# Questions tagged [proportional-hazards]

Proportional hazards is an assumption of the Cox proportional hazards model of survival analysis and some other models as well. The assumption is that a linear increase in the predictor will have a uniform multiplicative relationship with the hazard.

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### When computing period-specific hazard ratio using Cox, should I add variable:strata or full variable * strata?

Let's asusme I want to calculate separate hazards ratio in two periods, split like below. ...
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### In Cox regression, what does it mean if just one category of a categorical variable with >2 levels is time-dependent?

I ran a Cox regression analysis using BMI (categorical: underweight, normal(baseline), overweight and obese) with time to death as outcome and age, sex, blood pressure, heart rate, smoking status, ...
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### How do you present results of a proprtional hazards model when the outcome is a good thing?

We have run several Cox proportional hazards models. One of the outcomes is a beneficial thing (discharge from hospital), while the others are all negative outcomes (these are not competing outcomes ...
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### Way to simulate or calculate event numbers in survival analysis?

I would like to conduct a meta analysis on a subgroup that's often included in larger studies but not typically studied alone. I am trying to investigate the effect the presence or absence of a ...
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### Survival Analysis: Quantifying Survival Differences when Proportional Hazards is Violated

I am comparing survival between two groups distinguished by a single factor. The survival curves converge at both ends (near time 0 and near the maximum time) but never cross, and R's survival::cox....
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### Is it possible to calculate number of events in each treatment arm if we have hazard ratio and number of patients in each treatment group

I have a question regarding calculating event numbers. I have a trial where the hazard ratio of treatment arm compared to control arm is 0.75 (95% CI: 0.59-0.96). I know the number of patients ...
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### Extracting hazard ratio for subgroup from overall hazard ratio and hazard ratio of another subgroup?

Hi I have a relatively naive question here. Suppose in a clinical trial the overall HR of treatment A compared to treatment B is 0.66 (95% CI: 0.61 to 0.73). Now we perform a subgroup analysis of the ...
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### Step functions for non-proportional hazards

I have a stratified Cox model with covariates ("big") which violate proportional hazard assumptions: ...
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### Dealing with non-proportional hazards ratios (change in variance)

I am currently analysing some data from a simulation model, on which I'd like to fit a Cox regression model. The simulations are based on a completely average model, and thus I know that none of the ...
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### Informative censoring in Regularized Cox proportional hazard model

I am studying Cox proportional hazard models, and in particular Regularization Paths for Cox's Proportional Hazards Model via Coordinate Descent, by Tibshirani, Hastie and Friedman. I would like to ...
1 vote
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### What if proportional hazard assumption does not hold for a confounder in Cox PH model

If proportionality hazard assumption does not appear to hold for a covariate in the Cox PH model, is it a serious matter? The covariate is included in order to adjust for potential confounding. I am ...
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### Test for PH assumption vs visual inspection of Schoenfeld residuals

I am inspecting the PH assumption of a Cox model, both by testing it (with cox.zph in R) and visualizing the Schoenfeld residuals. I found many references with ...
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### How to simulate a time dependent variable on a existing dataset?

I made a coursera course abouth survival analysis. It uses a heart failure dataset for the examples. (That same dataset can be found on Kaggle https://www.kaggle.com/jackleenrasmybareh/heart-failure) ...
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### cox.zph p-value indicates proportional hazards but plot shows non-flat and non-straight line

I created a Cox model using the following code: ...
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### Statistically significant Cox PH model, but non statistically significant covariates

I have fitted a Cox PH model with three covariates, age (continuous), risk group (factor) and treatment (factor). The variable of interest is the treatment, which is statistically significant but the ...
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### Effects of not testing Proportional Hazard Assumption

I have encountered numerous journal articles where the PH-assumption of a Cox model is not tested. However, when I raise the issue with statisticians, I have been told that it is unimportant unless ...
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### Use an arbitrary number of features to predict an individuals life expectancy

Objective I want to predict someone's life expectancy (age they will die) based on their lifestyle, current conditions, medications, biomarkers etc. Limitations of supervised learning There are no ...
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### Test/validate a random forest survival model

I have around 7,588 features for 100 subjects with time to event and status data. I have built 100 random forest survival models with 75/25 train-test splits using ...
1 vote
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### Plot of hazard ratio for primary endpoint and continuous covariate

I wonder if you could tell me the R code to use to obtain a graph similar to the one below. (from: https://www.nejm.org/doi/full/10.1056/NEJMoa1215740) That is, I would like to graph the association ...
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### About the interpretation of time-varying variables with time interaction in Cox-PH model

My question is that in what condition that the Cox-PH assumption said to be satisfied after including the time-varying covariates with time interaction in the Cox-PH model? is that must all variables ...
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### feature sealection/elimination and multi-collinearity in a Cox proportional hazards models?

I am looking into how differing brain tumor genetics affects patient survival. I have a gene dataset with around 4600 predictors, which are often strongly correlated with each other. Now I want to ...
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### How to best correct for repeated testing in cox proportional hazards models? [duplicate]

I am looking into how differing brain tumor genetics affects patient survival. I have a gene dataset with around 4600 predictors. Now I calculated a cox proportional hazards model using the ...
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### What is censoring distribution and how to get it from accruing period, follow-up period and stopping time of trial?

I am reading Dirk Moore's Applied Survival Analysis 11.8 Example 11.1 on page 173. The book is trying to simulate power of logrank test. I cannot see the book's conclusion on censoring distribution. ...
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### Schoenfeld residuals - Plain English explanation, please!

I have created a Cox model for lung adenocarcinoma patients. Several variables make up the model and I have assessed whether or not the proportional hazards assumption holds. Using the cox.zph ...
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### Violation of PH assumption Cox model

So, i have seen similar questions to mine here but still can´t quite understand why this is happening. I´ve ajusted a cox model and now i´m testing the PH assumption. This are my results: It is ...
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### Merging survival data with time varying covariates

In merging the data in R the censored observations are merged well but the observed subjects are not. For example, the second subject had an event at time 0.546. How can I merge the time varying ...
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### Survival curve from time-dependent coefficients in the Cox model

I fitted a Cox Model that does not satisfy the proportional hazards assumption. Thus, I included time-dependent coefficients using the tt() function in the same way ...
1 vote
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### Can one compare Hazard Ratio and Average Hazard Ratio?

I would like to compare three predictors of survival by comparing three cox regression models. One model violates the PH assumption which brought me to weighted cox regression as implemented by ...
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### deviance residual plot abnormal for cox proportional model

Hi, is the cox proportion hazard model violated? I'm not sure whether the problem is censored data or wrong prediction? But, there is only few significant variables can fit the hazard model adequately....
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### Constructing hazard for x-year survival in cox models

If a person wants to assess the 1,5, or 10 year survival of a group of patients how should they consider right censoring for the patients? Between these 2 options what would be best for this 5 year ...
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### Computing Chi-square values from Schoenfeld residuals

Based on page 164-165 of [Collett:Modelling Survival data in medical research (Third edition-2014)] the Schoenfeld for individual test and for global test can be obtained as follows[1]. However, ...
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### How to calculate Schoenfeld Residuals in R

I am trying to manually calculate the schoenfeld residuals in Cox model. Please see the code below. Sresid gives the calculation in cox.zph function using schoenfeld residuals. Schoenfeld gives the ...
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### Test for proportional hazards assumption in coxme model - Error and abortion of R session

I'm trying to do a survival analysis using a mixed-effects cox proportional hazards model in R with coxme. My data is - actually - fairly simple. I followed the survival of insect that were kept in ...
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### How does time specific hazard ratios relate to time dependent incident dynamic ROC AUC?

I have a question related to time specific hazard and time dependent incident dynamic ROC analysis. I am currently working on some analysis where I evaluate a prognostic model (Cox model) on some ...
1 vote
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### Proportional Hazards Model and EM Algorithm

I am working with the standard proportional hazards model given by $\lambda(t|Z) = \lambda_0(t)e^{Z\beta}$ for a special type of data that requires an EM algorithm to estimate a discretized version of ...
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### How to explain large hazard ratio confidence intervals?

I did a multivariable cox proportional hazards analysis including variables with univariable p<0.2 , and 3 variables gave statistical significance. Their HRs are around 5 to 8, which is pretty high,...
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### Survival analysis: using time varying covariates for resolving violated PH

p1 is a factor p2 is a continuous variable Model m = Survival_function ~ p1 + p2 Both covariates - p1 and p2 - violate the proportional hazards assumption. I am ...
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### Stratified KM curve plot for estimation of proportional hazards assumption violation

I am reading a paper that attempts to investigate time varying covariates in Cox proportional hazard model for breast cancer patients. I read that we can plot stratified KM curves for two groups of ...
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### Likelihood term in Cox Proportional Hazards Model

I have just started learning on the Cox proportional hazards model. I understand that the hazard function is the multiplicative of the baseline hazard rate $h_0(t)$ and the hazard rates dependence on ...
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### Cox regression - proportional hazards - time to event variable in database with one line per individual per year

I have a question regarding my Time to Event variable. Since I am working with time-varying variables (which can change every year), I use a data structure with one line per individual per year. ...
1 vote
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### What measure to use to compare stratified and non stratified Cox proportional hazards in R

I am doing past papers studying for an exam on medical statistics and am unsure about one of the questions. The question reads as follows: "Consider now a second model where we stratify by sex ...
1 vote
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### Closed form expression for survfit function used in R (Cox proportional hazard survival model)

I have a dataset of patient survival times that I am trying to predict based on n covariates X1...Xn (patient co-morbidities, other diagnoses, lab results) using a Cox proportional hazard model. I'm ...
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### Efficient influence function in proportional hazards model

I was hoping someone could help me with this problem in the cox proportional hazards model. I am given the following setup. T is a non-negative random variable with continous distribution and hazard ...
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### Cox PH non-proportionality: time-dependent variable?

I am performing Cox regression modelling, searching for predictors for various clinical outcomes. Now, based on Schoenfeld residuals test, some of my binary predictors have p-value <0.05 with ...
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### Would you used prediction from Cox or stratified KM for drawing survival curves and testing them?

Let's assume I have an experiment, where I track some event. I want to analyse the time to this event between two levels of a group G: g1 and g2 I want to do the comparative analysis in sub groups, ...
1 vote
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### Why do my survival curves generated by the Cox differ from Kaplan-Meier for the simplest model?

I was told, that the Cox with a single categorical covariate is equal to the Kaplan-Meier stratified by the levels of this covariate. But the two graphs below don't support it. I also use strata() in ...
1 vote
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### Is doing Kaplan-Meier for 2 curves equivalent to ajdusting for a covarite or stratyfing in Cox? I want the HR for my KM curves

Using the R terminology (but this is software independent statistical problem), is survfit(surv_object ~ rx, data = ovarian) returning 2 Kaplan-Meier curves the ...
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### Survival Analysis - Hazard Ratios of One - Interpretation and Model Fit

I am using Cox Proportional Hazards for a set of data. I continue to find variables with hazard ratios equal to one. I understand that these variables are not hazardous/protective to the life of the ...
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### Assessing proportional hazards assumption: p-value from coxzph() vs. visual inspection of plot of scaled Schoenfeld residuals with time

The coxzph() function in the R package Survival shows a significant p-value for violation of the proportional hazards assumption ...
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### Can it be said, that in case of non-proportional hazards, Cox returns average hazard ratio over the entire period?

I have read two opposite statements about the hazard ratios obtained from the Cox procedure in presence of non-proportional hazards. One is that the HR for a certain covariate, that fails this ...