# Questions tagged [hazard]

The hazard rate is the instantaneous rate at which units that have survived until time $t$ die at $t$. The hazard ratio is the ratio of 2 specified hazards.

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27 views

### Hazard ratios - one unit increase for a continuous variable measuring diversity (Blau index/ coefficient of variation), how to interpret?

I am having difficulty understanding how to interpret a one-unit increase/decrease for continuous variables in a Cox model. Specifically, I have created the variables gender, age & nationality ...
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### thoughts on this log - log plot ?suitable for cox proportional hazards model

I'm quite new at using the cox proportional hazards model and was wondering if someone can please offer some advice on whether this log - log plot shows whether proportional hazards assumption has ...
6 views

### Understanding the output of AddHazard package

In a cohort study, I am trying to assess the excess number of deaths in patients with a specific condition during follw-up. I am trying to do this by using an additive hazard model and am using the ...
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### How is the non time dependent hazard ratio computed?

I'm a bit confused as it relates to the hazard ratio. It seems to me that the hazard ratio is a time varying quantity however it seems that studies report a single number. Read this https://www.ncbi....
1 vote
19 views

### Cumulative Incidence Function given no event before time $t_d$

Suppose we have a simple competing risks model and have a calculated $CIF_K$ for two events $\{k_1, k_2\} \in K$. By definition $CIF_{k_1}(t_i)$ gives us the probability that event $k_1$ has occurred ...
1 vote
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### How does length of follow-up affect hazard ratio (prop hazards vs non-prop hazards)

As the title says, I'm trying to figure out how the length of follow-up affects the value of the hazard ratio (e.g. from a Cox model). If proportional hazard holds, then presumably the hazard ratio ...
61 views

### Proportional hazard assumption: graphical approach vs subsampling

Hopefully someone can guide me on the following. I have a large dataset (> 151k firms with multiple observations per firm). My dataset looks at firm failure using counting process style and my ...
1 vote
24 views

### Predicting hazard function before left truncation point in survival analysis

I want to know if it is not only possible to handle left-truncation of data in a survival model, but to know/predict the hazard function (probability of event) before the start point, i.e. the point ...
16 views

### Why does one make TTT Plot instead of Empirical Hazard Rate Plot?

The total time on test (TTT) transform procedure is used as a tool to identify the hazard behavior of the data distribution. There is a correspondence of the TTT plot and the shape of the empirical ...
12 views

### Log-likelihood function for CoxTimeVaryingFitter

The mathematical formulation of partial log-likelihood function (https://in.mathworks.com/help/stats/cox-proportional-hazard-regression.html) is defined as: The above formulation does not take into ...
1 vote
24 views

### Making inferences from summary data: Can one relate chi squared tests to output from a Cox PH models?

This might be a silly question, but I've been asked about interpretation of a paper and have a query on how much one can ascertain without access to the raw data used, illustrated by example here. In ...
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### Direction of main effects in cox regression and negative binomial regression changes when adding variables

For a research I am conducting I am looking at the effect of two categorical variables (dummy with values 0 and 1 for each group) on the speed and quantity with which customers make future purchases. ...
1 vote
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### It is possible to calculate the Hazard Ratio and 95% CI on different reference groups

I'm working on a meta-analysis and pooling hazard ratio (HR) using the metafor package in R. While most of the studies compare two categories (Biopsy vs Surgical resection) some studies report HR and ...
1 vote
32 views

### How do I get the correct forestplot with each variable with its categories, indicating the reference variable and the values of those that are not

When doing the Coxph analysis with the variables selected from an excel file, it gives a numerical result indicating the HR of each one of them according to the reference one. However, when I ...
31 views

### p for interaction in cohort study

I have data from a cohort of 10,000 people who were followed for ten years to analyze the relationship between stress and the risk of dementia. The stress levels were independent variables, and the ...
1 vote
162 views

### When is a conditional hazard rate increasing?

Cross posted from Mathoverflow Let $X$ and $Y$ be two random variables such that $X\sim Exp(\lambda)$ and $Y$ have positive support and (strictly) increasing hazard rate $h_Y$. $X$ and $Y$ are ...
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### Can different hazard ratios be compared?

Let's say study 1 finds a HR in group X vs control of 1.5. Study 2 finds a HR of 5.4 in group Y vs control. As I understand it, HRs involve the rate of the event happening. Since we do not know the ...
71 views

### DIfference between hazard ratio and partial hazard in survival analysis

The hazard function in survival analysis is represented as (https://in.mathworks.com/help/stats/cox-proportional-hazard-regression.html): Here the exponential term is termed as hazard ratio as ...
51 views

### Confusion between hazard ratios and odds ratios

I am getting into survival analysis and am a bit confused about the definition of hazard ratio and odds ratios. This question implies that there is a clear difference between hazard ratios and odds ...
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### Relationship of incidence rate and hazard function

I like to figure out how I can retrieve an incidence rate based on a hazard function. So background could be that my hazard function models the prob of the event based on the age of a person (t = time ...
1 vote
25 views

### Logic to caluclate shape and scale parameter in survival analysis

I have the below dataset: ...
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### How to model breakage events for electronic devices using a Weibull distribution?

I got age data (in years) of gas heatings from a random sample of about N=700 participants. So participants were asked how old their gas heating is in years. Now I like to model that age distribution (...
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### Recovering hazard rate for interacted Poisson model in R

I am implementing the Wooldridge Two Way Mundlak regression and have an interacted model like so: ...
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### Study design when exposure more likely to lead to test for outcome

I am doing an observational study looking at the association between a baseline exposure (binary) and the first instance of an abnormal blood test result (binary) among people with serial blood tests. ...
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### Hazard ratio and skewness

Suppose the distribution $F$ is absolutely continuous. Is there a way to compare (i) the monotonocity of the hazard ratio (i.e., strictly decreasing/increasing); (ii) the skewness of the distribution (...
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### Is it useful to define the hazard function of distributions with support in the real line?

The hazard function is commonly used in models using distributions with positive support (gamma, weibull, lognormal, etcetera). However, I have not seen this concept (hazard) being used in the context ...
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### Is there any advanced version of Total Time on Test (TTT) Transform?

One parameter survival distribution with increasing hazard rate is (for example) Rayleigh and Lindley, where Rayleigh's hazard rate increases linearly and Lindley's hazard rate increases with a ...
22 views

### Options on modelling a hazard function with a turning point

I have some survival data and need to fit survival models to it and extrapolate. I plotted the log cumulative hazard and empirical hazard plot (using muhaz). There appears to be a change in the hazard ...
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### How do I interpret the interaction coefficients in a cox proportional hazards model with two factors?

I am trying to look at how two different factors A (levels A1, A2, A3, A4) and B (levels B1 and B2), as well as the interaction between the two, influence the time to an event X. As a result I am ...
108 views

### How to generate simulation paths for Weibull distribution in R?

I'm trying to generate simulation paths across time in R for survival and hazard functions using the Weibull distribution. Here are the steps I'm taking so far. I need direction because I'm not able ...
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### What is the minimum of 2 Weibull distributions with the same shape parameter

If X and Y are two independent Weibull distributions with the same shape parameter, what distribution is the min(X, Y). I am trying to find out the hazard ratio for the following case. If I model Z=...
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### Estimating the standard error or confidence interval of a hazard (or odds) ratio from other reported contrasts

I am performing a meta-analysis and have a dataset of hazard ratios and odds ratios collected from primary studies. Suppose for a study we have a recorded hazard ratio (HR) (or odds ratios (OR)) (both ...
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### interpreting HR with time dependent covariates cox regression

I did time-dependent covariate analyses with cox regression in R. But I wonder if the interpretation is the same as for a cox model with a fixed covariate? Context: in my analysis the physical ...
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### Calculate hazard difference and excess deaths from Aalen's additive hazard model

Given the results of an Aalen's additive hazard model, how can I compute the hazard difference in cases per 1000 person-years? Suppose the effect of my treatment variable is constant over time, I ...
1 vote
94 views

### Compare hazard ratios of a meta analysis

A meta-analysis reports that the hazard ratio of a prognostic marker A for predicting mortality in heart failure is 12.5 (95% CI 6.2 - 26.1) and the hazard ratio of a prognostic marker B is 3.2 (95% ...
1 vote
83 views

### Interpreting shape and rate parameters from a weibull model of mortality hazard in BaSTA

I am using the BaSTA package in R to estimate sex differences in survival parameters for a capture-recapture dataset. When I use a simple Gompertz model the parameters are very interpretable (b0 ...
1 vote
265 views

### Presenting spline terms from a Cox model

In the Survival vignette entitled "Spline terms in a Cox model" https://cran.r-project.org/web/packages/survival/vignettes/splines.pdf on page 3 there is this graph: The plot is showing the ...
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### Why the actual hazard ratio of the simulated time-to-event data is very different from the expected value?

I am trying to generate time-to-event data for two treatments, with 25 patients in each arm. I generated the survival time in the treatment arm using an exponential distribution with parameter 0.95, ...
1 vote
87 views

### Cox PH model HR - is it possible to measure against the general average?

Reproducible example: ...
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### Obtain the survival function plot by building an overall survival regression model

I need to build an overall survival regression model that can show the survival plots for id's with multiple rows. I have used the Weibull function to define the baseline hazard function h0(t) and Cox ...
1 vote
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### Hazard or survival function for data with different right-censor timings and different starting periods

I have 15 years of data of patients (2001-2015). T0 differs between them, i.e. the starting year for the survival period is strongly heterogenous. I want to model their survival rate, i.e. what is the ...
1 vote
40 views

### Log-concavity of a discrete random distribution

I'm working with a discrete distribution on the set of non-negative integers. The step-wise cumulative distribution function at any non-negative integer $i$ is  F_i = \frac{2}{\log w}[\log(1+w^{i+1})...
1 vote