributions in engineering and the applied sciences: Part I. Synthesis Lectures on Mathematics and Statistics, 13(2), 1173.Google Scholar
Crouch, R., & Haines, C. (2004). Mathematical modelling: Transitions between the real world and the mathematical model, International Journal of Mathematical Education in Science and Technology, 35(2), 197206.Google Scholar
Kapur, J. N. (1984). Mathematical models in medical sciences. International Journal of Mathematical Education in Science and Technology, 15(5), 587600.Google Scholar
Ozcan, Y. A. (2005). Quantitative Methods in Health Care Management: Techniques and Applications (Vol. 4). Hoboken, NJ: Wiley.Google Scholar
Perdikaris, S. C. (1994). A Markov chain model in mathematical skill learning. International Journal of Mathematical Education in Science and Technology, 25(1), 8185.Google Scholar
Plunkett, S. (1983). People, mathematics and philosophy. International Journal of Mathematical Education in Science and Technology, 14(1), 3336.CrossRefGoogle Scholar
Rosenfeld, A., & Kraus, S. (2018). Predicting human decision-making: From prediction to action. Synthesis Lectures on Artificial Intelligence and Machine Learning, 12(1), 1150.CrossRefGoogle Scholar
Schoenbach, V. J., & Rosamond, W. D. (2000). Understanding the Fundamentals of Epidemiology: An Evolving Text. Chapel Hill: University of North Carolina Press. www.epidemiolog.net/evolving/FundamentalsOfEpidemiology.pdf.Google Scholar
Shanmugam, R. (1985). An intervened Poisson model and its medical applications. Biometrics, 41, 10251030.CrossRefGoogle Scholar
Shanmugam, R. (1991). Incidence rate restricted Poissonness. Sankhya (Series B), 53, 191201.Google Scholar
Shanmugam, R. (1992). An inferential procedure for the Poisson intervention parameter. Biometrics, 48, 559565.Google Scholar
Shanmugam, R. (2001). Predicting a successful prevention of an epidemic. Communications in Statistics, 30, 93103.Google Scholar
Shanmugam, R. (2006a). Bivariate distributions. In Encyclopedia of Measurement and Statistics, edited by Salkind, N. J. (pp. 97103). Thousand Oaks, CA: Sage.Google Scholar
Shanmugam, R. (2006b). Poisson distribution. In Encyclopedia of Measurement and Statistics, edited by Salkind, N. J. (pp. 772775). Thousand Oaks, CA: Sage.Google Scholar
Shanmugam, R. (2008). Double anchored syllogisms for medical scenarios. Journal of Statistics and Applications, 3, 253277.Google Scholar
Shanmugam, R. (2009). A tutorial of diagnostic methodology with 2 × 2 dementia data. International Journal of Data Analysis Techniques and Strategies, 2, 385406.Google Scholar
Shanmugam, R. (2010). A diagnostic methodology for hazy data with “borderline” cases. Journal of Medical Systems, 34, 161177.Google Scholar
Shanmugam, R. (2011a). Correlation between dispersion and mean to assess healthcare service efficiency. American Journal of Biostatistics, 2(2), 3643.Google Scholar
Shanmugam, R. (2011b). Is next twelve months’ period tumor recurrence free under restricted rate due to medication? A probabilistic warning. Journal of Modern Applied Statistical Methods, 10(1), 329336.Google Scholar
Shanmugam, R. (2011c). Spinned Poisson model with health management application. Healthcare Management Science, 14(4), 299306.Google Scholar
Shanmugam, R. (2011d). Taylorized modified power series distributions with epileptic seizure incidence applications. International Journal of Applied Mathematics and Statistics, 7(A11), 2741.Google Scholar
Shanmugam, R. (2011e). What else do epileptic data reveal? American Medical Journal, 2(1), 1328.Google Scholar
Shanmugam, R. (2012a). Intervened 2-tier Poisson model for understanding hospital site infectivity. International Journal of Research in Nursing, 3(1),814.Google Scholar
Shanmugam, R. (2012b). Spiral binomial and related distributions for obsession to abortion. International Journal of Research in Nursing, 3(2), 2128.CrossRefGoogle Scholar
Shanmugam, R. (2013a). Alternate to traditional goodness of fit test with illustration using service duration to patients in hospitals. International Journal of Statistics and Economics, 11(2), 3143.Google Scholar
Shanmugam, R. (2013b). Alzheimer’s disease prognosis is captured by a down-upsized incidence Poisson distribution. American Medical Journal, 4(2),150159.Google Scholar
Shanmugam, R. (2013c). Does over or under dispersion in inverse binomial data suggest anything? A case in point is the waiting time for both heart-lung transplants. American Journal of Biostatistics, 3(2), 3037.Google Scholar
Shanmugam, R. (2013d). Is cancer recurrence postponed by a treatment? A new model answers. American Medical Journal, 4(1),4362.Google Scholar
Shanmugam, R. (2013e). Mosaic masonries to interpret diagnostic test results. American Medical Journal, 4(1),1220.Google Scholar
Shanmugam, R. (2013f). Probabilistic health-informatics and bioterrorism. International Journal of Communication and Computer, 10, 2832.Google Scholar
Shanmugam, R. (2013g). Shortage level of matching kidney and pancreas organs for implant is estimated. International Journal of Research in Nursing, 4(2), 4050.CrossRefGoogle Scholar
Shanmugam, R. (2013h). Tweaking exponential model to estimate the chance for more survival time if a cancerous kidney is removed. International Journal of Research in Nursing, 4(1),2933.Google Scholar
Shanmugam, R. (2013i). Unified survival functions are derived and illustrated using hospitals’ preparedness data to treat anthrax cases. International Journal of Statistics and Economics, 12(3), 8295.Google Scholar
Shanmugam, R. (2014a). An assessment of nurses’ sufficient immunity when treating infectious patients using bumped-up binomial model. International Journal of Research in Medical Sciences, 2(1), 132138.Google Scholar
Shanmugam, R. (2014b). Data envelopment analysis for operational efficiency. In Encyclopedia of Business Analytics and Optimization (Vol. 2), edited by Wang, J. (pp. 1828). New York: IGI Global.Google Scholar
Shanmugam, R. (2014c). Data guided public healthcare decision making. In Encyclopedia of Business Analytics and Optimization (Vol. 2), edited by Wang, J. (pp. 3043). New York: IGI Global.Google Scholar
Shanmugam, R. (2014d). Health broken woven Poisson spheres to manage deadly Ebola incidences. American Journal of Infectious Diseases, 10, 143154.Google Scholar
Shanmugam, R. (2014e). How do queuing concepts and tools help to effectively manage hospitals when the patients are impatient? A demonstration. International Journal of Research in Medical Sciences, 2, 10761084.Google Scholar
Shanmugam, R. (2014f). Probing non-adherence to prescribed medicines? A bivariate model with information nucleus clarifies. American Medical Journal, 5, 5460.Google Scholar
Shanmugam, R. (2014g). Encyclopedia of Business Analytics and Optimization (Vol. 5), edited by Wang, J. (pp. 1826). New York: IGI Global.Google Scholar
Shanmugam, R. (2014h). Tweaked binomial model to capture the impact of drilling to cure bioterror victims in hospitals. International Journal of Statistics and Economics, 13(1), 4045.Google Scholar
Shanmugam, R. (2015a). Curvature informatics about medical errors: Geometric view of incidence restricted Poisson. International Journal of Ecological Economics & Statistics. 36(4), 7180.Google Scholar
Shanmugam, R. (2015b). Entropy nucleus and use in waste disposal policies. International Journal on Information Theory, 4(2), 112.Google Scholar
Shanmugam, R. (2015c). Geometric view of odds tilted binomial model and its use to analyze asthma incidences data among monozygotic versus dizygotic twins. International Journal of Medical Science Research and Practice, 1(1), 15.Google Scholar
Shanmugam, R. (2015d). Never, once, and repeated illness: A geometric view for insights and interpretations. International Journal of Research in Medical Sciences, 3(6), 13361341.Google Scholar
Shanmugam, R. (2015e). Refined randomized response model for suspicious answers: Illicit drug users in U.S.A. are illustrated. International Journal of Ecological Economics & Statistics. 36, 1527.Google Scholar
Shanmugam, R. (2015f). Visual curvatures of H1N1 incidences in African, Asian, European, American, and Oceanic nations. American Medical Journal, 6(2), 1426.Google Scholar
Shanmugam, R. (2016a). Data directed root cause analyses of hospital adversities and their proximities. International Journal of Research in Medical Sciences, 4(9), 41584165.CrossRefGoogle Scholar
Shanmugam, R. (2016b). Data guided unraveling of mysteries in Zika virus incidences. Kenkyu Journal of Epidemiology & Community Medicine, SI 20161: 100101, 112.Google Scholar
Shanmugam, R. (2016c). Entropy in Nucleus to tab data information and its illustration with Wolfram syndrome cases. International Journal of Ecological Economics and Statistics, 37(3), 4463.Google Scholar
Shanmugam, R. (2016d). Whether Gaussian nucleus entropy helps? Case in point is prediction of number of cesarean births. American Journal of Biostatisticis, 6(2), 2029.Google Scholar
Shanmugam, R. (2018a). Impact of raising copayment and/or reducing reimbursement benefits on healthcare according to “eisequilibrium bivariate distribution.” Biostatistics and Biometrics Open Access Journal, 5(1), 113.Google Scholar
Shanmugam, R. (2018b). Jumping over zero mass point convex Poisson model and its fecundability application. International Journal of Applied Mathematics and Statistics, 57(6), 2135.Google Scholar
Shanmugam, R. (2018c). Patient’s over-visit phobia versus physician’s over-prescription phobia. International Journal of Research in Medical Sciences, 6(9), 29292936.Google Scholar
Shanmugam, R. (2019a). Integrating physician’s and patient’s interest before judging the efficiency of a diagnostic test. International Journal of Research in Medical Sciences, 7(11), 39693978.CrossRefGoogle Scholar
Shanmugam, R. (2019b). Parity between prescription and visitation rates in healthcare. Wireless Networks, 1–10. https://doi.org/10.1007/s11276-019-02204-2.Google Scholar
Shanmugam, R. (2019c). A type-1 imbalanced bivariate Poisson model demystifies patient’s phobia visiting physician often and its implications. Journal of Statistical Theory and Practice, 13(1), 120.Google Scholar
Shanmugam, R. (2020a). Distracted multinomial model for corona screening at entry ports. International Journal of Research in Medical Sciences, 8(5), 16061611.Google Scholar
Shanmugam, R. (2020b). Probabilistic patterns among coronavirus confirmed, cured and deaths in thirty-two India’s states/territories. International Journal of Ecological Economics and Statistics, 41(4), 4556.Google Scholar
Shanmugam, R. (2020c). Restricted prevalence rates of COVID-19’s infectivity, hospitalization, recovery, mortality in the USA and their implications. Journal of Healthcare Informatics Research, 5(2), 133150.Google Scholar
Shanmugam, R., Bartolucci, A., & Singh, K. (2002). The analysis of neurological studies using extended exponential model. Mathematical and Computers in Simulation, 59(1–3), 8185.Google Scholar
Shanmugam, R., & Chattamvelli, R. (2015). Statistics for Scientists and Engineers. Hoboken, NJ: Wiley Inter-Science.Google Scholar
Shanmugam, R., Johnson, C., & Cutter, G. (2006). Examining whether an epidemic is excessive. Journal of Statistics and Applications, 1, 5162.Google Scholar
Shanmugam, R., & Radhakrishnan, R. (2011). Incidence jump rate reveals over/under dispersion in count data. International Journal of Data Analysis and Information Systems, 3(1), 18.Google Scholar
Shanmugam, R., & Singh, K. (2001). Testing of Poisson incidence rate restriction. International Journal of Reliability and Applications, 4, 263268.Google Scholar
Shanmugam, R., Tripathi, R., & Singh, K. (2017). Road safety when drivers use alcohol and marihuana: Confounded Poisson model helps to understand. International Journal of Research in Nursing, 8(1), 39.Google Scholar
Stiglic, G., Kocbek, P., Fijacko, N., Zitnik, M., Verbert, K., & Cilar, L. (2020). Interpretability of machine learning‐based prediction models in healthcare. Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery, 10(5), e1379.Google Scholar
Uche, P. I. (1987). Some aspects of transition proportions. International Journal of Mathematical Education in Science and Technology, 18(3), 375380.Google Scholar
Veney, J. E. (2003). Statistics for Health Policy and Administration using Microsoft Excel (Vol. 6). San Francisco, CA: Jossey-Bass.Google Scholar
Voskoglou, M. G. (1994). An application of Markov chain to the process of modelling. International Journal of Mathematical Education in Science and Technology, 25(4), 475480.Google Scholar
Walck, C. (2007). Handbook on Statistical Distributions for Experimentalists. Stockholm: University of Stockholm.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×