![]() ![]() Subject i = 4 is included in cross section k = 1, but then becomes (and remains) treatment-ineligible until some a time after cross section k = 2. Subject i = 3 is excluded from cross-section k = 1 and k = 2 due to starting and finishing follow-up between CS 1 and CS 2. Subject i = 2 is treated and, hence, dependently censored at time T 22 following cross section k = 2. Note subject i = 1 is not censored at the treatment-ineligible time after cross section k = 2. For subject i = 1, failure times D 11 and D 12 correspond to cross sections k = 1 and k = 2, respectively. The four subjects begin follow-up at different calendar dates. Four subjects ( i = 1, …, i = 4) and two cross sections ( k = 1, 2) are shown. © 2016, The International Biometric Society.Įxamples of the relationship between cross-section time and follow-up time. Landmark analysis Observational data Partly conditional model Proportional hazards regression Time-varying covariates Treatment effect. The proposed methods are applied to liver transplant data in order to estimate the effect of liver transplantation on survival among transplant recipients under current practice patterns. Asymptotic properties are derived and evaluated through simulation. For each treated patient, fitted pre- and posttreatment survival curves are projected out, then averaged in a manner which accounts for the censoring of treatment times. The pre-treatment model is estimated through recently developed landmark analysis methods. The pre- and posttreatment models are partly conditional, in that they use the covariate history up to the time of treatment. We propose semiparametric methods for estimating the average difference in restricted mean survival time attributable to a time-dependent treatment, the average effect of treatment among the treated, under current treatment assignment patterns. In the data structure of our interest, subjects typically begin follow-up untreated time-until-treatment, and the pretreatment death hazard are both heavily influenced by longitudinal covariates and subjects may experience periods of treatment ineligibility. Most existing methods which quantify the treatment effect through the survival function are applicable to treatments assigned at time 0. Treatments are usually compared using a hazard ratio. In settings where randomization of treatment is not feasible, observational data are employed, necessitating correction for covariate imbalances. Treatments are frequently evaluated in terms of their effect on patient survival. ![]()
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