Maximum likelihood estimation for tied survival data under Cox regression model via EM-algorithm

Scheike, Thomas H.; Sun, Yanqing

doi:10.1007/s10985-007-9043-3

Cited by 21 publications

(9 citation statements)

References 7 publications

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“…Besides these two standard approaches there are various so-called exact methods of dealing with ties. However, all these methods lead to biased estimates when the true underlying model is in fact a Cox model (see Scheike and Sun, 2007). Thus, to summarize, heavy ties will lead to biased parameter estimates and standard errors, and there is no sufficient way to tackle this problem in a Cox model framework.…”

Section: Tied Duration Timesmentioning

confidence: 99%

The Duration of Trade Revisited: Continuous-Time vs. Discrete-Time Hazards

Heß

Persson

2010

SSRN Journal

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The recent literature on the duration of trade has predominantly analyzed the determinants of trade flow durations using Cox proportional hazards models. The purpose of this paper is to show why it is inappropriate to analyze the duration of trade with continuous-time models such as the Cox model, and to propose alternative discrete-time models which are more suitable for estimation. Briefly, the Cox model has three major drawbacks when applied to large trade data sets. First, it faces problems in the presence of many tied duration times, leading to biased coefficient estimates and standard errors. Second, it is difficult to properly control for unobserved heterogeneity, which can result in spurious duration dependence and parameter bias. Third, the Cox model imposes the restrictive and empirically questionable assumption of proportional hazards. By contrast, with discrete-time models there is no problem handling ties; unobserved heterogeneity can be controlled for without difficulty; and the restrictive proportional hazards assumption can easily be bypassed. By replicating an influential study by Besedeš and Prusa from 2006, but employing discrete-time models as well as the original Cox model, we find empirical support for each of these arguments against the Cox model. Moreover, when comparing estimation results obtained from a Cox model and our preferred discrete-time specification, we find significant differences in both the predicted hazard rates and the estimated effects of explanatory variables on the hazard. In other words, the choice between models affects the conclusions that can be drawn.

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Section: Tied Duration Timesmentioning

confidence: 99%

The Duration of Trade Revisited: Continuous-Time vs. Discrete-Time Hazards

Heß

Persson

2010

SSRN Journal

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“…We extend their work to settings with censored data across a broad range of hazard ratios, along with an important comparison of Wald and score tests for each tie‐handling method, including the ubiquitous logrank test. Related simulation results have also been reported by Scheike and Sun; however, they too did not study score tests, restricted attention to a single hazard ratio, and simulated scenarios with smaller tie densities relative to those shown for our motivating examples in Table . Furthermore, neither set of authors examined type I error rate and power properties of the methods studied.…”

Section: Introductionmentioning

confidence: 68%

“…Hence, as noted by the authors, using a confidence interval for obtained by inverting the statistic in (18) will ensure inferential alignment with the logrank test p-value. Equations (13) and (14) reveal that the statistic in (18) is constructed by using the same numerator but a modified denominator in the Breslow 11 score statistic; the modification inserts the multiplier (n iA + n iB − d i )/(n iA + n iB − 1) in (14). (=̂[ B] ) is generally biased, the test-based confidence interval for based on (18) will sometimes suffer from inadequate coverage; we confirm this using simulations reported in the next section.…”

Section: Efron Methods {Ties = Efron In Sas Proc Phreg}mentioning

confidence: 99%

Hazard ratio estimation and inference in clinical trials with many tied event times

Mehrotra

Zhang

2018

Statistics in Medicine

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The medical literature contains numerous examples of randomized clinical trials with time-to-event endpoints in which large numbers of events accrued over relatively short follow-up periods, resulting in many tied event times. A generally common feature across such examples was that the logrank test was used for hypothesis testing and the Cox proportional hazards model was used for hazard ratio estimation. We caution that this common practice is particularly risky in the setting of many tied event times for two reasons. First, the estimator of the hazard ratio can be severely biased if the Breslow tie-handling approximation for the Cox model (the default in SAS and Stata software) is used. Second, the 95% confidence interval for the hazard ratio can include one even when the corresponding logrank test p-value is less than 0.05. To help establish a better practice, with applicability for both superiority and noninferiority trials, we use theory and simulations to contrast Wald and score tests based on well-known tie-handling approximations for the Cox model. Our recommendation is to report the Wald test p-value and corresponding confidence interval based on the Efron approximation. The recommended test is essentially as powerful as the logrank test, the accompanying point and interval estimates of the hazard ratio have excellent statistical properties even in settings with many tied event times, inferential alignment between the p-value and confidence interval is guaranteed, and implementation is straightforward using commonly used software.

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“…We have implemented the "efron" and the "breslow" method but not the "exact" method. For a comparison of these methods and yet another method see Scheike and Sun (2007). We now state the formula for the baseline hazard function under Breslow's (Breslow, 1974) and Efron's method (Efron, 1977) for the handling of ties.…”

Section: Handling Of Tied Event Timesmentioning

confidence: 99%

riskRegression: Predicting the Risk of an Event using Cox Regression Models

Ozenne¹,

Sørensen²,

Scheike³

et al. 2017

The R Journal

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In the presence of competing risks a prediction of the time-dynamic absolute risk of an event can be based on cause-specific Cox regression models for the event and the competing risks (Benichou and Gail, 1990). We present computationally fast and memory optimized C++ functions with an R interface for predicting the covariate specific absolute risks, their confidence intervals, and their confidence bands based on right censored time to event data. We provide explicit formulas for our implementation of the estimator of the (stratified) baseline hazard function in the presence of tied event times. As a by-product we obtain fast access to the baseline hazards (compared to survival::basehaz()) and predictions of survival probabilities, their confidence intervals and confidence bands. Confidence intervals and confidence bands are based on point-wise asymptotic expansions of the corresponding statistical functionals. The software presented here is implemented in the riskRegression package.

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Maximum likelihood estimation for tied survival data under Cox regression model via EM-algorithm

Cited by 21 publications

References 7 publications

The Duration of Trade Revisited: Continuous-Time vs. Discrete-Time Hazards

The Duration of Trade Revisited: Continuous-Time vs. Discrete-Time Hazards

Hazard ratio estimation and inference in clinical trials with many tied event times

riskRegression: Predicting the Risk of an Event using Cox Regression Models

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