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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What's the difference between univariate and multivariate cox regression?

I'm dealing with oncology patients so it would be nice to know whether to use univariate or multivariate cox regression. I have some books on survival analysis but they don't elaborate the academic ...
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30 views

Cox Proportional Hazards Model with time-varying covariates data structure [closed]

I am currently shifting away from a static hazards model to a one with time-varying covariates while using the same original data source. I have some difficulty understanding the data structure needed ...
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24 views

What imputation methods can be used for missing not at random covariate values in a survival analysis?

I'm new to survival analysis and trying to understand how to use it properly. My dataset is a time series dataset where most dependent variable values are available, 2 dependent variable values are ...
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Hazard model for three-tiered-response dependent variable

My time-series dataset is composed of measurements for a number of independent variables and one dependent variable. The dependent variable accepts 3 responses: weak reaction, strong reaction, or no ...
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8 views

Estimate the treatment effect in each level of a subgroup with Cox regression

People generate forest plots to determine the benefit of one treatment regimen over another through univariate hazard ratios. How do you generate them? Is there an R package that handles that? (This ...
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3answers
217 views

Intuition behind Hazard Rate

I am confused about the equation definition of hazard rate. I get the idea of what the hazard rate is, but I just don't see how the equation expresses that intuition. If $x$ is a random variable ...
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33 views

Expectation of a hazard rate

I need to estimate the expectation of a hazard function, $E[h(x)]$. For instance, for the exponential distribution the result is equal $\lambda$ $E[h(x)]=\int_0^\infty \! h(x)f(x)\mathrm{d}x=\...
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26 views

hazard rate ratio and confidence intervals with zero events

Apologies if this has been asked; I haven't been able to easily find a related thread. I'm doing a survival analysis; how do you calculate hazard rate ratios and CIs when there are 0 events in one ...
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Different forms of Inverse Mills Ratio & their interpretation

I have noticed different authors using different forms of IMR i.e. f/F or f/(1-F) depending on whether they are modelling selection or non-selection in stage 1 model. I did some simulations in my case ...
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Hazard ratio with confindence interval for dummy variable

I have covariate Length which is 1 or 0, I'd like to get an estimate with confidence interval for hazard ratio of having an event when ...
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12 views

Observed information matrix in Cox model with constant baseline hazard

I am trying to explore properties of Cox model with (parametric) constant baseline hazard function. So the hazard function for the model is $\lambda(t|Z_i) = \lambda_0(t) \exp(\beta^\mathsf{T}Z_i)$,...
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Can I work out the numbers in the groups, based on the results of hazard ratio?

I need to extract data from a paper that report a hazard ratio=0.72, 95% CI=0.57, 0.92, p=0.010. Knowing that the one group that did better had 255 individuals and the other 252. How can I find out ...
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Applying Cox's Porportional Hazard model

I have a dataset on two groups. Group 1 (18 subjects) and group 2 (5 subjects). Each subject in the groups had to perform a number of tasks which was timed. The time restriction was 60 seconds. If ...
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1answer
58 views

What kind of model should I use for churn risk prediction?

I have a data set containing many client's id, and its behavior characteristics measured each month before churn or censored. Data looks like: id || lifetime period || folow-up time before churn of ...
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31 views

Cox PH model with quadratic effect interpretation

I'm fitting a Cox model with non-linear continuous variable with and without a time varying effect (to correct non-PH). My goal is to get risk ratio (hazard ratio) associated with X. I have the Cox PH ...
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How do you calculate the compared populations in cox hazard ratio problems?

Take a look at the following open-access paper http://www.ncbi.nlm.nih.gov/pubmed/26506242 I've tried doing cox regression in both R and SPSS but I cannot get ...
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93 views

What does the p value mean for Cox hazard ratio? [duplicate]

I am puzzled about the interpretation of P value in the Cox hazard ratio analysis. I read from literature that the P value is to "reject the null hypothesis that HR=1". However, in many cases, we have ...
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28 views

Problem with initial guess in Newton-Raphson iteration method

I'm working on estimating the four parameters of Exponentiated Modified Weibull Extension Distribution introduced by Sarhan and Apaloo (2013) with the Maximum Likelihood Estimation (MLE). Because the ...
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89 views

Nonparametric Estimation of the Hazard Ratio

I am not sure if this is appropriate here, but I'm hoping someone would be able to help. The following is an excerpt from the following paper "Nonparametric Estimation of the Hazard Ratio" by H.T....
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Comparing plot from survfit with plot of cox baseline hazard converted to survival rate

Based on the initial question: Cox Baseline Hazard I would like to plot survival curves by gender for this model using the kidney dataset. Following the example codes, I subset the dataset by gender, ...
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57 views

Categorical variable with hierarchical structure - Cox regression

What is the best way to build a cox model with a categorical variable that has a hierarchical structure (20 levels).
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Survival analysis book with R language

I am looking for a good book for survival analysis in R . Also, I wnat the focus to be on cox model and its extensions). Better if free
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How to interpret parameter in proportional hazard model?

How can I show that $b$ in this proportional hazard model $y=1-x^{e^{bz}}$ is the percent change in $y$ with a unit change in $z$? For brevity, I have neglected to show the functional form of $x$, ...
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Many categorical variables in Cox regression model

I am using Cox regression to model my data (time to an event). One of the covariates has 29 categories. I would like to compare the categories to one another and identify which category has shortest ...
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How to model “time-to-adopt”

I have data of many users (several millions) and the timing of when each of then has adopted a product. All of then have adopted so it is not a matter of the propensity to adopt - in their case they ...
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32 views

Need help to simulate Survival Times with a time-varying Covariate

I would really appreciate if someone can help me figure this out as I have been working on it for few days now and I don't know what I'm missing that it's not working. Basically, my goal is to sample ...
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Survival/hazard models with multiple hazard occurrences for each individual

I'm new to survival/hazard models. My data contains information about many users (millions), each of them has done some action (let's say, for simplicity - adopted a product). Some of the users did it ...
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56 views

How to interpret hazard ratios for a cox model with 100% failure rate

I am studying the impact of temperature on the onset of flowering of trees. I am using a cox model for time dependent covariates as implemented in the R package survival. I only have one (cumulative) ...
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are hazard ratios additive?

I have data from Cox regression which indicates that compared to a baseline condition condition A => has hazard ratio= 2 condition B => has hazard ratio= 6.5 Is it possible to say if condition A and ...
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What is the definition of “death rate” in survival analysis?

I am reading a text on survival analysis (Smith's 2002 Analysis of Failure and Survival Data). All concepts like hazard function, survival function, density of survival variable $Y$ are rigorously ...
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74 views

Survival Analysis: Cox Proportion Assumption

I know i'm missing something here, please help me understand the cox proportion assumption. What is the point of having a hazard rate function over time if it first has to meet the cox proportion ...
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44 views

Calculate confidence interval for hazard ratio given maximum likelihood and standard error

I'm doing a meta-analysis and one of the studies presents the hazard ratio (HR) with the maximum likelihood estimate (MLE) with its standard error (SE). The rest of the studies give the HR and the ...
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53 views

log hazard function in R

I'm trying to write out the log hazard function of the lognormal distribution and use this in R. Using the survival function: and the hazard function: I have the following for the log(hazard): ...
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functional form for modeling hazard function

What functional form do you suggest to model this hazard function? Can it be a quadratic form, even tough it's skewed?
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Converting log hazard function to survival probability

I am currently working through a survival problem and I wanted to get some advice with how to proceed. I wanted to estimate survival probabilities over time based on knowing only the $\log({\rm ...
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Time Series Shocks with Exponential Decay

Imagine a piano key played in an auditorium: The amplitude of the sound wave is perhaps highest in the first milliseconds, then slowly decays to zero if no other notes are played. If other notes are ...
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Difference between survival and hazard

I am trying to find an intuitive explanation of the difference between the hazard and survival rates? Are the two the same thing but expressed differently?
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How to get event hazard rates from a survfit object for sample size calculation

I want to calculate the sample size for a clinical trial (right-censored time to event data). I have data of a retrospective analysis and would like to use nSurv ...
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Multilevel Model for time to event data

How can I write the general equation for multilevel parametric proportional hazard model and multilevel cox proportional hazard model?
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The difference between average and marginal treatment effect

I have been reading some papers, and I am unclear about the specific definitions of Average Treatment Effect (ATE), and Marginal Treatment Effect (MTE). Are they the same? According to Austin... ...
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How to interpret hazard ratios for time-segmented variables?

I'm constructing a Cox regression model where patients were randomised to treatment or placebo, and then had certain continuous covariates measured at multiple time points through the course of the ...
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48 views

How to scale the Hazard Function?

Please help me understand this: Imagine one has a population of 30 subjects, and their failure times are described by the Weibull distribution with parameters i.e: $ \alpha=1.9,\ \beta=1.3 $. \...
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Modelling retirement of employees by age where only data of very few years are available

We want to model the retirement of employees. We have data on a yearly base for about 20,000 employees by age and some other properties. There are two questions: Suitable Approach In most cases we ...
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1answer
73 views

Non-proportional Weibull hazard model with heaviside functions

I am trying to model a non-constant (and non-linear) hazard ratio between two groups (Group A and Group B), assuming that the baseline hazard for one of the groups can be described with the Weibull ...
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Understanding Hazard Function Values Exceeding 1

I keep running into problems in understanding hazard rates. I know, for example, that in a strict sense a hazard rate is not a probability and it is continually mentioned that because of this the ...
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Is there any guideline for interpreting a hazard ratio as 'small', 'medium' or 'large'?

I would appreciate if anyone can share a reference that discusses magnitudes of hazard ratios as effect sizes. Specific subject matter obviously weighs in when trying to determine what a relevant ...
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(1) A flight has a 1% chance of crashing. (2) It's scheduled to fly 200 flights that week. Does (2) add any info re: your risk?

And assuming that: a) This is that particular airplane's very first flight, ever (not just for the week). b) Any distributions involved should be discrete in the sense that they should be functions ...
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Proportional hazard assumption in survival analysis

Which is the best method to check proportional hazard assumption in survival analysis?
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expectation of $e^{-x}$ when x is log-normal

I'm trying to find the expected value of $ e^{-x} $ when $ x$ is log-normal. I know that if $ x \sim N(\mu, \sigma) $ then $ E[e^x] = e^{\mu + \frac{1}{2}\sigma^2} $, the expectation of a log-normal. ...