Estimating the average treatment effect on survival based on observational data and using partly conditional modeling

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/136506/1/biom12542.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136506/2/biom12542_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/136506/3/biom12542-sup-0001-SuppData.pd

Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards

Often in medical studies of time to an event, the treatment effect is not constant over time. In the context of Cox regression modeling, the most frequent solution is to apply a model that assumes the treatment effect is either piecewise constant or varies smoothly over time, i.e., the Cox nonproportional hazards model. This approach has at least two major limitations. First, it is generally difficult to assess whether the parametric form chosen for the treatment effect is correct. Second, in the presence of nonproportional hazards, investigators are usually more interested in the cumulative than the instantaneous treatment effect (e.g., determining if and when the survival functions cross). Therefore, we propose an estimator for the aggregate treatment effect in the presence of nonproportional hazards. Our estimator is based on the treatment-specific baseline cumulative hazards estimated under a stratified Cox model. No functional form for the nonproportionality need be assumed. Asymptotic properties of the proposed estimators are derived, and the finite-sample properties are assessed in simulation studies. Pointwise and simultaneous confidence bands of the estimator can be computed. The proposed method is applied to data from a national organ failure registry.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65785/1/j.1541-0420.2007.00947.x.pd

Partly Conditional Estimation of the Effect of a Time‐Dependent Factor in the Presence of Dependent Censoring

Summary We propose semiparametric methods for estimating the effect of a time‐dependent covariate on treatment‐free survival. The data structure of interest consists of a longitudinal sequence of measurements and a potentially censored survival time. The factor of interest is time‐dependent. Treatment‐free survival is of interest and is dependently censored by the receipt of treatment. Patients may be removed from consideration for treatment, temporarily or permanently. The proposed methods combine landmark analysis and partly conditional hazard regression. A set of calendar time cross‐sections is specified, and survival time (from cross‐section date) is modeled through weighted Cox regression. The assumed model for death is marginal in the sense that time‐varying covariates are taken as fixed at each landmark, with the mortality hazard function implicitly averaging across future covariate trajectories. Dependent censoring is overcome by a variant of inverse probability of censoring weighting (IPCW). The proposed estimators are shown to be consistent and asymptotically normal, with consistent covariance estimators provided. Simulation studies reveal that the proposed estimation procedures are appropriate for practical use. We apply the proposed methods to pre‐transplant mortality among end‐stage liver disease (ESLD) patients.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98799/1/biom12023.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/98799/2/biom12023-sm-0001-SupData.pd

Variance estimation for clustered recurrent event data with a small number of clusters

Often in biomedical studies, the event of interest is recurrent and within-subject events cannot usually be assumed independent. In semi-parametric estimation of the proportional rates model, a working independence assumption leads to an estimating equation for the regression parameter vector, with within-subject correlation accounted for through a robust (sandwich) variance estimator; these methods have been extended to the case of clustered subjects. We consider variance estimation in the setting where subjects are clustered and the study consists of a small number of moderate-to-large-sized clusters. We demonstrate through simulation that the robust estimator is quite inaccurate in this setting. We propose a corrected version of the robust variance estimator, as well as jackknife and bootstrap estimators. Simulation studies reveal that the corrected variance is considerably more accurate than the robust estimator, and slightly more accurate than the jackknife and bootstrap variance. The proposed methods are used to compare hospitalization rates between Canada and the U.S. in a multi-centre dialysis study. Copyright © 2005 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/48761/1/2157_ftp.pd

Penalized survival models for the analysis of alternating recurrent event data

Recurrent event data are widely encountered in clinical and observational studies. Most methods for recurrent events treat the outcome as a point process and, as such, neglect any associated event duration. This generally leads to a less informative and potentially biased analysis. We propose a joint model for the recurrent event rate (of incidence) and duration. The two processes are linked through a bivariate normal frailty. For example, when the event is hospitalization, we can treat the time to admission and length‐of‐stay as two alternating recurrent events. In our method, the regression parameters are estimated through a penalized partial likelihood, and the variance‐covariance matrix of the frailty is estimated through a recursive estimating formula. Moreover, we develop a likelihood ratio test to assess the dependence between the incidence and duration processes. Simulation results demonstrate that our method provides accurate parameter estimation, with a relatively fast computation time. We illustrate the methods through an analysis of hospitalizations among end‐stage renal disease patients.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155997/1/biom13153_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155997/2/biom13153-sup-0003-supmat.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155997/3/biom13153-sup-0001-Supplement_Lili_accepted_paper_1_10SEP2019.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155997/4/biom13153.pd

Evaluating center‐specific long‐term outcomes through differences in mean survival time: Analysis of national kidney transplant data

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149342/1/sim8076.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149342/2/sim8076_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149342/3/SIM_8076-Supp-0002-Web_Supple.pd

Evaluating center performance in the competing risks setting: Application to outcomes of wait‐listed end‐stage renal disease patients

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/142886/1/biom12739_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142886/2/biom12739.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/142886/3/biom12739-sup-0001-SuppData.pd

A weighted cumulative sum (WCUSUM) to monitor medical outcomes with dependent censoring

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108011/1/sim6139.pd

Non-parametric estimation of gap time survival functions for ordered multivariate failure time data

Times between sequentially ordered events (gap times) are often of interest in biomedical studies. For example, in a cancer study, the gap times from incidence-to-remission and remission-to-recurrence may be examined. Such data are usually subject to right censoring, and within-subject failure times are generally not independent. Statistical challenges in the analysis of the second and subsequent gap times include induced dependent censoring and non-identifiability of the marginal distributions. We propose a non-parametric method for constructing one-sample estimators of conditional gap-time specific survival functions. The estimators are uniformly consistent and, upon standardization, converge weakly to a zero-mean Gaussian process, with a covariance function which can be consistently estimated. Simulation studies reveal that the asymptotic approximations are appropriate for finite samples. Methods for confidence bands are provided. The proposed methods are illustrated on a renal failure data set, where the probabilities of transplant wait-listing and kidney transplantation are of interest. Copyright © 2004 John Wiley & Sons, Ltd.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/34861/1/1777_ftp.pd

A Sequential Stratification Method for Estimating the Effect of a Time-Dependent Experimental Treatment in Observational Studies

Survival analysis is often used to compare experimental and conventional treatments. In observational studies, the therapy may change during follow-up and such crossovers can be summarized by time-dependent covariates. Given the ever-increasing donor organ shortage, higher-risk kidneys from expanded criterion donors (ECD) are being transplanted. Transplant candidates can choose whether to accept an ECD organ (experimental therapy), or to remain on dialysis and wait for a possible non-ECD transplant later (conventional therapy). A three-group time-dependent analysis of such data involves estimating parameters corresponding to two time-dependent indicator covariates representing ECD transplant and non-ECD transplant, each compared to remaining on dialysis on the waitlist. However, the ECD hazard ratio estimated by this time-dependent analysis fails to account for the fact that patients who forego an ECD transplant are not destined to remain on dialysis forever, but could subsequently receive a non-ECD transplant. We propose a novel method of estimating the survival benefit of ECD transplantation relative to conventional therapy (waitlist with possible subsequent non-ECD transplant). Compared to the time-dependent analysis, the proposed method more accurately characterizes the data structure and yields a more direct estimate of the relative outcome with an ECD transplant.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66010/1/j.1541-0420.2006.00527.x.pd