Graphical comparison of cumulative hazards for two populations

Dabrowska, Dorata M.; Doksum, Kjell A.; Song, Jae-Kee

doi:10.1093/biomet/76.4.763

Cited by 26 publications

(23 citation statements)

References 20 publications

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“…Dabrowska, Doksum, and Song (1989) introduced a relative change function involving the survival functions for two populations and constructed pointwise confidence intervals. Dabrowska, Doksum, and Song (1989) introduced a relative change function involving the survival functions for two populations and constructed pointwise confidence intervals.…”

Section: Introductionmentioning

confidence: 99%

Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards

Wei

Schaubel

2007

Biometrics

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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.

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Section: Introductionmentioning

confidence: 99%

Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards

Wei

Schaubel

2007

Biometrics

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“…This plot is related to a plot of the relative cumulative hazard difference (RCHD)

({\overset{Λ}{false}}_{2} (t) - {\overset{Λ}{false}}_{1} (t)) / {\overset{Λ}{false}}_{1} (t)

versus t , which should also resemble a horizontal straight line if the hazards are proportional. This plot had been proposed by Dabrowska et al , .…”

Section: Existing Graphical Testsmentioning

confidence: 77%

“…Dabrowska et al , provided asymptotic confidence bands of the RTF and proposed a conservative graphical test for the hypothesis of proportional hazards by checking whether the band contains a straight line through the origin. This procedure can be adapted in a straightforward manner to the trend function

{\overset{Λ}{false}}_{2}^{K} \circ {({\overset{Λ}{false}}_{1}^{K})}^{- 1} (u)

based on the weighted cumulative hazard functions.…”

Section: Existing Graphical Testsmentioning

confidence: 99%

“…A well‐known drawback of analytical tests is that, in the case of rejection, they do not provide a clear pointer towards possible alternative modeling. In view of this limitation, plots for checking the proportionality of hazards in two samples have become increasingly popular in recent years . These plots permit the human eye to pick up patterns that may suggest specific forms of departure from the ideal shape corresponding to proportional hazards.…”

Section: Introductionmentioning

confidence: 99%

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On graphical tests for proportionality of hazards in two samples

Sahoo

Sengupta

2015

Statistics in Medicine

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In this paper, we present a class of graphical tests of the proportional hazards hypothesis for two-sample censored survival data. The proposed tests are improvements over some existing tests based on asymptotic confidence bands of certain functions of the estimated cumulative hazard functions. The new methods are based on the comparison of unrestricted estimates of the said functions and their restricted versions under the hypothesis. They combine the rigour of analytical tests with the descriptive value of plots. Monte Carlo simulations suggest that the proposed asymptotic procedures have reasonable small sample properties. The power is much higher than existing graphical tests and comparable with existing analytical tests. The method is then illustrated through the analysis of a data set on bone marrow transplantation for Leukemia patients.

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“…Initial investigations involved the use of piece-wise constant hazard functions, examples of which can be found in Holford, 36,37 Laird and Olivier 38 and Taulbee. 39 Other methods address non-proportionality issues by pretesting and comparison of two survival or hazard functions through graphics and asymptotic confidence bands, 40–42 or through asymptotic confidence bands for changes in the predictor effects over time. 43,44 Some of these methods mentioned require large sample sizes for inference, and their performance can degrade over time in studies with sparser outcomes in later periods.…”

Section: Non-proportional Hazards Modelsmentioning

confidence: 99%

Flexible modeling of the hazard rate and treatment effects in long-term survival studies

Hagar

Dignam

Dukić

2017

Stat Methods Med Res

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The effects of predictors on time to failure may be difficult to assess in cancer studies with longer follow-up, as the commonly used assumption of proportionality of hazards holding over an extended period is often questionable. Motivated by a long-term prostate cancer clinical trial, we contrast and compare four powerful methods for estimation of the hazard rate. These four methods allow for varying degrees of smoothness as well as covariates with effects that vary over time. We pay particular attention to an extended multiresolution hazard estimator, which is a flexible, semi-parametric, Bayesian method for joint estimation of predictor effects and the hazard rate. We compare the results of the extended multiresolution hazard model to three other commonly used, comparable models: Aalen’s additive model, Kooperberg’s hazard regression model, and an extended Cox model. Through simulations and the analysis of a large-scale randomized prostate cancer clinical trial, we use the different methods to examine patterns of biochemical failure and to estimate the time-varying effects of androgen deprivation therapy treatment and other covariates.

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Graphical comparison of cumulative hazards for two populations

Cited by 26 publications

References 20 publications

Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards

Estimating Cumulative Treatment Effects in the Presence of Nonproportional Hazards

On graphical tests for proportionality of hazards in two samples

Flexible modeling of the hazard rate and treatment effects in long-term survival studies

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