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Proportional Hazards Assumption (proportional + hazard_assumption)
Selected AbstractsComparing alternative models: log vs Cox proportional hazard?HEALTH ECONOMICS, Issue 8 2004Anirban Basu Abstract Health economists often use log models (based on OLS or generalized linear models) to deal with skewed outcomes such as those found in health expenditures and inpatient length of stay. Some recent studies have employed Cox proportional hazard regression as a less parametric alternative to OLS and GLM models, even when there was no need to correct for censoring. This study examines how well the alternative estimators behave econometrically in terms of bias when the data are skewed to the right. Specifically we provide evidence on the performance of the Cox model under a variety of data generating mechanisms and compare it to the estimators studied recently in Manning and Mullahy (2001). No single alternative is best under all of the conditions examined here. However, the gamma regression model with a log link seems to be more robust to alternative data generating mechanisms than either OLS on ln(y) or Cox proportional hazards regression. We find that the proportional hazard assumption is an essential requirement to obtain consistent estimate of the E(y,x) using the Cox model. Copyright © 2004 John Wiley & Sons, Ltd. [source] Choice of parametric models in survival analysis: applications to monotherapy for epilepsy and cerebral palsyJOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES C (APPLIED STATISTICS), Issue 2 2003G. P. S. Kwong Summary. In the analysis of medical survival data, semiparametric proportional hazards models are widely used. When the proportional hazards assumption is not tenable, these models will not be suitable. Other models for covariate effects can be useful. In particular, we consider accelerated life models, in which the effect of covariates is to scale the quantiles of the base-line distribution. Solomon and Hutton have suggested that there is some robustness to misspecification of survival regression models. They showed that the relative importance of covariates is preserved under misspecification with assumptions of small coefficients and orthogonal transformation of covariates. We elucidate these results by applications to data from five trials which compare two common anti-epileptic drugs (carbamazepine versus sodium valporate monotherapy for epilepsy) and to survival of a cohort of people with cerebral palsy. Results on the robustness against model misspecification depend on the assumptions of small coefficients and on the underlying distribution of the data. These results hold in cerebral palsy but do not hold in epilepsy data which have early high hazard rates. The orthogonality of coefficients is not important. However, the choice of model is important for an estimation of the magnitude of effects, particularly if the base-line shape parameter indicates high initial hazard rates. [source] Extent of mesorectal invasion is a prognostic indicator in T3 rectal carcinomaANZ JOURNAL OF SURGERY, Issue 7 2002Malcolm C. A. Steel Background: The aim of this study was to determine if local recurrence (LR) rates in patients with minimally invasive and advanced T3 rectal cancer are different. This may influence the use of adjuvant therapy. Methods: Consecutive patients with T3 rectal cancer undergoing curative surgery were classified into minimally invasive or advanced groups. Minimally invasive T3 was defined as a tumour that had invaded beyond the muscularis propria on microscopic examination only, whereas advanced T3 tumours had invasion beyond the muscularis propria that was obvious on macroscopic examination and confirmed histologically. Local recurrence rates of the two groups were compared by construction of Kaplan,Meier curves. The log-rank test was used to determine equivalence, and Cox regression to estimate the hazard ratio. The Grambsch, Therneau test and graphical comparison of predicted and observed Kaplan,Meier curves was used to test the proportional hazards assumption. Results: There were 222 patients in total, 74 in the minimally invasive group and 148 in the advanced. The overall LR rate was 11.2%. The LR rates in the minimally invasive and advanced groups were 5.4% and 14.2%, respectively. The log-rank test gives a P value of 0.042 for equivalence, with the minimally invasive patients doing significantly better. The hazard ratio estimated by Cox regression was 0.35 (early relative to advanced), 95% confidence intervals (0.12, 1.0). There was no evidence of confounding by age at surgery, pathology type, gender or postoperative adjuvant therapy. Conclusions: The extent of invasion into the mesorectum appears to be an independent prognostic variable. If oncologically sound surgical techniques are employed, the LR rate of patients with minimal invasion is low. Adjuvant therapy may not confer additional benefit in this group. [source] Bayesian Nonparametric Nonproportional Hazards Survival ModelingBIOMETRICS, Issue 3 2009Maria De Iorio Summary We develop a dependent Dirichlet process model for survival analysis data. A major feature of the proposed approach is that there is no necessity for resulting survival curve estimates to satisfy the ubiquitous proportional hazards assumption. An illustration based on a cancer clinical trial is given, where survival probabilities for times early in the study are estimated to be lower for those on a high-dose treatment regimen than for those on the low dose treatment, while the reverse is true for later times, possibly due to the toxic effect of the high dose for those who are not as healthy at the beginning of the study. [source] Smoothing Spline-Based Score Tests for Proportional Hazards ModelsBIOMETRICS, Issue 3 2006Jiang Lin Summary We propose "score-type" tests for the proportional hazards assumption and for covariate effects in the Cox model using the natural smoothing spline representation of the corresponding nonparametric functions of time or covariate. The tests are based on the penalized partial likelihood and are derived by viewing the inverse of the smoothing parameter as a variance component and testing an equivalent null hypothesis that the variance component is zero. We show that the tests have a size close to the nominal level and good power against general alternatives, and we apply them to data from a cancer clinical trial. [source] A Semiparametric Estimate of Treatment Effects with Censored DataBIOMETRICS, Issue 3 2001Ronghui Xu Summary. A semiparametric estimate of an average regression effect with right-censored failure time data has recently been proposed under the Cox-type model where the regression effect ,(t) is allowed to vary with time. In this article, we derive a simple algebraic relationship between this average regression effect and a measurement of group differences in K -sample transformation models when the random error belongs to the Gp family of Harrington and Fleming (1982, Biometrika69, 553,566), the latter being equivalent to the conditional regression effect in a gamma frailty model. The models considered here are suitable for the attenuating hazard ratios that often arise in practice. The results reveal an interesting connection among the above three classes of models as alternatives to the proportional hazards assumption and add to our understanding of the behavior of the partial likelihood estimate under nonproportional hazards. The algebraic relationship provides a simple estimator under the transformation model. We develop a variance estimator based on the empirical influence function that is much easier to compute than the previously suggested resampling methods. When there is truncation in the right tail of the failure times, we propose a method of bias correction to improve the coverage properties of the confidence intervals. The estimate, its estimated variance, and the bias correction term can all be calculated with minor modifications to standard software for proportional hazards regression. [source] | |||||||||||||