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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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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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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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Obtain hazard ratio from other hazard ratios

Given a hazard ratio($HR$) as $$𝐻𝑅_{b}=β„Žπ‘Žπ‘§π‘Žπ‘Ÿπ‘‘(b)/β„Žπ‘Žπ‘§π‘Žπ‘Ÿπ‘‘(a)$$ and another hazard ratio as $$𝐻𝑅_{c}=β„Žπ‘Žπ‘§π‘Žπ‘Ÿπ‘‘(c)/β„Žπ‘Žπ‘§π‘Žπ‘Ÿπ‘‘(a)$$ 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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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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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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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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The difference between the cumulative baseline hazard and the cumulative hazard?

I'm not sure what is the difference between the cumulative baseline hazard and the cumulative hazard? Could you please explain it if you are an expert in this field? Thanks
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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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Survival model building with time dependent covariates

I am looking to build a Cox proportional survival hazard model in SAS on time dependent covariates. Ultimately, I will put this model in production and score on recurring basis to target the right ...
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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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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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Relationship between survival probabilities and cox proportional hazard parameter estimates

I am building a home lending model through Survival technique. Since, I wanted to use a lot of time varying covariates (change in marital status, cash balance, residence etc.), I decided not to go ...
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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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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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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
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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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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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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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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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1answer
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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, ...
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1answer
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Cox Proportional Hazard models for more than 2 treatments and covariates

I am trying to figure out how to properly interpret the results of this cox proportional hazard model, represented by a forest plot. I have looked into a lot of references, but almost all of them ...
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How to estimate full distributions in Cox Proportional Hazard model?

A Cox Proportional Hazard model outputs both the coefficients $\beta$ and the baseline hazard $\lambda_0$ (eg, Breslow's method). From these two quantities one can estimate the distribution of time to ...
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Dataset set splitting in survival analysis?

I have a dataset of 100,000 composed by the time during the study (time) dead status (status); about 10% deaths presence of 10 different traits as binary variables (trait1...traitX) I'm using a cox-...
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369 views

Estimate the cumulative baseline hazard function from a Cox model coefficients

CoxPh model described as $h(t|X)=h_{0}(t)e^{\beta X}$ where $h_{0}(t)$ is the baseline hazard function and is non-parametric. If you have the following model, ...
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1answer
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How to calculate HR using attained age? [closed]

I want to calculate the hazard ratio for death by comparing individuals with a disease versus others without the disease, but I don't know if the calculation that I'm doing is correct. Participants ...
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1answer
131 views

Should I correct the p-value when testing Proportionnal Hazard assumption with cox.zph()?

When testing the Proportionnal Hazard assumption in a cox model in R, you usually use the survival::cox.zph() function. Output is something like this: ...
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Survival analysis of a population - Proportional hazards

first time here :) here's my problem. I developed an agent-based model (ABM) that I used to generate some data that I would like to analyze, but I couldn’t find a methodology that I can be confident ...
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Can I force the direction of hazards ratio?

I am doing a survival analysis using Cox's proportional hazards model with several predictive variables. Some of the estimated hazards ratio goes in an implausible direction, which contradicts what we ...
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Is my explanation of the limits of Cox PH correct?

one of the limitations of the Cox PH model is, that it can not change the hazard ratio of two different inputs over time. I would explain this with the following hypothetical example: A ...
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1answer
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Significant but very small beta coefficients in Cox proportional hazards calculation (survival analysis)

I'm analyzing TCGA data to investigate the effects of lncRNAs on survival. Among other things, I wanted to calculate a univariate CoxPH model for each gene to find genes whose expression levels have a ...
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interpretation of cox HR under non-proportional hazard

When the true hazard ratio $\lambda(t)$ is time varying as shown below, I used a standard cox regression to get a hazard ratio. If the hazard ratio of $\lambda=0.78$, how can this value be interpreted?...
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How do I interpret these categorical main effects in the case of a one level significant interaction in a cox PH model?

So I have a cox proportional hazards model in which an interaction comes out as significant. This interaction is between a categorical variable (tree species) and a continuous variable (diameter at ...
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Frailty or median values in my cox proportional hazards model?

I am analysing data of woodpecker-made holes and I am interested in seeing what covariates and to what degree affect the survival of these holes (otherwise known as cavities). However, I encounter the ...
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1answer
243 views

Use median survival time to calculate CPH c-statistic?

I'm interested in calculating the concordance ($c$-statistic) of a proportional hazards model. For reference, the c-statistic is detailed in Stat Med. 1996 Feb 28;15(4):361-87. The relevant quote ...
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fixed time covariates idetification in Cox regression

For my survival class i have been given a dataset which i want to use to conduct some basic analysis. The description of the dataset is as follows: ...
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Cox Regression in Propensity Score Matched cohort after multiple imputation

I have a follow-up question on the question of this thread: Manipulating data for propensity score matching following multiple imputation with mice package In aforementioned topic we can see the ...
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bias from aging in a cox regression with time dependent covariate

I am trying to analyse a population cohort with every person followed-up after their 50th birthday until some health related event. Exposure can happen at any time after the 50th birthday, so I have ...
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351 views

Hazard Ratio Meta-Analysis

I've being reading around the forum and couldn't find exactly what I wanted. I am trying to do an meta-analysis where the HR of each study and the 95% CI were available. I understand variance can be ...
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1answer
438 views

Formatting data for Cox PH with time-dependent covariates

I was hoping for some guidance on the appropriateness of my modeling approach to the following problem. Problem: I'd like to know whether the days receiving nutrition support (cumulative days on ...
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2answers
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What is the meaning of “t” in Cox hazard proportional model?

I'm learning survival analysis and currently have questions about the Cox proportional hazards model. The following figure wants to show that for a certain smoking subject, the hazard of a 10-year ...
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1answer
891 views

How can one invert hazard ratios and their confidence intervals?

Imagine that when we compare treatment A to treatment B there is an associated hazard ratio of 0.56 (95% CI: 0.36 to 0.87). Let's say that instead of this, I want the hazard ratio associated with ...
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Is the supremum test of cumulative martingales residuals OK to assess proportional hazards of both groups and covariates?

Is the supremum test of cumulative martingales residuals (as implemented by assess in SAS PROC PHREG, and other software) OK for testing PH of both continuous ...
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Proportional Hazards, Competing Risks, or something else?

I'm looking to do a time-to-event analysis. My data set set has a binary response variable representing 2 distinct outcomes, a time variable, and some censoring. I am mainly interested in the time ...
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1answer
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Calculating the Cox Hazard Rate

I want to write a code that calculates the Cox Proportional Hazard rate: $h(t|x_it,e_i)=e^{x_it \beta + \lambda(t) + e_i}$ where $\lambda_t$ is a spline in slopes and $e_i$ is an unobserved term. My ...
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What is the dependent variable in a coxph regression in R?

I am trying to build a Cox proportional hazards model using the coxph function in the survival package in R. My function call is: ...
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What variant of interaction when the PH assumption is violated in a CoxPH Model?

When the assumption of proportional hazards is violated, the suggestion is to interact offending covariates with time (or a function of time). In this blog post, the author suggests to include only ...
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How to manually calculate concordance for a coxPH model

I am struggling to work out how the concordance statistic of a coxPH model is derived. I have built a coxPH model on a small dataset (4 observations). The resultant model is given below: ...