# 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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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### 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: ...
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### Cox-Hazard Ratio differences in Software suits; Manual calculation

Working in clinical research my task is to calculate the Hazard ratio, better to check the calculations of someone else. This first calculation was based on ARM=(3 different treatments) with only t=(...
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### How to calculate the cumulative baseline hazard function for a CoxPH model

I have read that the following formula is used to estimate the cumulative baseline hazard function: I also know that the basehaz command in R will also calculate an estimate for the cumulative ...
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### Expected survival time for Weibull proportional hazards model with R's predict.survreg

The predictions for a Weibull proportional hazards model from R's predict.survreg() are not the expected survival times. Please help me understand this behaviour. ...
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### How to estimate an additive hazards model?

Consider the additive hazards model: $$\lambda(t) = \lambda_0(t) + \beta^T Z.$$ I want to assume that the baseline hazard $\lambda_0(t)$ is Weibull. However, $\lambda(t)$ has to be positive by ...
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### Cox Proportional-Hazards Regression vs. Regression modeling of competing risk using Fine and Gray

30000 patients all have one diagnosis in common, 3000 of them have been exposed to a potential risk factor before the common diagnosis. 1500 patients develop a malignancy after the common diagnosis. ...
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### How should I smooth / average semi-sparse service usage data used in a time series regression?

I am using time series regression and survival models to predict future user outcomes based on past usage trends. I am dealing with a data set of daily service usage per user which, on a given day ...
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### I multiplied a predictor variable by 10. Why does my univariate cox regression HR and p-value change entirely?

I calculated the waist-to-hip ratio from, well, waist and hip measurements in cm. The ratio's values would come out in the range of 0.8-1.1, for my population. When I performed a univariate cox ...
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### Do multiple observations per individual imply pseudo-replication in time-varying Cox proportional survival model (coxme in R)?

I’m running a survival analysis using a cox mixed-effect proportional hazard model with time-varying covariates (using package and function coxme in R). My ...
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### Time scale in survival analysis

I am doing a churn analysis of some bank customers with survival analysis. Right now I am using the customers' years in the bank [0;17] as time scale, and then use the customers' entry age as a ...
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### How does time factor into Cox regression or a Cox proportional hazards model?

The hazard function for the Cox proportional hazard model is written as follows. $$\lambda(t|X_i) = \lambda_0(t)\exp(\beta_1X_{i1} + \cdots + \beta_pX_{ip}) = \lambda_0(t)\exp(X_i \cdot \beta)$$ I ...
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### Proportional hazards assumption and time-dependent covariates

Is there a way to check that the proportional hazards assumption is correct for a Cox model with time-varying covariates ?
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I have a dataset of about 9k rows and 60 features (columns). I have a binary status column (1 - dead, 0 - alive) and a lifetime column in days which is right censored. I am currently using the cox-PH ...
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### Cox proportional hazard - can hazard be treated as instantaneous probability?

I'm doing a question on cox proportional hazard models that at the very last step leaps from hazards to probabilities, and I'm not sure how it does this. I've paraphrased it below to keep it simple, ...
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### Training on censored data with varying sequence length

I have a sequence of daily events, along with times between events. Each such sequence is labeled by $i$ and consists of $n_i$ events. For every $i$, each event $j$ has a list of features $x_{ij}$, ...
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### Interpretation of hazard rate for multiple failures

I'm trying to run survival analysis of Cox proportional model with panel data that consists of IDs and time variable. Each individuals are allowed to fail more than once in the sample period. My ...
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### How to interpret insignificance of time-varying coefficient and main effect

I have a survival-time dataset where entities (countries) are measured at discrete intervals (years). I'm interested in examining the effect of some fixed treatments (i.e. ones that occur at the ...