The Annals of Applied Statistics

Evaluating epoetin dosing strategies using observational longitudinal data

Cecilia A. Cotton and Patrick J. Heagerty

Full-text: Open access

Abstract

Epoetin is commonly used to treat anemia in chronic kidney disease and End Stage Renal Disease subjects undergoing dialysis, however, there is considerable uncertainty about what level of hemoglobin or hematocrit should be targeted in these subjects. In order to address this question, we treat epoetin dosing guidelines as a type of dynamic treatment regimen. Specifically, we present a methodology for comparing the effects of alternative treatment regimens on survival using observational data. In randomized trials patients can be assigned to follow a specific management guideline, but in observational studies subjects can have treatment paths that appear to be adherent to multiple regimens at the same time. We present a cloning strategy in which each subject contributes follow-up data to each treatment regimen to which they are continuously adherent and artificially censored at first nonadherence. We detail an inverse probability weighted log-rank test with a valid asymptotic variance estimate that can be used to test survival distributions under two regimens. To compare multiple regimens, we propose several marginal structural Cox proportional hazards models with robust variance estimation to account for the creation of clones. The methods are illustrated through simulations and applied to an analysis comparing epoetin dosing regimens in a cohort of 33,873 adult hemodialysis patients from the United States Renal Data System.

Article information

Source
Ann. Appl. Stat., Volume 8, Number 4 (2014), 2356-2377.

Dates
First available in Project Euclid: 19 December 2014

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1419001747

Digital Object Identifier
doi:10.1214/14-AOAS774

Mathematical Reviews number (MathSciNet)
MR3292501

Zentralblatt MATH identifier
06408782

Keywords
Marginal Structural Models observational studies survival analysis

Citation

Cotton, Cecilia A.; Heagerty, Patrick J. Evaluating epoetin dosing strategies using observational longitudinal data. Ann. Appl. Stat. 8 (2014), no. 4, 2356--2377. doi:10.1214/14-AOAS774. https://projecteuclid.org/euclid.aoas/1419001747


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References

  • Besarab, A., Bolton, W. K., Browne, J. K., Egrie, J. C., Nissenson, A. R., Okamoto, D. M., Schwab, S. J. and Goodkin, D. A. (1998). The effects of normal as compared with low hematocrit values in patients with cardiac disease who are receiving hemodialysis and epoetin. N. Engl. J. Med. 339 584–590. PMID: 9718377.
  • Brookhart, M. A., Schneeweiss, S., Avorn, J., Bradbury, B. D., Liu, J. and Winkelmayer, W. C. (2010). Comparative mortality risk of anemia management practices in incident hemodialysis patients. JAMA: The Journal of the American Medical Association 303 857–864.
  • Cain, L. E., Robins, J. M., Lanoy, E., Logan, R., Costagliola, D. and Hernán, M. A. (2010). When to start treatment? A systematic approach to the comparison of dynamic regimes using observational data. Int. J. Biostat. 6 Art. 18, 26.
  • Cain, L. E., Logan, R., Robins, J. M., Sterne, J. A. C., Sabin, C., Bansi, L., Justice, A., Goulet, J., van Sighem, A., de Wolf, F., Bucher, H. C., von Wyl, V., Esteve, A., Casabona, J., del Amo, J., Moreno, S., Seng, R., Meyer, L., Perez-Hoyos, S., Muga, R., Lodi, S., Lanoy, E., Costagliola, D. and Hernan, M. A. (2011). When to initiate combined antiretroviral therapy to reduce mortality and AIDS-defining illness in HIV-infected persons in developed countries: An observational study. Ann. Intern. Med. 154 509–515.
  • Canadian Erythropoietin Study Group (1990). Association between recombinant human erythropoietin and quality of life and exercise capacity of patients receiving haemodialysis. BMJ 300 573–578.
  • Chakraborty, B. and Moodie, E. E. M. (2013). Statistical Methods for Dynamic Treatment Regimes. Springer, New York.
  • Cotton, C. A. and Heagerty, P. J. (2011). A data augmentation method for estimating the causal effect of adherence to treatment regimens targeting control of an intermediate measure. Statistics in Biosciences 3 28–44.
  • Cotton, C. A. and Heagerty, P. J. (2014). Supplement to “Evaluating epoetin dosing strategies using observational longitudinal data.” DOI:10.1214/14-AOAS774SUPP.
  • Drüeke, T. B., Locatelli, F., Clyne, N., Eckardt, K.-U., Macdougall, I. C., Tsakiris, D., Burger, H.-U. and Scherhag, A. (2006). Normalization of hemoglobin level in patients with chronic kidney disease and anemia. N. Engl. J. Med. 355 2071–2084.
  • Eschbach, J. W. (1994). Erythropoietin: The promise and the facts. Kidney International Supplements 44 S70–S76.
  • Hernán, M. A., Brumback, B. and Robins, J. M. (2000). Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology 11 561–570.
  • Hernán, M. A., Brumback, B. and Robins, J. M. (2001). Marginal structural models to estimate the joint causal effect of nonrandomized treatments. J. Amer. Statist. Assoc. 96 440–448.
  • Hernán, M. A., Lanoy, E., Costagliola, D. and Robins, J. M. (2006). Comparison of dynamic treatment regimes via inverse probability weighting. Basic Clin. Pharmacol. Toxicol. 98 237–242.
  • Jung, S.-H. (1999). Rank tests for matched survival data. Lifetime Data Anal. 5 67–79.
  • Lee, E. W., Wei, L. J. and Amato, D. A. (1992). Cox-type regression analysis for large numbers of small groups of correlated failure time observations. In Survival Analysis: State of the Art (Columbus, OH, 1991) (J. P. Klein and P. K. Goel, eds.) 237–247. Kluwer Academic, Dordrecht.
  • Liang, K. Y. and Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika 73 13–22.
  • Miskulin, D. C., Weiner, D. E., Tighiouart, H., Ladik, V., Servilla, K., Zager, P. G., Martin, A., Johnson, H. K. and Meyer, K. B. (2009). Computerized decision support for EPO dosing in hemodialysis patients. Am. J. Kidney Dis. 54 1081–1088.
  • Miskulin, D. C., Zhou, J., Tangri, N., Bandeen-Roche, K., Cook, C., Ephraim, P. L., Crews, D. C., Scialla, J. J., Sozio, S. M., Shafi, T. et al. (2013). Trends in anemia management in US hemodialysis patients 2004–2010. BMC Nephrology 14 264.
  • National Kidney Foundation (2006). K/DOQI clinical practice guidelines and clinical practice recommendations for anemia in chronic kidney disease. American Journal of Kidney Diseases 47: Suppl 3 S11–S145.
  • Orellana, L., Rotnitzky, A. and Robins, J. M. (2010). Dynamic regime marginal structural mean models for estimation of optimal dynamic treatment regimes, Part I: Main content. Int. J. Biostat. 6 Art. 8, 49.
  • Palmer, S. C., Navaneethan, S. D., Craig, J. C., Johnson, D. W., Tonelli, M., Garg, A. X., Pellegrini, F., Ravani, P., Jardine, M., Perkovic, V., Graziano, G., McGee, R., Nicolucci, A., Tognoni, G. and Strippoli, G. F. M. (2010). Meta-analysis: Erythropoiesis-stimulating agents in patients with chronic kidney disease. Ann. Intern. Med. 153 23–33.
  • Pepe, M. S. and Couper, D. (1997). Modeling partly conditional means with longitudinal data. J. Amer. Statist. Assoc. 92 991–998.
  • Pepe, M. S., Heagerty, P. J. and Whitaker, R. (1999). Prediction using partly conditional time-varying coefficients regression models. Biometrics 55 944–950.
  • Pfeffer, M. A., Burdmann, E. A., Chen, C.-Y., Cooper, M. E., de Zeeuw, D., Eckardt, K.-U., Feyzi, J. M., Ivanovich, P., Kewalramani, R., Levey, A. S., Lewis, E. F., McGill, J. B., McMurray, J. J. V., Parfrey, P., Parving, H.-H., Remuzzi, G., Singh, A. K., Solomon, S. D. and Toto, R. (2009). A trial of darbepoetin alfa in type 2 diabetes and chronic kidney disease. N. Engl. J. Med. 361 2019–2032.
  • Robins, J. M. (1993). Information recovery and bias adjustment in proportional hazards regression analysis of randomized trials using surrogate markers. In Proceedings of the Biopharmaceutical Section, American Statistical Association 24–33. American Statistical Association, Alexandria, VA.
  • Robins, J. M. (1998). Marginal structural models. In 1997 Proceedings of the Section on Bayesian Statistical Science 1–10. American Statistical Association, Alexandria, VA.
  • Robins, J. M. (2000). Marginal structural models versus structural nested models as tools for causal inference. In Statistical Models in Epidemiology, the Environment, and Clinical Trials (Minneapolis, MN, 1997) (M. E. Halloran and D. Berry, eds.) 95–133. Springer, New York.
  • Robins, J. M. and Finkelstein, D. M. (2000). Correcting for noncompliance and dependent censoring in an AIDS clinical trial with inverse probability of censoring weighted (IPCW) log-rank tests. Biometrics 56 779–788.
  • Robins, J. M., Hernán, M. A. and Brumback, B. (2000). Marginal structural models and causal inference in epidemiology. Epidemiology 11 550–560.
  • Robins, J., Orellana, L. and Rotnitzky, A. (2008). Estimation and extrapolation of optimal treatment and testing strategies. Stat. Med. 27 4678–4721.
  • Robins, J. M., Rotnitzky, A. and Zhao, L. P. (1995). Analysis of semiparametric regression models for repeated outcomes in the presence of missing data. J. Amer. Statist. Assoc. 90 106–121.
  • Robins, J. M., Blevins, D., Ritter, G. and Wulfsohn, M. (1992). G-estimation of the effect of prophylaxis therapy for pneumocystis carinii pneumonia on the survival of AIDS patients. Epidemiology 3 319–336.
  • Rubin, D. B. (1980). Discussion of “Randomization analysis of experimental data in the Fisher randomization test,” by D. Basu. J. Amer. Statist. Assoc. 75 591–593.
  • Shortreed, S. M. and Moodie, E. E. M. (2012). Estimating the optimal dynamic antipsychotic treatment regime: Evidence from the sequential multiple-assignment randomized clinical antipsychotic trials of intervention and effectiveness schizophrenia study. J. R. Stat. Soc. Ser. C. Appl. Stat. 61 577–599.
  • Singh, A. K., Szczech, L., Tang, K. L., Barnhart, H., Sapp, S., Wolfson, M. and Reddan, D. (2006). Correction of anemia with epoetin alfa in chronic kidney disease. N. Engl. J. Med. 355 2085–2098.
  • Unger, E. F., Thompson, A. M., Blank, M. J. and Temple, R. (2010). Erythropoiesis-stimulating agents, a time for a reevaluation. N. Engl. J. Med. 362 189–192.
  • United States Government Accountability Office (2006). Report to the Chairman, Committee on Ways and Means, House of Representatives. End-stage renal disease: Bundling of Medicare’s payment for drugs with payment for all ESRD services would promote efficiency and clinical flexibility (GAO-07-77). Accessed May 2, 2013, at http://www.gao.gov/assets/260/253347.pdf.
  • Wang, O., Kilpatrick, R. D., Critchlow, C. W., Ling, X., Bradbury, B. D., Gilbertson, D. T., Collins, A. J., Rothman, K. J. and Acquavella, J. F. (2010). Relationship between epoetin alfa dose and mortality: Findings from a marginal structural model. Clin. J. Am. Soc. Nephrol. 5 182–188.
  • Xie, J. and Liu, C. (2005). Adjusted Kaplan–Meier estimator and log-rank test with inverse probability of treatment weighting for survival data. Stat. Med. 24 3089–3110.
  • Young, J., Cain, L., Robins, J., O’Reilly, E. and Hernán, M. (2011). Comparative effectiveness of dynamic treatment regimes: An application of the parametric g-gormula. Statistics in Biosciences 3 119–143.
  • Zhang, Y., Thamer, M., Stefanik, K., Kaufman, J. and Cotter, D. J. (2004). Epoetin requirements predict mortality in hemodialysis patients. Am. J. Kidney Dis. 44 866–876.
  • Zhang, Y., Thamer, M., Kaufman, J. S., Cotter, D. J. and Hernán, M. A. (2011). High doses of epoetin do not lower mortality and cardiovascular risk among elderly hemodialysis patients with diabetes. Kidney Int. 80 663–669.
  • Zheng, Y. and Heagerty, P. J. (2005). Partly conditional survival models for longitudinal data. Biometrics 61 379–391.

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