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Questions tagged [hazard]

In survival analysis, the hazard rate at time $t$ is the instantaneous probability of death at $t$, conditional on survival until $t$.

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How does the probability of events change if an event does not occur

Suppose that someone tells me I will collect $\$100$ dollars within some time interval. Those time intervals are 1 to 7 days, 8 to 30 days and eventually after 30 days. Let $A$ be the event I ...
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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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23 views

Simple elaboration on Joint Models' linear equations/trajectory functions

I have been struggling with grasping the intuition behind joint models, and I hope someone can elucidate a particular aspect of theirs. Joint models, first of all, are essentially combinations of ...
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14 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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cureregr: post-estimation problem predicting hazards

What is the problem: I am using the post-estimation 'predict' command to estimate the hazard rates for individuals after running a cure model (cureregr) and I get the following error message: Maximum ...
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16 views

Parameter Estimation using hazard function

Following the notation in this paper [ref], assume we have a random sample of $x_1, \dots, x_n$ of a distribution with PDF $f(x)=f(x,\theta)$ and CDF $F(X)=F(x,\theta)$ and we wish to estimate $\...
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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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50 views

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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Survival analysis with external non-competing events

I'm new to survival analysis and struggling to find the best approach to my problem: Assume that we want to model the time to the death event $X$ given some prior subject data. I'm aware that ...
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Interpretation of cox.zph Output with Smoothing Splines in R

In Luke Keele's paper, "Covariate Functional Form in Cox Models", Dr. Keele carries out two Grambsch and Therneau non-proportionality tests, that is, one for a model without splines and one for a ...
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1answer
38 views

Little problem calculating hazard function

I'm starting to study maths again after a long time without having touch them and I'm currently with survival analysis. I want to get a hazard function h(x), and I know that it can be calculated as ...
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69 views

Cox's Proportional Hazard coefficients clarification

I'd like a clarification about the Cox proportional hazard coefficients reported on this page. For example, doesn't the hazard ratio (HR) for gender in that ...
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2answers
45 views

Hazard function equality $T = \min(T_1, T_2, …, T_n)$ [closed]

Let $T_i, i = 1, ..., n$ be independent continuous random variables. Denote by $h_i(t)$ the corresponding hazard function of $T_i$. Let $T = \min(T_1, T_2, ..., T_n)$. Denote by $h_T(t)$ the ...
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Meta analysis: Pooling hazard ratios of continuous vs. dichotomous parameters?

I have a question regarding pooling hazard ratios derived through different means for a meta-analysis. Software: RevMan 5; Method: generic inverse variance (log hazard ratios). My issue is that some ...
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1answer
30 views

Can the hazard function be defined on a continuous state

The hazard function is defined as the instantaneous failure rate or instantaneous hazard rate as $\Delta t$ tends to zero $$ h(t)= \lim_{\Delta t \to 0} \frac{R(t)-R(t+\Delta t)}{\Delta t * R(t)} $$ ...
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Kernel Density Estimation of Hazard rate using R

How can we estimate the hazard rate using Kernel density estimation? For the time being I am simulating 1000 observations from exponential distribution, then estimate its hazard rate using gaussian ...
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Facilitating Comparisons - 1 SD difference

I came across a paper that mentions this in their statistical analysis: To facilitate comparisons among variables, the hazard rate ratio (HRR) was calculated for a 1-SD difference for each of the ...
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24 views

Survival prediction

I want to estimate the hazard ratio for a case-control study, and I want to test how the value of a continuous covariate affects survival. Does the covariate have to be normally distributed?, that is ...
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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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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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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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Non-monotone hazard functions

I should start with the caveat that I am relatively new to Survival analysis. I was watching a Hulu documentary about Crocodiles last night, and they mentioned that baby crocodiles have a low chance ...
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What is the bandwidth in a hazard rate plot?

I am doing some Survival Analysis using SAS. On the Hazard Plots I noticed some values on each curve labeled "bw" which after some research, I assume it means bandwidth. However, after much searching, ...
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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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Extremely huge Hazard Ratios from Cox regression

We made a cox regression and ended up with huge HR for some of our variables. One of them (which was an interaction) gave us a HR=2747,093. Our dataset consists of only 74 observations. What is wrong?
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Finding the limit of a quotient of hazard functions

Let $\lambda_i(t),S_i(t)$ be the hazard and survival functions of two populations for $i=1,2$ and satisfy that: $\frac{S_2(t)}{1-S_2(t)}=\phi\frac{S_1(t)}{1-S_1(t)}$ (1) I want to proof that $\lim_{t\...
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Why is Stata smothed hazard estimate pruned to interval?

I have played through this R example to calculate hazard estimates. I chased the whole thing through Stata and obtained a different graph, though. R graph: Stata graph: What's the rationale ...
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1answer
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Who invented the hazard function?

The hazard function or instantaneous failure rate is very popular in survival analysis: https://en.wikipedia.org/wiki/Failure_rate $$\lambda(t) = \dfrac{f(t)}{1-F(t)}.$$ However, I cannot find a ...
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397 views

How to interpret hazard ratios of Cox output?

I'm really struggling to understand how to interpret my R outputs in terms of hazards ratios. I have ran a Cox proportional hazard regression to compare survival between 2 treatment groups (neutron ...
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1answer
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Survival model for an epidemic — can the observations be treated as independent?

I've been thinking about ways to tackle an epidemic modelling problem I've been working on, and I've come up against a conceptual difficulty over the way survival analysis works. Here's a really ...
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1answer
35 views

Interpret hazard ratio < 1

In my book the example for interpreting a hazard ratio < 1 includes just a single example with a hazard ratio of 0.5. It is very confusing. If you have a hazard ratio of 0.2, does that mean the ...
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was it the correct interpretation of hazard ratio by the authors of an article?

My question is not a pure statistics question but is a daily application of statistics and how we interpret the statistics result - A study found that the hazard ratio (HR) of patients with high ...
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1answer
47 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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361 views

Evaluating the hazard function when the CDF is close to 1?

I need to evaluate a hazard function $h(t;\theta) = \dfrac{f(t;\theta)}{1-F(t;\theta)}$, where $f$ and $F$ are a pdf and a cdf, respectively, at many values of $t$ (and for several values of the ...
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1answer
52 views

PCA Dimension Reduction for Cox Proportional Hazard Model

I am trying to figure out if it is possible and appropriate to use PCA to reduce the dimensions of my dataset? A little background - I have survival data with 8 covariates. I have run a Pearson's ...
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1answer
93 views

Hazard function for a growing population

I want to model the expected failure rate in a growing population. Each individual has a high infant mortality (e.g. Weibull(shape=0.5, scale=100)). So the ...
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Hazard model for multiple streams of events

I've got multiple streams of events (suppose that only two) : for two countries we mark day by 1 if there is at least one new infection of rear disease, 0 otherwise, how to treat such dataset (2000 ...
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1answer
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Is the assumption of risks proportionality required when we assessing the difference of two KM branches (curves)?

There are two KM branches (curves) (for example, for male and female). Can I use a log-rank test if the assumption of risk proportionality is not satisfied? P.S. I checked this with the code: plot(Y~...
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1answer
452 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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hazard rate linear function instead of hazard rate lambda( Ξ») [closed]

Can we find survival function from any hazard rate linear function? Lets say we do not have hazard rate of y as Lambda( Ξ») but we have hazard rate of y as a linear function. can we find the survival ...
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215 views

MLE estimation: Inverse gamma duration model with exogenous variables

I observe a cross section of durations, $t_1, \ldots, t_n$ which are all strictly positive and a corresponding vector of exogenous variables $x_i$ which are assumed not to change from time $T=0$ until ...
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1answer
24 views

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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1answer
137 views

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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Why is Hazard Function called rate of failure?

I am confused why Hazard Function is called rate of failure. Here is what I understood about Hazard Function. Suppose we are dealing with Weibull and let $f(X)$ be the pdf, $F(X)$ be the cdf. Now, I ...
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Estimation of standard errors in conditional discrete time logistic regression models

I'm estimating a conditional discrete time logistic regression model in STATA and predict hazard and survival functions after logit using predictnl predictnl hazard= predict(pr), ci(hazard_lb1 ...
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Comparing two KM estimates outputs without raw data

Some raw data has gone missing, but I have the outputs of two KM curves - Both their survival estimates and patients at risk. Is there any way for me to use just the estimates to test the difference ...
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45 views

Which duration model to use with a fully right censored database

Currently I'm examining the duration of residence of households. I have a database at my disposal that indicates how long a specific household resides in its current home. I want to explain their ...
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1answer
193 views

Piecewise exponential model - how to fit

I'm trying to go through the following paper: https://projecteuclid.org/download/pdf_1/euclid.aos/1176345693 it covers the piece wise exponential model for modelling hazard rates in a non-parametric ...