Individualizing treatment according to patients' characteristics is central for personalized or precision medicine. There has been considerable recent research in developing statistical methods to determine optimal personalized treatment strategies by modeling the outcome of patients according to relevant covariates under each of the alternative treatments, and then relying on so-called predicted individual treatment effects. In this paper, we use potential outcomes and principal stratification frameworks and develop a multinomial model for left and right-censored data to estimate the probability that a patient is a responder given a set of baseline covariates. The model can apply to RCT or observational study data. This method is based on the monotonicity assumption, which implies that no patients would respond to the control treatment but not to the experimental one. We conduct a simulation study to evaluate the properties of the proposed estimation method. Results showed that the predictions of the probability of being a responder were well calibrated even if we observed variability and a small bias when many parameters were estimated. We finally applied the method to a cohort study on the selection of patients for additional radiotherapy after resection of a soft-tissue sarcoma.
DaskivichTJChamieKKwanL, et al.Overtreatment of men with low-risk prostate cancer and significant comorbidity. Cancer2011; 117: 2058–2066.
2.
GnantMMlineritschBSchippingerW, et al.Endocrine therapy plus zoledronic acid in premenopausal breast cancer. N Engl J Med2009; 360: 679–691.
3.
CaiTTianLWongPH, et al.Analysis of randomized comparative clinical trial data for personalized treatment selections. Biostatistics2011; 12: 270–282.
4.
FosterJCTaylorJMRubergSJ. Subgroup identification from randomized clinical trial data. Stat Med2011; 30: 2867–2880.
5.
LipkovichIDmitrienkoADenneJ, et al.Subgroup identification based on differential effect search – a recursive partitioning method for establishing response to treatment in patient subpopulations. Stat Med2011; 30: 2601–2621.
6.
ZhangZWangCNieL, et al.Assessing the heterogeneity of treatment effects via potential outcomes of individual patients. J R Stat Soc Ser C Appl Stat2013; 62: 687–704.
7.
ZhaoLTianLCaiT, et al.Effectively selecting a target population for a future comparative study. J Am Stat Assoc2013; 108: 527–539.
8.
LiJZhaoLTianL, et al.A predictive enrichment procedure to identify potential responders to a new therapy for randomized, comparative controlled clinical studies. Biometrics2016; 72: 877–887.
9.
QianMMurphySA. Performance guarantees for individualized treatment rules. Ann Stat2011; 39: 1180–1210.
10.
ZhangBTsiatisAALaberEB, et al.A robust method for estimating optimal treatment regimes. Biometrics2012; 68: 1010–1018.
11.
ZhaoYZengDRushAJ, et al.Estimating individualized treatment rules using outcome weighted learning. J Am Stat Assoc2012; 107: 1106–1118.
12.
ShenJWangLDaignaultS, et al.Estimating the optimal personalized treatment strategy based on selected variables to prolong survival via random survival forest with weighted bootstrap. J Biopharm Stat2018; 28: 362–381.
13.
JanesHPepeMSBossuytPM, et al.Measuring the performance of markers for guiding treatment decisions. Ann Int Med2011; 154: 253–259.
14.
SongXZhouXH. Evaluating markers for treatment selection based on survival time. Stat Med2011; 30: 2251–2264.
15.
JanesHBrownMDHuangY, et al.An approach to evaluating and comparing biomarkers for patient treatment selection. Int J Biostat2014; 10: 99–121.
16.
HuangYLaberEBJanesH. Characterizing expected benefits of biomarkers in treatment selection. Biostatistics2015; 16: 383–399.
17.
SennS. Mastering variation: Variance components and personalised medicine. Stat Med2016; 35: 966–977.
18.
RubinDB. Estimating causal effects of treatments in randomized and nonrandomized studies. J Educ Psychol1974; 66: 688–701.
19.
RubinDB. Comment: Which ifs have causal answers. J Am Stat Assoc1986; 81: 961–962.
20.
FrangakisCERubinDB. Principal stratification in causal inference. Biometrics2002; 58: 21–29.
21.
RubinDB. Causal inference using potential outcomes. J Am Stat Assoc2005; 100: 322–331.
22.
PearlJ. Principal stratification – a goal or a tool?. Int J Biostat2011, pp. 7. Article 20.
23.
VanderWeeleTJ. Principal stratification – uses and limitations. Int J Biostat2011, pp. 7. . Article 28.
24.
GilbertPBBoschRJHudgensMG. Sensitivity analysis for the assessment of causal vaccine effects on viral load in HIV vaccine trials. Biometrics2003; 59: 531–541.
25.
FrangakisCERubinDBAnMW, et al.Principal stratification designs to estimate input data missing due to death. Biometrics2007; 63: 641–649.
26.
PorcherRLeyratCBaronG, et al.Performance of principal scores to estimate the marginal compliers causal effect of an intervention. Stat Med2016; 35: 752–767.
27.
BiauDJFergusonPCChungP, et al.Local recurrence of localized soft tissue sarcoma: a new look at old predictors. Cancer2012; 118: 5867–5877.
28.
RobinsJMHernánMÁBrumbackB. Marginal structural models and causal inference in epidemiology. Epidemiology2000; 11: 550–560.
29.
LuncefordJKDavidianM. Stratification and weighting via the propensity score in estimation of causal treatment effects: a comparative study. Statistics in Medicine2004; 23: 2937–2960.
30.
RobinsJ. A new approach to causal inference in mortality studies with a sustained exposure period – application to control of the healthy worker survivor effect. Math Model1986; 7: 1393–1512.
31.
PearlJ. On the consistency rule in causal inference: axiom, definition, assumption, or theorem?. Epidemiology2010; 21: 872–875.
32.
RubinDB. Comment on ‘Randomization analysis of experimental data: The Fisher randomization test’ by D. Basu. J Am Stat Assoc1980; 75: 591–593.
33.
AngristJDImbensGWRubinDB. Identification of causal effects using instrumental variables. J Am Stat Assoc1996; 91: 444–455.
34.
HuangYGilbertPBJanesH. Assessing treatment-selection markers using a potential outcomes framework. Biometrics2012; 68: 687–696.
35.
RoystonPAltmanDG. Regression using fractional polynomials of continuous covariates: Parsimonious parametric modelling. Appl Stat1994; 43: 429–467.
36.
R Core Team. R: a language and environment for statistical computing. Vienna, Austria: R Foundation for Statistical Computing, 2015. http://www.R-project.org/ (accessed 13 August 2018).
37.
ScheikeTHZhangMJGerdsTA. Predicting cumulative incidence probability by direct binomial regression. Biometrika2008; 95: 205–220.
38.
SullivanTRWhiteIRSalterAB, et al.Should multiple imputation be the method of choice for handling missing data in randomized trials?. Stat Methods Med Res2018; 27: 2610–2626.
39.
RubinDB. Multiple imputation for nonresponse in surveys, New York: John Wiley & Sons, 2004.
40.
ScheikeTHZhangMJ. Analyzing competing risk data using the R timereg package. J Stat Softw2011; 38: 1–15.
41.
BallmanKV. Biomarker: predictive or prognostic?. J Clin Oncol2015; 33: 3968–3971.
42.
VickersAJKattanMWDanielS. Method for evaluating prediction models that apply the results of randomized trials to individual patients. Trials2007; 8: 14.
43.
VanderWeeleTJDingP. Sensitivity analysis in observational research: introducing the E-value. Ann Int Med2017; 167: 268–274.
44.
CollinsGSReitsmaJBAltmanDG, et al.Transparent reporting of a multivariable prediction model for individual prognosis or diagnosis (TRIPOD): The TRIPOD statement. Ann Int Med2015; 162: 55–63.
45.
RoystonPAltmanDGSauerbreiW. Dichotomizing continuous predictors in multiple regression: a bad idea. Stat Med2006; 25: 127–141.
46.
MoonsKGMRoystonPVergouweY, et al.Prognosis and prognostic research: what, why, and how?. BMJ2009; 388: b375.
47.
HuangEJFangEXHanleyDF, et al.Inequality in treatment benefits: can we determine if a new treatment benefits the many or the few?. Biostatistics2017; 18: 308–324.
48.
TaylorJMMurraySHsuCH. Survival estimation and testing via multiple imputation. Stat Probab Lett2002; 58: 221–232.
49.
HsuCHTaylorJMMurrayS, et al.Survival analysis using auxiliary variables via non-parametric multiple imputation. Stat Med2006; 25: 3503–3517.
50.
ZhaoYQZengDLaberEB, et al.Doubly robust learning for estimating individualized treatment with censored data. Biometrika2015; 102: 151–168.
51.
ZhengYCaiTFengZ. Application of the time-dependent ROC curves for prognostic accuracy with multiple biomarkers. Biometrics2006; 62: 279–287.
Supplementary Material
Please find the following supplemental material available below.
For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.
For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.
