Latent Class Survival Models Linked by Principal Stratification to Investigate Heterogenous Survival Subgroups Among Individuals With Early-Stage Kidney Cancer

References

• Abramowitz, M. , and Stegun, I. A. (1972), Handbook of Mathematical Functions With Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Applied Mathematics Series (Vol. 55), Washington, DC: U.S. Government Printing Office.
   Google Scholar
• Bandeen-Roche, K. , Miglioretti, D. L. , Zeger, S. L. , and Rathouz, P. J. (1997), “Latent Variable Regression for Multiple Discrete Outcomes,” Journal of the American Statistical Association , 92, 1375–1386.
   Web of Science ®Google Scholar
• Bieler, G. S. , and Williams, R. L. (1995), “Cluster Sampling Techniques in Quantal Response Teratology and Developmental Toxicity Studies,” Biometrics , 51, 764–776.
   PubMed Web of Science ®Google Scholar
• Charlson, M. E. , Pompei, P. , Ales, K. L. , and MacKenzie, C. R. (1987), “A New Method of Classifying Prognostic Comorbidity in Longitudinal Studies: Development and Validation,” Journal of Chronic Diseases , 40, 373–383.
   PubMedGoogle Scholar
• Chow, W. H. , Devesa, S. S. , Warren, J. L. , and Fraumeni Jr., J. F. (1999), “Rising Incidence of Renal Cell Cancer in the United States,” Journal of the American Medical Association , 281, 1628–1631.
   PubMed Web of Science ®Google Scholar
• Cole, S. R. , and Frangakis, C. E. (2009), “The Consistency Statement in Causal Inference. A Definition or an Assumption?” Epidemiology , 20, 3–5.
   PubMed Web of Science ®Google Scholar
• Desai, N. R. , Bradley, S. M. , Parzynski, C. S. , Nallamothu, B. K. , Chan, P. S. , Spertus, J. A. , Patel, M. R. , Ader, J. , Soufer, A. , Krumholz, H. M. , and Curtis, J. P. (2015), “Appropriate Use Criteria for Coronary Revascularization and Trends in Utilization, Patient Selection, and Appropriateness of Percutaneous Coronary Intervention,” Journal of the American Medical Association , 314, 2045–2053.
   PubMed Web of Science ®Google Scholar
• Deyo, R. A. , Cherkin, D. C. , and Ciol, M. A. (1992), “Adapting a Clinical Comorbidity Index for Use With ICD-9-CM Administrative Databases,” Journal of Clinical Epidemiology , 45, 613–619.
   PubMed Web of Science ®Google Scholar
• Dominici, F. , Zeger, S. L. , Parmigiani, G. , Katz, J. , and Christian, P. (2006), “Estimating Percentile-Specific Effects in Counterfactual Models: A Case Study of Micronutrient Supplementation, Birth Weight, and Infant Mortality,” Journal of the Royal Statistical Society , Series C, 55, 261–280.
   Google Scholar
• Egleston, B. L. , Cropsey, K. L. , Lazev, A. B. , and Heckman, C. J. (2010), “A Tutorial on Principal Stratification-Based Sensitivity Analysis: Application to Smoking Cessation Studies,” Clinical Trials , 7, 286–298.
   PubMed Web of Science ®Google Scholar
• Egleston, B. L. , Scharfstein, D. O. , Freeman, E. E. , and West, S. K. (2007), “Causal Inference for Non-Mortality Outcomes in the Presence of Death,” Biostatistics , 8, 526–545.
   PubMed Web of Science ®Google Scholar
• Egleston, B. L. , Scharfstein, D. O. , and MacKenzie, E. (2009), “On Estimation of the Survivor Average Causal Effect in Observational Studies When Important Confounders are Missing Due to Death,” Biometrics 65, 497–504.
   PubMed Web of Science ®Google Scholar
• Elixhauser, A. , Steiner, C. , Harris, D. R. , and Coffey, R. M. (1998), “Comorbidity Measures for Use With Administrative Data,” Medical Care , 36, 8–27.
   PubMed Web of Science ®Google Scholar
• Farewell, V. T. (1982), “The Use of Mixture Models for the Analysis of Survival Data With Long-Term Survivors,” Biometrics , 38, 1041–1046.
   PubMed Web of Science ®Google Scholar
• Frangakis, C. E. , and Rubin, D. B. (2002), “Principal Stratification in Causal Inference,” Biometrics , 58, 21–29.
   PubMed Web of Science ®Google Scholar
• Frumento, P. , Mealli, F. , Pacini, B. , and Rubin, D. B. (2012), “Evaluating the Effect of Training on Wages in the Presence of Noncompliance, Nonemployment, and Missing Outcome Data,” Journal of the American Statistical Association , 107, 450–466.
   Web of Science ®Google Scholar
• Gallop, R. , Small, D. S. , Lin, J. Y. , Elliott, M. R. , Joffe, M. , and Ten Have, T. R. (2009), “Mediation Analysis With Principal Stratification,” Statistics in Medicine , 28, 1108–1130.
   PubMed Web of Science ®Google Scholar
• Gray, R. J. (1988), “A Class of K-Sample Tests for Comparing the Cumulative Incidence of a Competing Risk,” Annals of Statistics , 16, 1141–1154.
   Web of Science ®Google Scholar
• Grilli, L. (2011), “Causal Inference Through Principal Stratification: A Special Type of Latent Class Modelling,” in Classification and Multivariate Analysis for Complex Data Structures , eds. B. Fichet, D. Piccolo, R. Verde, and M. Vichi, Berlin Heidelberg: Springer-Verlag, pp. 265–270.
   Google Scholar
• Halpern, S. D. , French, B. , Small, D. S. , Saulsgiver, K. , Harhay, M. O. , Audrain-McGovern, J. , Loewenstein, G. , Brennan, T. A. , Asch, D. A. , and Volpp, K. G. (2015), “Randomized Trial of Four Financial-Incentive Programs for Smoking Cessation,” New England Journal of Medicine , 372, 2108–2117.
   PubMed Web of Science ®Google Scholar
• Harrell, F. E. Jr. , (2001), Regression Modeling Strategies , New York: Springer, pp. 11–40.
   Google Scholar
• Hayden, D. , Pauler, D. K. , and Schoenfeld, D. (2005), “An Estimator for Treatment Comparisons Among Survivors in Randomized Trials,” Biometrics , 61, 305–310.
   PubMed Web of Science ®Google Scholar
• Ho, D. , Imai, K. , King, G. , and Stuart, E. (2007), “Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference,” Political Analysis , 15, 199–236.
   Web of Science ®Google Scholar
• Hock, L. M. , Lynch, J. , and Balaji, K. C. (2002), “Increasing Incidence of All Stages of Kidney Cancer in the Last 2 Decades in the United States: An Analysis of Surveillance, Epidemiology, and End Results Program Data,” Journal of Urology , 167, 57–60.
   PubMed Web of Science ®Google Scholar
• Hollingsworth, J. M. , Miller, D. C. , Daignault, S. , and Hollenbeck, B. K. (2006), “Rising Incidence of Small Renal Masses: A Need to Reassess Treatment Effect,” Journal of the National Cancer Institute , 98, 1331–1334.
   PubMed Web of Science ®Google Scholar
• Huber, P. J. (1964), “Robust Estimation of a Location Parameter,” Annals of Mathematical Statistics , 35, 73–101.
   Google Scholar
• Imai, K. , and Yamamoto, T. (2013), “Identification and Sensitivity Analysis for Multiple Causal Mechanisms: Revisiting Evidence From Framing Experiments,” Political Analysis , 21, 141–171.
   Web of Science ®Google Scholar
• Jo, B. , and Stuart, E. A. (2009), “On the Use of Propensity Scores in Principal Causal Effect Estimation,” Statistics in Medicine , 28, 2857–2875.
   PubMed Web of Science ®Google Scholar
• Jo, B. , Wang, C. P. , and Ialongo, N. S. (2009), “Using Latent Outcome Trajectory Classes in Causal Inference,” Statistics and Its Interface , 2, 403–412.
   PubMed Web of Science ®Google Scholar
• Kristensen, V. N. , Lingjærde, O. C. , Russnes, H. G. , Vollan, H. K. M. , Frigessi, A. , and Borrenson-Dale, A. L. (2014), “Principles and Methods of Integrative Genomic Analyses in Cancer,” Nature Reviews Cancer , 14, 299–313.
   PubMed Web of Science ®Google Scholar
• Kunkle, D. A. , Egleston, B. L. , and Uzzo, R. G. (2008), “Excise, Ablate or Observe: The Small Renal Mass Dilemma—A Meta-Analysis and Review,” Journal of Urology , 179, 1227–1234.
   PubMed Web of Science ®Google Scholar
• Lambert, P. C. (2007), “Modeling the Cure Fraction in Survival Studies,” STATA Journal , 7, 351–375.
   Web of Science ®Google Scholar
• Lanza, S. T. , and Rhoades, B. L. (2013), “Latent Class Analysis: An Alternative Perspective on Subgroup Analysis in Prevention and Treatment,” Prevention Science , 14, 157–168.
   PubMed Web of Science ®Google Scholar
• Lehmann, E. L. (2010), Elements of Large-Sample Theory , New York: Springer.
   Google Scholar
• Mair, P. , and Hudec, M. (2009), “Multivariate Weibull Mixtures With Proportional Hazard Restrictions for Dwell-Time-Based Session Clustering With Incomplete Data,” Applied Statistics , 58, 619–639.
   Web of Science ®Google Scholar
• Marin, J. M. , Rodriguez-Bernal, M. T. , and Wiper, M. P. (2005), “Using Weibull Mixture Distributions to Model Heterogeneous Survival Data,” Communications in Statistics—Simulation and Computation , 34, 673–684.
   Web of Science ®Google Scholar
• Muthén, B. , and Brown, H. C. (2009), “Estimating Drug Effects in the Presence of Placebo Response: Causal Inference Using Growth Mixture Modeling,” Statistics in Medicine , 28, 3363–3385.
   PubMed Web of Science ®Google Scholar
• Muthén, B. , Brown, C. H. , Masyn, K. , Jo, B. , Khoo, S. T. , Yang, C. C. , Wang, C. P. , Kellam, S. G. , Carlin, J. B. , and Liao, J. (2002), “General Growth Mixture Modeling for Randomized Preventive Interventions,” Biostatistics , 3, 459–475.
   PubMed Web of Science ®Google Scholar
• Muthén, B. , and Masyn, K. (2005), “Discrete-Time Survival Mixture Analysis,” Journal of Educational and Behavioral Statistics , 30, 27–58.
   Web of Science ®Google Scholar
• Pearl, J. (2009), Causality: Models, Reasoning, and Inference (2nd ed.), Cambridge, UK: Cambridge University Press.
   Google Scholar
• Piantadosi, S. (1997), Clinical Trials: A Methodologic Perspective . New York: Wiley, pp. 197–521.
   Google Scholar
• Qu, P. , Barlogie, B. , and Crowley, J. (2015), “Using a Latent Class Model to Refine Risk Stratification in Multiple Myeloma,” Statistics in Medicine , 21, 2971–2980.
   Web of Science ®Google Scholar
• Razali, A. M. , and Al-Wakeel, A. A. (2013), “Mixture Weibull Distributions for Fitting Failure Times Data,” Applied Mathematics and Computation , 219, 11358–11364.
   Web of Science ®Google Scholar
• Romano, P. S. , Roos, L. L. , and Jollis, J. G. (1993), “Adapting a Clinical Comorbidity Index for Use With ICD-9-CM Administrative Data: Differing Perspectives,” Journal of Clinical Epidemiology , 46, 1075–1079.
   PubMed Web of Science ®Google Scholar
• Rosenbaum, P. R. , and Rubin, D. B. (1983), “The Central Role of the Propensity Score in Observational Studies for Causal Effects,” Biometrika , 70, 41–55.
   Web of Science ®Google Scholar
• Roy, J. , Hogan, J. W. , and Marcus, B. H. (2008), “Principal Stratification With Predictors of Compliance for Randomized Trials With 2 Active Treatments,” Biostatistics , 9, 277–289.
   PubMed Web of Science ®Google Scholar
• Rubin, D. B. (1986), “Which Ifs Have Causal Answers. Commentary on Holland PW. Statistics and Causal Inference,” Journal of the American Statistical Association , 81, 961–962.
   Web of Science ®Google Scholar
• Shepherd, B. E. , Gilbert, P. B. , Jemai, Y. , and Rotnitzky, A. (2006), “Sensitivity Analyses Comparing Outcomes Only Existing in a Subset Selected Post-Randomization, Conditional on Covariates, With Application to HIV Vaccine Trials,” Biometrics , 62, 332–342.
   PubMed Web of Science ®Google Scholar
• Shepherd, B. E. , Gilbert, P. B. , and Lumley, T. (2007), “Sensitivity Analyses Comparing Time-to-Event Outcomes Existing Only in a Subset Selected Postrandomization,” Journal of the American Statistical Association , 102, 573–582.
   PubMed Web of Science ®Google Scholar
• Smaldone, M. C. , Kutikov, A. , Egleston, B. L. , Canter, D. J. , Viterbo, R. , Chen, D. Y. , Jewett, M. A. , Greenberg, R. E. , and Uzzo, R. G. (2012), “Small Renal Masses Progressing to Metastases Under Active Surveillance: A Systematic Review and Pooled Analysis,” Cancer , 118, 997–1006.
   PubMed Web of Science ®Google Scholar
• Sun, M. , Becker, A. , Tian, Z. , Roghmann, F. , Abdollah, F. , Larouche, A. , Karakiewicz, P. I. , and Trinh, Q. D. (2014), “Management of Localized Kidney Cancer: Calculating Cancer-specific Mortality and Competing Risks of Death for Surgery and Nonsurgical Management,” European Urology , 65, 235–241.
   PubMed Web of Science ®Google Scholar
• van Walraven, C. , Austin, P. C. , Jennings, A. , Quan, H. , and Forster, A. J. (2009), “A Modification of the Elixhauser Comorbidity Measures Into a Point System for Hospital Death Using Administrative Data,” Medical Care , 47, 626–633.
   PubMedGoogle Scholar
• Viatte, S. , Plant, D. , Han, B. , Fu, B. , Yarwood, A. , Thomson, W. , Symmons, D. P. M , Worthington, J. , Young, A. , Hyrich, K. L. , Morgan, A. W. , Wilson, A. G. , Isaacs, J. D. , Raychaudhuri, S. , and Barton, A. (2015), “Association of HLA-DRB1 Haplotypes With Rheumatoid Arthritis Severity, Mortality, and Treatment Response,” Journal of the American Medical Association , 313, 1645–1656.
   PubMed Web of Science ®Google Scholar
• Wang, C. P. , Jo, B. , and Brown, C. H. (2014), “Causal Inference in Longitudinal Comparative Effectiveness Studies With Repeated Measures of a Continuous Intermediate Variable,” Statistics in Medicine , 33, 3509–3527.
   PubMed Web of Science ®Google Scholar
• Williams, R. L. (2000), “A Note on Robust Variance Estimation for Cluster-Correlated Data,” Biometrics , 56, 645–646.
   PubMed Web of Science ®Google Scholar