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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18 views

How robust is coxph when the proportional hazards assumption is violated?

How robust is the coxph when I don’t have proportional hazards? How common is non prop hazards and how do I fix it? Does transforming variables help? Does non parametric survival analysis handle non ...
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38 views

Is the Breslow estimator over-adjusted?

In a proportional hazard model with a Breslow estimator, I wondered why do we adjust on covariates in the cumulative hazard and in the model. On these few lines from Xia et al.[2], we can see that ...
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Survival analysis with two events

Suppose we have a cohort of subjects, we have followed them up over a period of 10 years and several subjects develop either of two complications of interest (A and B) that are complications as a ...
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30 views

Cox PH - R 'rms' package - Concordance (Train, CV & Test)

Please could someone verify if my methodology for calculating these three versions of concordance are correct when using the rms package? I have really struggled to ...
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1answer
35 views

Checking PH assumption using scaled Schoenfeld residual tests

My cox model violates the PH assumption (according to cox.zph test), and I'm trying to interpret the scaled Schoenfeld residual plot, but I've never seen a plot with points lying in such a flat manner....
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Cox Proportional Hazards - Survival Function Estimation (on new data)?

I understand that the relationship between the hazard function, the baseline hazard function and the covariates is the following: $$ ln(\frac{h(T)}{h_0(T)}) = \beta_1 x_1 + \beta_2 x_2 + \dots + \...
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76 views

Case-Cohort analysis in R

I am attempting to conduct a Case-Cohort analysis with Cox's Proportional Hazards Model. The data set looks similar to the one below: ...
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Different results for Cox regression

I am trying to get my head around Cox regression. I found quite a good paper on the subject by R. Tibshirani: A plain man's guide to the proportional hazards model. On page 67 he gives a toy example, ...
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Why is the exponential function used in Cox regression?

I am trying to get my head around Cox regression. I found quite a good paper on the subject by R. Tibshirani: A plain man's guide to the proportional hazards model. On page 66 he states: For ...
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26 views

Continuous Variable No Longer Follows PH Assumption When Categorized

I am creating a cox regression model with multiple covariates. I have two models: model A contains my variable of interest in its original continuous form, and model B contains my variable of ...
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2answers
65 views

Expressing a hazard function with a Cox proportional hazards model

I'm trying to wrap my head around Cox models as well as how to express them in the form of hazard functions when you have both categorical AND numeric covariates. I need some assistance with this ...
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Hazard ratio endpoint vs Odds ratio

This study (https://academic.oup.com/cid/article/65/1/100/3097834) seems to conduct a cox proportional hazard regression on survival data, but reports hazard ratios for 30- and 90-day mortality: ...
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What are the hazard ratios in this plot referring to?

With the following code in R, I created this graph: ...
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242 views

Schoenfeld test (cox.zph) shows no covariate violates PH assumption but global test suggests whole model does (p<0.001). What to do?

Using cox.zph (part of the survival package), I find that no covariate violates the PH assumption in a Cox regression model (p > ...
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1answer
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How to model the Hazard Rate?

I'm interested in modeling the Hazard Rate $\lambda$ from a Survival dataset so I can calculate the Cumulative Distribution $F(t)=1-e^{-\lambda t}$ but I'm not sure how to go about computing $\lambda$...
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Is the Cumulative Hazard Function simply estimated using the Empirical CDF?

I'm just starting to learn about Survival Analysis and I understand the theoretical proofs but I'm still unclear about how to do some of the estimations practically.
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Cox Proportional Hazard calibration with same it's meant to predict

I want to model time to churn with a Cox Proportional Hazard model and use it to predict people likely to churn. The question I have is how valid is to calibrate the model with the same people I want ...
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Predicting survival probability at a future time for proportional hazard model

I have a Weibull proportional hazard model with fitted parameters $\lambda$ and $k$ and a time dependent covariate $x(t)$ with fitted coefficient $\beta$, such that the hazard function is given by, $...
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25 views

Prediction of survival time using cox regression in R

I'm aware that we can get survival function and probability in R but is there a way to predict survival time given it is Cox regression
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Likelihood function for a unit $i$ with death at time $t_{i}$ and non - death at time $t_{i}$

The survival function with respect to time is defined to be $S(t) = 1 - F(T) = \int_{t}^{\infty}f(x)dx$ With a bit of algebraic manipulation, one arrives at the time dependent hazard rate ...
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1answer
114 views

Cox regression model - testing the proportionality assumption for an interaction term?

I'm interested in testing sex differences in the outcome Y (e.g., mortality), and if there are sex differences in the effect of BMI on mortality. I planned to use a Cox regression model primary<-...
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39 views

Why is my output for nominal_test incomplete?

I am currently using the nominal_test function, in the ordinal package, to test for the proportional odds assumption but have encountered a problem. Here is my code: ...
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Test assumption of common baseline - Adersen-Gill Cox regression?

I'm running a Andersen-Gill recurrent (multiple events) cox model and I want to test the assumption of common baseline across events. Is this as simple as entering 'event' into the model and checking ...
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241 views

What does 'km' transform in cox.zph function mean?

I'm trying to understand how cox.zph function in r programming language works and I find myself not knowing what km transform ...
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300 views

Interpreting hazard ratios in stratified models

I am unsure how to interpret hazard ratios from cox-proportional hazard models that include 1 or more stratified terms. For example, say I run a cox regression with treatment as a covariate and ...
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How best to represent changing risk over time in data set with groups of different duration

Here is an example outline of my dataset: I have 20 shops that are open for a period of time, but the duration is not the same (i.e. some locations are open for 4 years, others are open for 2 months, ...
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Adapting Cox Regression to Time dependent continuous variables [duplicate]

I am interested in using cox survival regression model when the covariates are not expected to be constant over time and also continuous. I did check a few books and the time dependent Cox Regression ...
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Survival Analysis - 30% right censored data

Just looking for some clarity regarding time-to-event (death) data when there is a large proportion of right censored data (lots of survival). Is this a serious problem for a proportional hazards ...
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Time variable as a fraction when using Cox proportional hazard model

We are trying to estimate the lifetime cumulative default rates for consumer loans, using the Cox proportional hazard model. Since we have a number of different maturities (and the majority have not ...
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1answer
52 views

Checking PH assumption for a time dependent (T_COV) variable in a Cox PH-regression: with or without the original covariate in the regression?

I am performing a cox proportional hazard regression on survival, in a sample in which almost everyone dies in the follow up period. I have little knowledge on statistics in general but i am reading ...
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77 views

Relation between hazard function and Kaplan-Meier survival curves

Could someone please explain intuitively and mathematically the relation between hazard function and Kaplan-Meier survival curves? If there is a relation, please give and example of deriving one from ...
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292 views

Schoenfled Residua test shows proportionality hazard assumptions holds but Kaplan-Meier plots intersect

"If Kaplan-Meier plots cross each other then proportional hazard assumption does not hold". The issue I am facing is that I got the Kaplam-Meier plot(bleow). We can clearly see that it is overlapping. ...
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89 views

Obtain hazard ratio from other hazard ratios

Given a hazard ratio($HR$) as $$𝐻𝑅_{b}=ℎ𝑎𝑧𝑎𝑟𝑑(b)/ℎ𝑎𝑧𝑎𝑟𝑑(a)$$ and another hazard ratio as $$𝐻𝑅_{c}=ℎ𝑎𝑧𝑎𝑟𝑑(c)/ℎ𝑎𝑧𝑎𝑟𝑑(a)$$ How can we obtain the hazard ratio between $b$ and $c$ ...
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Hazard ratio for more than two groups

Consider the line of code below for implementing Cox model in R and finding the hazard ratio: fitcox <- coxph(Surv(Survival,Death) ~ clusters, data = data) ...
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How to calculate Hazard ratio if there are more than two Kaplan-Meier curves

A population was sub-typed into 4 groups and Kaplan-Meier curves were plotted. If there were only two survival curves then the hazard ratio would be the hazard of one group divided by the hazard of ...
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154 views

Violation of proportional hazard assumption with big sample size - how to correct for it?

I am looking at a sample of about 95,000 firms in Switzerland and I want to find out if having an external auditor (such as PwC, KPMG, EY) reduces the likelihood that a firm goes bankrupt. In ...
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142 views

How to calculate conditional hazard at time zero

I am looking for a statistical method to calculate the conditional hazard before the diagnoses or study has started; in other words, time is not a variable. For example, here is a hypothetical ...
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21 views

Shared Frailty Assumptions

Do we need to check the proportional hazards assumption when running a shared frailty model for clustered data?
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Competing Risks Likelihood in each State

I have a competing risks model where every observation starts in state 0 and ends up in either state 1 or state 2. I have the following cumulative hazard functions for each transition to state 1 and ...
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1answer
402 views

Connection between Hazard Ratios, Survival, and Probability

According to this wiki link, the hazard ratio relates to survival according to the following equation $$ S_1(t)=S_0(t)^r \quad (1) $$ where $S$ is the survival and $r$ is the hazard ratio. So from ...
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Proportional hazards assumption for cox regression - global test or graphical assessment

I have run a cox regression with only a treatment in mind so far and have then tested the proportional hazards assumption along with a graphical assessment using the log-log survival plot. My global ...
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58 views

Cox hazard Model: HR of 1 variable greater than 1 in simple regression becomes smaller than 1 in a multiple regression

I'm performing a simple and multiple Cox regression. I have 1 dependent variable $y$ and 10 independent variables: $$X = x_1, x_2, x_3, x_4, x_5, x_6, x_7, x_8, x_9, x_{10}$$ A particularity of the ...
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1answer
200 views

Interpretation of Cox Hazard Model with quadratic term

I am having trouble finding information on how to interpret coxph model hazard ratios with a quadratic term. Some of my variables are continuous count data, whereas others are continuous percentages. ...
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210 views

Cox proportional hazards model, problem with correlated predictors or overfitting?

I have a question concerning a Cox proportional hazard model (in R) on which I would love to get your opinion and feed back! I think that there is a problem, however I would like to be sure and ...
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1answer
860 views

Violation of the proportional hazard assumption, interaction with time. Am I taking the correct steps?

I will try to keep my question as short as possible. For my thesis I am researching if a risk score can predict graft failure in a cohort of $596$ patients over the course of $10$ years. (The ...
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1answer
271 views

Changing the baseline hazard ratio at each event in a PWP Cox model

I am performing a PWP (conditional) recurrent cox regression analysis over medical records. For each individual, events are indicated by dates in their medical record. It is, therefore very easy to ...
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190 views

Interpreting outputs in R coxph model

This is a follow-up question to the one posted here. I have run a proportional hazards model in R using the coxph function. The model includes 3 covariates: ...
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1answer
78 views

Cox proportional hazards model and dummy variables

I have some doubts while doing this question. I tried out parts (a) - (c) and am quite confused by (d). Would appreciate if someone can help to check my work to see if I have done it correctly, ...
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83 views

hazard ratio interpretation

Imagine that when we compare treatment A to treatment B (the group A is a high expression and group B is a low expression of gene X) and the pooled hazard ratio (group A in comparison to group B) is 0....
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Cox regression - non-time dependent continuous covariate deemed singular

I have this model I want to run that has no main treatment effect because I subsetted the data just to look at this one treatment (For example I have 1200 points from three treatments: control, ...