• Asian Pacific Journal of Cancer Prevention
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• v.15 no.1
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• pp.441-447
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• 2014

Background: Multi-state models are appropriate for cancer studies such as gastrectomy which have high mortality statistics. These models can be used to better describe the natural disease process. But reaching that goal requires making assumptions like Markov and homogeneity with time. The present study aims to investigate these hypotheses. Materials and Methods: Data from 330 patients with gastric cancer undergoing surgery at Iran Cancer Institute from 1995 to 1999 were analyzed. To assess Markov assumption and time homogeneity in modeling transition rates among states of multi-state model, Cox-Snell residuals, Akaikie information criteria and Schoenfeld residuals were used, respectively. Results: The assessment of Markov assumption based on Cox-Snell residuals and Akaikie information criterion showed that Markov assumption was not held just for transition rate of relapse (state 1 ${\rightarrow}$ state 2) and for other transition rates - death hazard without relapse (state 1 ${\rightarrow}$ state 3) and death hazard with relapse (state 2 ${\rightarrow}$ state 3) - this assumption could also be made. Moreover, the assessment of time homogeneity assumption based on Schoenfeld residuals revealed that this assumption - regarding the general test and each of the variables in the model- was held just for relapse (state 1 ${\rightarrow}$ state 2) and death hazard with a relapse (state 2 ${\rightarrow}$ state 3). Conclusions: Most researchers take account of assumptions such as Markov and time homogeneity in modeling transition rates. These assumptions can make the multi-state model simpler but if these assumptions are not made, they will lead to incorrect inferences and improper fitting.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.349-359
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• 2017

In this paper, we conducted survival analyses by fitting the Cox proportional hazards model to stage III proximal colon cancer data obtained from the Surveillance, Epidemiology, and End Results program of the National Cancer Institute. We investigated the effect of covariates on the hazard function for death from proximal colon cancer in stage III with surgery performed and estimated the survival probability for a patient with specific covariates. We showed that the proportional hazards assumption is satisfied for covariates that were used to analyses, using a test based on the Schoenfeld residuals and plots of the Schoenfeld residuals and $log[-log\{{\hat{S}}(t)\}]$. We evaluated the model calibration and discriminatory accuracy by calibration plot and time-dependent area under the ROC curve, which were calculated using 10-fold cross validation.

• Communications for Statistical Applications and Methods
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• v.24 no.6
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• pp.583-604
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• 2017

The most popular regression model for the analysis of time-to-event data is the Cox proportional hazards model. While the model specifies a parametric relationship between the hazard function and the predictor variables, there is no specification regarding the form of the baseline hazard function. A critical assumption of the Cox model, however, is the proportional hazards assumption: when the predictor variables do not vary over time, the hazard ratio comparing any two observations is constant with respect to time. Therefore, to perform credible estimation and inference, one must first assess whether the proportional hazards assumption is reasonable. As with other regression techniques, it is also essential to examine whether appropriate functional forms of the predictor variables have been used, and whether there are any outlying or influential observations. This article reviews diagnostic methods for assessing goodness-of-fit for the Cox proportional hazards model. We illustrate these methods with a case-study using available R functions, and provide complete R code for a simulated example as a supplement.

• Journal of Gastric Cancer
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• v.15 no.4
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• pp.238-245
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• 2015

Purpose: This study aimed to identify time-dependent prognostic factors and demonstrate the time-dependent effects of important prognostic factors in patients with advanced gastric cancer (AGC). Materials and Methods: We retrospectively evaluated 3,653 patients with AGC who underwent curative standard gastrectomy between 1991 and 2005 at the Korea Cancer Center Hospital. Multivariate survival analysis with Cox proportional hazards regression was used in the analysis. A non-proportionality test based on the Schoenfeld residuals (also known as partial residuals) was performed, and scaled Schoenfeld residuals were plotted over time for each covariate. Results: The multivariate analysis revealed that sex, depth of invasion, metastatic lymph node (LN) ratio, tumor size, and chemotherapy were time-dependent covariates violating the proportional hazards assumption. The prognostic effects (i.e., log of hazard ratio [LHR]) of the time-dependent covariates changed over time during follow-up, and the effects generally diminished with low slope (e.g., depth of invasion and tumor size), with gentle slope (e.g., metastatic LN ratio), or with steep slope (e.g., chemotherapy). Meanwhile, the LHR functions of some covariates (e.g., sex) crossed the zero reference line from positive (i.e., bad prognosis) to negative (i.e., good prognosis). Conclusions: The time-dependent effects of the prognostic factors of AGC are clearly demonstrated in this study. We can suggest that time-dependent effects are not an uncommon phenomenon among prognostic factors of AGC.