# 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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### Extended Weibull-Cox model survival function

I'm reading an article where the authors use an extended Cox-Weibull hazard model with time-varying covariates to model survival time of an individual. This individual is allowed to start at week $m$, ...
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### Proportional hazards violation after restrcited cubic spline application, Cox

I am using Cox for the purposes of assessing the effect of a treatment on mortality. I have 50 covariates with 120df and n = 100k. I have read in various locations about the utility of using ...
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### "System is computationally singular" error after using restricted cubic splines

To permit appropriate specification of functional form, I am using restricted cubic splines (rcs() from rms) in my Cox model. I'...
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### How to deal with non-proportional risk?

Let's start with a toy example. We have an RCT with 2 treatment arms (Treatment A vs. Treatment B), and one outcome. When we analyse survival curves according to the treatment arm, we found the ...
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### Schoenfeld plots after restricted cubic spline

I'm using a Cox model with 100k subjects and 1624 events to model the effects of a treatment with respect to 49 covariates, 127df. Due to proportional hazard violation of some continuous variables, I'...
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### Help interpreting Bivariate Cox Proportional Hazard Model results

I have done an analysis using Bivariate Cox Proportional Hazards Model Regression, to estimate the rate of exits from unemployment for people with mental illness relative to people without mental ...
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### Visualization after restricted cubic splines in Cox

I've used pspline to add restricted cubic splines to certain continuous covariates that violated the PH assumption upon first analysis. I identified these covarites ...
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### Cox survival PH violated variable is part of an interaction

One of my main predictors violates the PH assumption. I've been reading different ways to deal with this for a while and have decided on an interaction with time after making a person-period file (...
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### Survival analysis proportional hazards violation

I've been using Cox for survival analysis with the goal of identifying the effect of 5 different levels of a treatment on survival. My dataset is not small and has 130 covariates after dummy encoding. ...
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### In joint frailty model with competing risks and recurrent events - how to interpret the coefficients?

I took the output from the example described in manual to one of R's packags for frailty modelling. Apart from the statistical package, how to interpret the outcome for recurrent events? Is this HR ...
1 vote
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### How to compute marginal hazard rate from parametric survival models?

Suppose that the conditional hazard rate for subject $i$ follows a proportional hazard model in the form of: $h_i(t)=h_0(t) exp(\beta_1X_{i1}+\beta_2X_{i2}+\beta_3X_{i3})$ $X_i$ are subject-specific ...
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### Interpretation of interaction between variable and time in cox regression

I was running a model to check the survival rate among different treatments. Basically, the treatment has four groups. I firstly plot a K-M curve and noticed clear interactions among the four ...
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### P trend and association

what does p trend mean for categorical analyzes with HR (proportionnal regression cox) ? Do we have to interpret this with HR on our result ?
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### What qualifies as "slight violation" of proportional hazards?

I'm using Cox survival analysis to find predictors of mortality in a health dataset. Although Cox assumes proportional hazards of the variables, my reading tells me that "slight violations" ...
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### Interpreting Schoenfeld Residuals Trend vs P-Value

Edit: added new plots generated with plot.cox.zph(), to replace those I had generated with survminer::ggcoxzph(), due to an ...
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### Correct way to specify model - using lm in R

I have a dataset with 2 groups called variable X (placebo vs trial). I want to compare the outcomes (continuous variable) between these two groups. Im aware of how to do basic models in R like ...
1 vote
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### Is proportional hazard regression unbiased?

I am studying the results from a simple Cox PH regression, and I'm curious about the unbiasedness of the estimated log hazard ratios (i.e. coefficients) from the model: Are those estimates universally ...
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### How to interpret the schoenfeld residuals plot

I want to check the proportional hazard assumption. I used both test using cox.zph() in R and schoenfeld residuals plot using hggcoxzph(). I want to know if the plot is fine and how I can interprete ...
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### Cox Proportional Hazards regression where event is most likely to occur at set intervals

I'm interested in evaluating the effect of various factors on the lifespan of borrower-lender relationships using a Cox Time-Varying Proportional Hazards regression. However, as the relationships we ...
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### Cox regression hazard ratio (group 1 vs. group 4) changes calculation changes after combining group 2 and 3?

I am working on a project which involves fitting a Cox proportional hazard model to a time to event situation in SAS. We have the variables: y - event or censor (0/1) timeto - time to event y x - ...
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### Assessing violations of the Cox proportional hazards assumptions

Cox models assume proportionality. These assumptions can often be formally tested (an example in R is cox.zph from the ...
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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, ...
1 vote
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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 ...
• 531
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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 ...
1 vote
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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