zbMATH — the first resource for mathematics

Bayesian nonparametric policy search with application to periodontal recall intervals. (English) Zbl 1441.62362
Summary: Tooth loss from periodontal disease is a major public health burden in the United States. Standard clinical practice is to recommend a dental visit every six months; however, this practice is not evidence-based, and poor dental outcomes and increasing dental insurance premiums indicate room for improvement. We consider a tailored approach that recommends recall time based on patient characteristics and medical history to minimize disease progression without increasing resource expenditures. We formalize this method as a dynamic treatment regime which comprises a sequence of decisions, one per stage of intervention, that follow a decision rule which maps current patient information to a recommendation for their next visit time. The dynamics of periodontal health, visit frequency, and patient compliance are complex, yet the estimated optimal regime must be interpretable to domain experts if it is to be integrated into clinical practice. We combine nonparametric Bayesian dynamics modeling with policy-search algorithms to estimate the optimal dynamic treatment regime within an interpretable class of regimes. Both simulation experiments and application to a rich database of electronic dental records from the HealthPartners HMO shows that our proposed method leads to better dental health without increasing the average recommended recall time relative to competing methods.
62P10 Applications of statistics to biology and medical sciences; meta analysis
62F15 Bayesian inference
Full Text: DOI
[1] AAP, Glossary of Periodontal Terms (2001), Chicago, IL: American Academy of Periodontology, Chicago, IL
[2] AAP, “American Academy of Periodontology Task Force Report on the Update to the 1999 Classification of Periodontal Diseases and Conditions,”, Journal of Periodontology, 86, 835-838 (2005)
[3] Almirall, D.; Nahum-Shani, I.; Sherwood, N. E.; Murphy, S. A., “Introduction to SMART Designs for the Development of Adaptive Interventions: With Application to Weight Loss Research,”, Translational Behavioral Medicine, 4, 260-274 (2014)
[4] Arjas, E.; Saarela, O., “Optimal Dynamic Regimes: Presenting a Case for Predictive Inference,”, The International Journal of Biostatistics, 6 (2010)
[5] Axelsson, P.; Lindhe, J.; Nyström, B., “On the Prevention of Caries and Periodontal Disease,”, Journal of Clinical Periodontology, 18, 182-189 (1991)
[6] CDC, Oral Health: Preventing Cavities, Gum Disease, Tooth Loss, and Oral Cancers at a Glance 2011 (2010), Atlanta, GA: CDC, Division of Oral Health, National Center for Chronic Disease Prevention and Health Promotion, Atlanta, GA
[7] Chakraborty, B.; Moodie, E. E., Statistical Methods for Dynamic Treatment Regimes (2013), New York: Springer, New York · Zbl 1278.62169
[8] Ciarleglio, A.; Petkova, E.; Ogden, R. T.; Tarpey, T., “Treatment Decisions Based on Scalar and Functional Baseline Covariates,”, Biometrics, 71, 884-894 (2015) · Zbl 1419.62328
[9] Cleveland, W. S.; Devlin, S. J., “Locally Weighted Regression: An Approach to Regression Analysis by Local Fitting.”, Journal of the American Statistical Association, 83, 596-610 (1988) · Zbl 1248.62054
[10] Davenport, C.; Elley, K.; Fry-Smith, A.; Taylor-Weetman, C.; Taylor, R., “The Effectiveness of Routine Dental Checks: A Systematic Review of the Evidence Base,”, British Dental Journal, 195, 87-98 (2003)
[11] Fardal, Ø.; Johannessen, A. C.; Linden, G. J., “Tooth Loss During Maintenance Following Periodontal Treatment in a Periodontal Practice in Norway,”, Journal of Clinical Periodontology, 31, 550-555 (2004)
[12] Fenol, A.; Mathew, S., “Compliance to Recall Visits by Patients With Periodontitis - Is the Practitioner Responsible?”, Journal of Indian Society of Periodontology, 14, 106-108 (2010)
[13] Ferguson, T. S., “A Bayesian Analysis of Some Nonparametric Problems,”, The Annals of Statistics, 1, 209-230 (1973) · Zbl 0255.62037
[14] Giannobile, W. V.; Braun, T. M.; Caplis, A. K.; Doucette-Stamm, L.; Duff, G. W.; Kornman, K. S., “Patient Stratification for Preventive Care in Dentistry,”, Journal of Dental Research, 92, 694-701 (2013)
[15] Gramacy, R. B.; Lee, H. K., “Cases for the Nugget in Modeling Computer Experiments,”, Statistics and Computing, 22, 713-722 (2012) · Zbl 1252.62098
[16] Guan, Q.; Laber, E. B.; Reich, B. J., “Discussion of ‘Bayesian Nonparametric Estimation for Dynamic Treatment Regimes With Sequential Transition Times’,”, Journal of the American Statistical Association, 111, 936-942 (2016)
[17] Hill, E. G.; Slate, E. H.; Wiegand, R. E.; Grossi, S. G.; Salinas, C. F., “Study Design for Calibration of Clinical Examiners Measuring Periodontal Parameters,”, Journal of Periodontology, 77, 1129-1141 (2006)
[18] Holtfreter, B.; Albandar, J. M.; Dietrich, T.; Dye, B. A.; Eaton, K. A.; Eke, P. I.; Papapanou, P. N.; Kocher, T., “Standards for Reporting Chronic Periodontitis Prevalence and Severity in Epidemiologic Studies: Proposed Standards From the Joint EU/USA Periodontal Epidemiology Working Group,”, Journal of Clinical Periodontology, 42, 407-412 (2015)
[19] Jones, D. R.; Schonlau, M.; Welch, W. J., Efficient Global Optimization of Expensive Black-Box Functions, Journal of Global Optimization, 13, 455-492 (1998) · Zbl 0917.90270
[20] Kornman, K.; Duff, G., “Personalized Medicine Will Dentistry Ride the Wave or Watch From the Beach?”, Journal of Dental Research, 91, S8-S11 (2012)
[21] Kosorok, M. R.; Moodie, E. E., Adaptive Treatment Strategies in Practice: Planning Trials and Analyzing Data for Personalized Medicine, 21 (2015), Philadelphia, PA: SIAM, Philadelphia, PA · Zbl 1334.92005
[22] Laber, E.; Zhao, Y., “Tree-based Methods for Individualized Treatment Regimes,”, Biometrika, 102, 501-514 (2015) · Zbl 1452.62821
[23] Laber, E. B.; Lizotte, D. J.; Ferguson, B., “Set-valued Dynamic Treatment Regimes for Competing Outcomes,”, Biometrics, 70, 53-61 (2014) · Zbl 1419.62382
[24] Laber, E. B.; Lizotte, D. J.; Qian, M.; Pelham, W. E.; Murphy, S. A., “Dynamic Treatment Regimes: Technical Challenges and Applications,”, Electronic Journal of Statistics, 8, 1225-1272 (2014) · Zbl 1298.62189
[25] Laber, E. B.; Staicu, A.-M., “Functional Feature Construction for Personalized Treatment Regimes,”, Journal of the American Statistical Association, 113, 1219-1227 (2018) · Zbl 1402.62276
[26] Laber, E. B.; Wu, F.; Munera, C.; Lipkovich, I.; Colucci, S.; Ripa, S., “Identifying Optimal Dosage Regimes Under Safety Constraints: An Application to Long Term Opioid Treatment of Chronic Pain,”, Statistics in Medicine, 37, 1407-1418 (2018)
[27] Lakkaraju, H.; Rudin, C., Learning Cost-effective Treatment Regimes Using Markov Decision Processes, arXiv preprint arXiv:1610.06972 (2016)
[28] Linn, K.; Laber, E.; Stefanski, L.; Kosorok, M. R.; Moodie, E. E. M., Adaptive Treatment Strategies in Practice: Planning Trials and Analyzing Data for Personalized Medicine, Estimation of Dynamic Treatment Regimes for Complex Outcomes: Balancing Benefits and Risks,”, 249-262 (2016), Philadelphia, PA: ASA-SIAM, Philadelphia, PA
[29] Lizotte, D. J.; Laber, E. B., Multi-Objective Markov Decision Processes for Data-Driven Decision Support,”, Journal of Machine Learning Research, 17, 1-28 (2016) · Zbl 1433.90152
[30] Lövdal, A.; Arno, A.; Schei, O.; Werhaug, J., “Combined Effect of Subgingival Scaling and Controlled Oral Hygiene on the Incidence of Gingivitis,”, Acta Odontologica Scandinavica, 19, 537-555 (1961)
[31] Lu, X.; Nahum-Shani, I.; Kasari, C.; Lynch, K. G.; Oslin, D. W.; Pelham, W. E.; Fabiano, G.; Almirall, D., “Comparing Dynamic Treatment Regimes Using Repeated-measures Outcomes: Modeling Considerations in SMART Studies,”, Statistics in Medicine, 35, 1595-1615 (2016)
[32] Luedtke, A. R.; van der Laan, M. J., “Optimal Individualized Treatments in Resource-limited Settings,”, The International Journal of Biostatistics, 12, 283-303 (2016)
[33] Mason, R. L.; Gunst, R. F.; Hess, J. L., Statistical Design and Analysis of Experiments: With Applications to Engineering and Science, 474 (2003), Hoboken, NJ: Wiley, Hoboken, NJ · Zbl 1029.62068
[34] Mattila, P. T.; Niskanen, M. C.; Vehkalahti, M. M.; Nordblad, A.; Knuuttila, M. L., “Prevalence and Simultaneous Occurrence of Periodontitis and Dental Caries,”, Journal of Clinical Periodontology, 37, 962-967 (2010)
[35] Mealey, B. L.; Oates, T. W., “Diabetes Mellitus and Periodontal Diseases,”, Journal of Periodontology, 77, 1289-1303 (2006)
[36] Mettes, D., “Insufficient Evidence to Support or Refute the Need for 6-monthly Dental Check-ups,”, Evidence-based Dentistry, 6, 62-63 (2005)
[37] Michalowicz, B. S.; Hodges, J. S.; Pihlstrom, B. L., “Is Change in Probing Depth a Reliable Predictor of Change in Clinical Attachment Loss?”, The Journal of the American Dental Association, 144, 171-178 (2013)
[38] Montgomery, D. C., Design and Analysis of Experiments (2008), Hoboken, NJ: John Wiley & Sons, Hoboken, NJ
[39] Murphy, S. A., Optimal dynamic treatment regimes, Journal of the Royal Statistical Society, Series B, 65, 331-355 (2003) · Zbl 1065.62006
[40] Murray, T. A.; Thall, P. F.; Yuan, Y.; McAvoy, S.; Gomez, D. R., “Robust Treatment Comparison Based on Utilities of Semi-competing Risks in Non-small-cell Lung Cancer,”, Journal of the American Statistical Association, 112, 11-23 (2017)
[41] Nyman, S.; Rosling, B.; Lindhe, J., “Effect of Professional Tooth Cleaning on Healing After Periodontal Surgery,”, Journal of Clinical Periodontology, 2, 80-86 (1975)
[42] Orellana, L.; Rotnitzky, A.; Robins, J. M., “Dynamic Regime Marginal Structural Mean Models for Estimation of Optimal Dynamic Treatment Regimes, Part I: Main Content,”, The International Journal of Biostatistics, 6, 1-48 (2010)
[43] Osbom, J. B.; Stoltenberg, J. L.; Huso, B. A.; Aeppli, D. M.; Pihlstrom, B. L., “Comparison of Measurement Variability in Subjects With Moderate Periodontitis Using a Conventional and Constant Force Periodontal Probe,”, Journal of Periodontology, 63, 283-289 (1992)
[44] Page, R. C.; Martin, J.; Krall, E. A.; Mancl, L.; Garcia, R., “Longitudinal Validation of a Risk Calculator for Periodontal Disease,”, Journal of Clinical Periodontology, 30, 819-827 (2003)
[45] Persson, G. R.; Mancl, L. A.; Martin, J.; Page, R. C., “Assessing Periodontal Disease Risk: A Comparison of Clinicians’ Assessment Versus a Computerized Tool,”, The Journal of the American Dental Association, 134, 575-582 (2003)
[46] Riley, P.; Worthington, H. V.; Clarkson, J. E.; Beirne, P. V., Recall Intervals for Oral Health in Primary Care Patients (Review), The Cochrane Library: Cochrane Database of Systematic Reviews, 12, 1-31 (2013)
[47] Robins, J., “A New Approach to Causal Inference in Mortality Studies With a Sustained Exposure Period-application to Control of the Healthy Worker Survivor Effect,”, Mathematical Modelling, 7, 1393-1512 (1986) · Zbl 0614.62136
[48] Robins, J.; Orellana, L.; Rotnitzky, A., “Estimation and Extrapolation of Optimal Treatment and Testing Strategies,”, Statistics in Medicine, 27, 4678-4721 (2008)
[49] Robins, J. M.; Lin, D. Y., Proceedings of the second Seattle Symposium in Biostatistics, Optimal Structural Nested Models for Optimal Sequential Decisions, 189-326 (2004), Berlin, Germany: Springer, Berlin, Germany
[50] Rosén, B.; Olavi, G.; Badersten, A.; Rönström, A.; Söderholm, G.; Egelberg, J., “Effect of Different Frequencies of Preventive Maintenance Treatment on Periodontal Conditions. 5-year Observations in General Dentistry Patients,”, Journal of Clinical Periodontology, 26, 225-233 (1999)
[51] Roustant, O.; Ginsbourger, D.; Deville, Y., “Dicekriging, Diceoptim: Two R Packages for the Analysis of Computer Experiments by Kriging-based Metamodelling and Optimization,”, Journal of Statistical Software, 51, 54 (2012)
[52] Ryu, D.; Sinha, D.; Mallick, B.; Lipsitz, S. R.; Lipshultz, S. E., “Longitudinal Studies With Outcome-dependent Follow-up: Models and Bayesian Regression,”, Journal of the American Statistical Association, 102, 952-961 (2007) · Zbl 05564423
[53] Schulte, P. J.; Tsiatis, A. A.; Laber, E. B.; Davidian, M., “Q-and A-learning Methods for Estimating Optimal Dynamic Treatment Regimes,”, Statistical Science, 29, 640-661 (2014) · Zbl 1331.62437
[54] Sethuraman, J., A Constructive Definition of Dirichlet Priors,”, Statistica Sinica, 4, 639-650 (1994) · Zbl 0823.62007
[55] Shortreed, S. M.; Moodie, E. E., “Estimating the Optimal Dynamic Antipsychotic Treatment Regime: Evidence From The Sequential Multiple-Assignment Randomized Clinical Antipsychotic Trials of Intervention and Effectiveness Schizophrenia Study,”, Journal of the Royal Statistical Society, Series C, 61, 577-599 (2012)
[56] Teich, S. T., Risk Assessment-based Individualized Treatment (RABIT): A Comprehensive Approach to Dental Patient Recall,”, Journal of Dental Education, 77, 448-457 (2013)
[57] Tobin, J., “Estimation of Relationships for Limited Dependent Variables,”, Econometrica: Journal of the Econometric Society, 26, 24-36 (1958) · Zbl 0088.36607
[58] van der Laan, M. J.; Petersen, M. L., “Causal Effect Models for Realistic Individualized Treatment and Intention to Treat Rules,”, The International Journal of Biostatistics, 3, 1-55 (2007) · Zbl 1165.62357
[59] Wall, Thomas; Guay, Albert, The Per-Patient Cost of Dental Care, 2013: A Look Under the Hood (2016)
[60] Wang, Y.; Fu, H.; Zeng, D., “Learning Optimal Personalized Treatment Rules in Consideration of Benefit and Risk: With An Application to Treating Type 2 Diabetes Patients With Insulin Therapies,”, Journal of the American Statistical Association, 113, 1-13 (2018) · Zbl 1398.62349
[61] Wu, F.; Laber, E. B.; Lipkovich, I. A.; Severus, E., “Who Will Benefit From Antidepressants in the Acute Treatment of Bipolar Depression? A Reanalysis of the STEP-BD Study by Sachs et al. 2007, Using Q-learning,”, International Journal of Bipolar Disorders, 3, 1-11 (2015)
[62] Xu, Y.; Müller, P.; Wahed, A. S.; Thall, P. F., “Bayesian Nonparametric Estimation for Dynamic Treatment Regimes With Sequential Transition Times,”, Journal of the American Statistical Association, 111, 921-950 (2016)
[63] Zanardi, G.; Proffit, W. R.; Frazier-Bowers, S. A., “The Future of Dentistry: How Will Personalized Medicine Affect Orthodontic Treatment?”, Dental Press Journal of Orthodontics, 17, 3-6 (2012)
[64] Zhang, B.; Tsiatis, A. A.; Davidian, M.; Zhang, M.; Laber, E., “Estimating Optimal Treatment Regimes From a Classification Perspective,”, Statistics, 1, 103-114 (2012)
[65] Zhang, B.; Tsiatis, A. A.; Laber, E. B.; Davidian, M., “A Robust Method for Estimating Optimal Treatment Regimes,”, Biometrics, 68, 1010-1018 (2012) · Zbl 1258.62116
[66] Zhang, B.; Tsiatis, A. A.; Laber, E. B.; Davidian, M., “Robust Estimation of Optimal Dynamic Treatment Regimes for Sequential Treatment Decisions,”, Biometrika, 100, 681-694 (2013) · Zbl 1284.62508
[67] Zhang, Y.; Laber, E. B.; Tsiatis, A.; Davidian, M., “Using Decision Lists to Construct Interpretable and Parsimonious Treatment Regimes,”, Biometrics, 71, 895-904 (2015) · Zbl 1419.62490
[68] Zhao, Y.-Q.; Zeng, D.; Laber, E. B.; Kosorok, M. R., “New Statistical Learning Methods for Estimating Optimal Dynamic Treatment Regimes,”, Journal of the American Statistical Association, 110, 583-598 (2015) · Zbl 1373.62557
[69] Zhao, Y.; Zeng, D.; Rush, A. J.; Kosorok, M. R., “Estimating Individualized Treatment Rules Using Outcome Weighted Learning,”, Journal of the American Statistical Association, 107, 1106-1118 (2012) · Zbl 1443.62396
[70] Zhou, X.; Kosorok, M. R., “Augmented Outcome-weighted Learning for Optimal Treatment Regimes, arXiv no. 1711.10654 (2017)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.