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Landmark estimation of survival and treatment effects in observational studies. (English) Zbl 1383.62221

Summary: Clinical studies aimed at identifying effective treatments to reduce the risk of disease or death often require long term follow-up of participants in order to observe a sufficient number of events to precisely estimate the treatment effect. In such studies, observing the outcome of interest during follow-up may be difficult and high rates of censoring may be observed which often leads to reduced power when applying straightforward statistical methods developed for time-to-event data. Alternative methods have been proposed to take advantage of auxiliary information that may potentially improve efficiency when estimating marginal survival and improve power when testing for a treatment effect. Recently, the first author, L. Tian and T. Cai [“Landmark estimation of survival and treatment effect in a randomized clinical trial”, J. Am. Stat. Assoc. 109, No. 505, 384–394 (2014; doi:10.1080/01621459.2013.842488)] proposed a landmark estimation procedure for the estimation of survival and treatment effects in a randomized clinical trial setting and demonstrated that significant gains in efficiency and power could be obtained by incorporating intermediate event information as well as baseline covariates. However, the procedure requires the assumption that the potential outcomes for each individual under treatment and control are independent of treatment group assignment which is unlikely to hold in an observational study setting. In this paper we develop the landmark estimation procedure for use in an observational setting. In particular, we incorporate inverse probability of treatment weights (IPTW) in the landmark estimation procedure to account for selection bias on observed baseline (pretreatment) covariates. We demonstrate that consistent estimates of survival and treatment effects can be obtained by using IPTW and that there is improved efficiency by using auxiliary intermediate event and baseline information. We compare our proposed estimates to those obtained using the Kaplan-Meier estimator, the original landmark estimation procedure, and the IPTW Kaplan-Meier estimator. We illustrate our resulting reduction in bias and gains in efficiency through a simulation study and apply our procedure to an AIDS dataset to examine the effect of previous antiretroviral therapy on survival.

MSC:

62N02 Estimation in survival analysis and censored data
62P10 Applications of statistics to biology and medical sciences; meta analysis

Software:

randomForest
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References:

[1] Amato DA (1988) A generalized Kaplan-Meier estimator for heterogenous populations. Commun Stat 17(1):263-286 · Zbl 0639.62092 · doi:10.1080/03610928808829621
[2] Austin PC (2007) The performance of different propensity score methods for estimating marginal odds ratios. Stat Med 26(16):3078-3094 · doi:10.1002/sim.2781
[3] Austin PC (2009) Balance diagnostics for comparing the distribution of baseline covariates between treatment groups in propensity-score matched samples. Stat Med 28:3083-3107 · doi:10.1002/sim.3697
[4] Austin PC, Stuart EA (2015) Moving towards best practice when using inverse probability of treatment weighting (IPTW) using the propensity score to estimate causal treatment effects in observational studies. Stat Med 34(28):3661-3679 · doi:10.1002/sim.6607
[5] Bai X, Tsiatis AA, O’Brien SM (2013) Doubly-robust estimators of treatment-specific survival distributions in observational studies with stratified sampling. Biometrics 69(4):830-839 · Zbl 1285.62124 · doi:10.1111/biom.12076
[6] Beran R (1981) Nonparametric regression with randomly censored survival data. Technical report, University of California Berkeley
[7] Bhatta L, Klouman E, Deuba K, Shrestha R, Karki DK, Ekstrom AM, Ahmed LA (2013) Survival on antiretroviral treatment among adult HIV-infected patients in Nepal: a retrospective cohort study in far-western region, 2006-2011. BMC Infect Dis 13(1):604 · doi:10.1186/1471-2334-13-604
[8] Breiman L, Friedman J, Stone CJ, Olshen RA (1984) Classification and regression trees. CRC Press, Boca Raton · Zbl 0541.62042
[9] Cai T, Tian L, Wei LJ (2005) Semiparametric Box-Cox power transformation models for censored survival observations. Biometrika 92(3):619-632 · Zbl 1152.62377 · doi:10.1093/biomet/92.3.619
[10] Cai T, Tian L, Uno H, Solomon S, Wei L (2010) Calibrating parametric subject-specific risk estimation. Biometrika 97(2):389-404 · Zbl 1205.62161 · doi:10.1093/biomet/asq012
[11] Chen PY, Tsiatis AA (2001) Causal inference on the difference of the restricted mean lifetime between two groups. Biometrics 57(4):1030-1038 · Zbl 1209.62267 · doi:10.1111/j.0006-341X.2001.01030.x
[12] Cook R, Lawless J (2001) Some comments on efficiency gains from auxiliary information for right-censored data. J Stat Plan Inference 96(1):191-202 · Zbl 0971.62055 · doi:10.1016/S0378-3758(00)00335-9
[13] Cox DR (1972) Regression models and life tables (with discussion). J R Stat Soc 34:187-220 · Zbl 0243.62041
[14] Du Y, Akritas M (2002) Uniform strong representation of the conditional Kaplan-Meier process. Math Methods Stat 11(2):152-182 · Zbl 1005.62082
[15] Faucett CL, Schenker N, Taylor JM (2002) Survival analysis using auxiliary variables via multiple imputation, with application to AIDS clinical trial data. Biometrics 58(1):37-47 · Zbl 1209.62283 · doi:10.1111/j.0006-341X.2002.00037.x
[16] Fine J, Jiang H, Chappell R (2001) On semi-competing risks data. Biometrika 88(4):907-919 · Zbl 0986.62091 · doi:10.1093/biomet/88.4.907
[17] Finkelstein DM, Schoenfeld DA (1994) Analysing survival in the presence of an auxiliary variable. Stat Med 13(17):1747-1754 · doi:10.1002/sim.4780131706
[18] Fleming TR, Prentice RL, Pepe MS, Glidden D (1994) Surrogate and auxiliary endpoints in clinical trials, with potential applications in cancer and AIDS research. Stat Med 13(9):955-968 · doi:10.1002/sim.4780130906
[19] Garcia TP, Ma Y, Yin G (2011) Efficiency improvement in a class of survival models through model-free covariate incorporation. Lifetime Data Anal 17(4):552-565 · Zbl 1279.62204 · doi:10.1007/s10985-011-9195-z
[20] Gray R (1994) A kernel method for incorporating information on disease progression in the analysis of survival. Biometrika 81(3):527-539 · Zbl 0812.62100 · doi:10.1093/biomet/81.3.527
[21] Griffin BA, Eibner C, Bird CE, Jewell A, Margolis K, Shih R, Slaughter ME, Whitsel EA, Allison M, Escarce JJ (2013) The relationship between urban sprawl and coronary heart disease in women. Health Place 20:51-61 · doi:10.1016/j.healthplace.2012.11.003
[22] Hammer S, Katzenstein D, Hughes M, Gundacker H, Schooley R, Haubrich R, Henry W, Lederman M, Phair J, Niu M et al (1996) A trial comparing nucleoside monotherapy with combination therapy in HIV-infected adults with CD4 cell counts from 200 to 500 per cubic millimeter. New Engl J Med 335(15):1081-1090 · doi:10.1056/NEJM199610103351501
[23] Hammer SM, Squires KE, Hughes MD, Grimes JM, Demeter LM, Currier JS, Eron JJ Jr, Feinberg JE, Balfour HH Jr, Deyton LR et al (1997) A controlled trial of two nucleoside analogues plus indinavir in persons with human immunodeficiency virus infection and CD4 cell counts of 200 per cubic millimeter or less. New Engl J Med 337(11):725-733 · doi:10.1056/NEJM199709113371101
[24] Hankey BF, Myers MH (1971) Evaluating differences in survival between two groups of patients. J Chron Dis 24(9):523-531 · doi:10.1016/0021-9681(71)90041-5
[25] Harder VS, Stuart EA, Anthony JC (2010) Propensity score techniques and the assessment of measured covariate balance to test causal associations in psychological research. Psychol Methods 15(3):234 · doi:10.1037/a0019623
[26] Hernán MÁ, Brumback B, Robins JM (2000) Marginal structural models to estimate the causal effect of zidovudine on the survival of HIV-positive men. Epidemiology 11(5):561-570 · doi:10.1097/00001648-200009000-00012
[27] Higashi T, Shekelle PG, Adams JL, Kamberg CJ, Roth CP, Solomon DH, Reuben DB, Chiang L, MacLean CH, Chang JT et al (2005) Quality of care is associated with survival in vulnerable older patients. Ann Intern Med 143(4):274-281 · doi:10.7326/0003-4819-143-4-200508160-00008
[28] Hill JL (2011) Bayesian nonparametric modeling for causal inference. J Comput Gr Stat 20(1):217-240 · doi:10.1198/jcgs.2010.08162
[29] Hirano K, Imbens GW (2004) The propensity score with continuous treatments. Applied bayesian modeling and causal inference from incomplete-data perspectives: an essential journey with donald rubin’s statistical family. Wiley, New York, pp 73-84 · Zbl 05274806
[30] Imai K, Ratkovic M (2014) Covariate balancing propensity score. J R Stat Soc 76(1):243-263 · Zbl 1411.62025 · doi:10.1111/rssb.12027
[31] Imai K, Van Dyk DA (2004) Causal inference with general treatment regimes. J Am Stat Assoc 99(467):854-866 · Zbl 1117.62361 · doi:10.1198/016214504000001187
[32] Imbens GW (2000) The role of the propensity score in estimating dose-response functions. Biometrika 87(3):706-710 · Zbl 1120.62334 · doi:10.1093/biomet/87.3.706
[33] Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53(282):457-481 · Zbl 0089.14801 · doi:10.1080/01621459.1958.10501452
[34] Lagakos S (1988) The loss in efficiency from misspecifying covariates in proportional hazards regression models. Biometrika 75(1):156-160 · Zbl 0632.62103 · doi:10.1093/biomet/75.1.156
[35] Lagakos S, Schoenfeld D (1984) Properties of proportional-hazards score tests under misspecified regression models. Biometrics 40:1037-1048 · Zbl 0567.62089 · doi:10.2307/2531154
[36] Lee BK, Lessler J, Stuart EA (2010) Improving propensity score weighting using machine learning. Stat Med 29(3):337-346
[37] Li Y, Taylor JM, Little RJ (2011) A shrinkage approach for estimating a treatment effect using intermediate biomarker data in clinical trials. Biometrics 67(4):1434-1441 · Zbl 1274.62818 · doi:10.1111/j.1541-0420.2011.01608.x
[38] Liaw A, Wiener M (2002) Classification and regression by randomforest. R News 2(3):18-22
[39] Lin D (2000) On fitting cox’s proportional hazards models to survey data. Biometrika 87(1):37-47 · Zbl 0974.62008 · doi:10.1093/biomet/87.1.37
[40] Lin D, Wei L (1989) The robust inference for the cox proportional hazards model. J Am Stat Assoc 84:1074-1078 · Zbl 0702.62042 · doi:10.1080/01621459.1989.10478874
[41] Lu X, Tsiatis A (2008) Improving the efficiency of the log-rank test using auxiliary covariates. Biometrika 95(3):679-694 · Zbl 1437.62548 · doi:10.1093/biomet/asn003
[42] Marcus SM, Siddique J, Ten Have TR, Gibbons RD, Stuart E, Normand SLT (2008) Balancing treatment comparisons in longitudinal studies. Psychiatr Ann 38(12):805 · doi:10.3928/00485713-20081201-05
[43] McCaffrey DF, Ridgeway G, Morral AR (2004) Propensity score estimation with boosted regression for evaluating causal effects in observational studies. Psychol Methods 9(4):403 · doi:10.1037/1082-989X.9.4.403
[44] Mocroft A, Madge S, Johnson AM, Lazzarin A, Clumeck N, Goebel FD, Viard JP, Gatell J, Blaxhult A, Lundgren JD et al (1999) A comparison of exposure groups in the eurosida study: starting highly active antiretroviral therapy (HAART), response to HAART, and survival. JAIDS 22(4):369-378
[45] Murray S, Tsiatis A (1996) Nonparametric survival estimation using prognostic longitudinal covariates. Biometrics 52:137-151 · Zbl 0874.62138 · doi:10.2307/2533151
[46] Murray S, Tsiatis AA (2001) Using auxiliary time-dependent covariates to recover information in nonparametric testing with censored data. Lifetime Data Anal 7(2):125-141 · Zbl 1009.62036 · doi:10.1023/A:1011392622173
[47] Nieto FJ, Coresh J (1996) Adjusting survival curves for confounders: a review and a new method. Am J Epidemiol 143(10):1059-1068 · doi:10.1093/oxfordjournals.aje.a008670
[48] Normand SLT, Landrum MB, Guadagnoli E, Ayanian JZ, Ryan TJ, Cleary PD, McNeil BJ (2001) Validating recommendations for coronary angiography following acute myocardial infarction in the elderly: a matched analysis using propensity scores. J Clin Epidemiol 54(4):387-398 · doi:10.1016/S0895-4356(00)00321-8
[49] Pan Q, Schaubel DE (2008) Proportional hazards models based on biased samples and estimated selection probabilities. Can J Stat 36(1):111-127 · Zbl 1143.62064 · doi:10.1002/cjs.5550360111
[50] Parast L, Tian L, Cai T (2014) Landmark estimation of survival and treatment effect in a randomized clinical trial. J Am Stat Assoc 109(505):384-394 · Zbl 1367.62296 · doi:10.1080/01621459.2013.842488
[51] Park Y, Wei LJ (2003) Estimating subject-specific survival functions under the accelerated failure time model. Biometrika 90:717-23 · Zbl 1436.62478 · doi:10.1093/biomet/90.3.717
[52] Patel K, Williams PL, Seeger JD, McIntosh K, Van Dyke RB, Seage GR et al (2008) Long-term effectiveness of highly active antiretroviral therapy on the survival of children and adolescents with HIV infection: a 10-year follow-up study. Clin Infect Dis 46(4):507-515 · doi:10.1086/526524
[53] Robins JM, Hernán MÁ, Brumback B (2000) Marginal structural models and causal inference in epidemiology. Epidemiology 11(5):550-560 · doi:10.1097/00001648-200009000-00011
[54] Rosenbaum PR, Rubin DB (1983a) Assessing sensitivity to an unobserved binary covariate in an observational study with binary outcome. J R Stat Soc 45:212-218 · Zbl 1322.62257
[55] Rosenbaum PR, Rubin DB (1983b) The central role of the propensity score in observational studies for causal effects. Biometrika 70(1):41-55 · Zbl 0522.62091 · doi:10.1093/biomet/70.1.41
[56] Rotnitzky A, Robins J (2005) Inverse probability weighted estimation in survival analysis. Encycl Biostat 4:2619-2625
[57] Therneau TM (2000) Modeling survival data: extending the Cox model. Springer, New York · Zbl 0958.62094 · doi:10.1007/978-1-4757-3294-8
[58] Tian L, Cai T, Zhao L, Wei LJ (2012) On the covariate-adjusted estimation for an overall treatment difference with data from a randomized comparative clinical trial. Biostatistics 13(2):256-273 · Zbl 1437.62631 · doi:10.1093/biostatistics/kxr050
[59] Van Houwelingen J, Putter H (2012) Dynamic prediction in clinical survival analysis. CRC Press, New York · Zbl 1272.62004
[60] Zhang M (2015) Robust methods to improve efficiency and reduce bias in estimating survival curves in randomized clinical trials. Lifetime Data Anal 2014:1-19 · Zbl 1322.62257
[61] Zhang M, Schaubel DE (2012b) Double-robust semiparametric estimator for differences in restricted mean lifetimes in observational studies. Biometrics 68(4):999-1009 · Zbl 1258.62117 · doi:10.1111/j.1541-0420.2012.01759.x
[62] Zhu Y, Coffman DL, Ghosh D (2015) A boosting algorithm for estimating generalized propensity scores with continuous treatments. J Causal Inference 3(1):25-40 · doi:10.1515/jci-2014-0022
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