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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Set new reference level for hazard ratios
I run a Cox Regression and afterwards, I predicted the Hazard Ratio (HR) for the predictor values 1 to 10. My data looks something like this:
...
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1answer
24 views
How to model the Hazard Rate?
I'm interested in modeling the Hazard Rate $\lambda$ from a Survival dataset so I can calculate the Cumulative Distribution $F(t)=1-e^{-\lambda t}$ but I'm not sure how to go about computing $\lambda$...
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21 views
Is the Cumulative Hazard Function simply estimated using the Empirical CDF?
I'm just starting to learn about Survival Analysis and I understand the theoretical proofs but I'm still unclear about how to do some of the estimations practically.
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24 views
Days Between Visits Model
I have a dataset from a digital service on a user-level and want to model the decrease in visits and usage over time. I want to explain the decrease (or increase) with the activities a customer ...
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24 views
Predicting survival probability at a future time for proportional hazard model
I have a Weibull proportional hazard model with fitted parameters $\lambda$ and $k$ and a time dependent covariate $x(t)$ with fitted coefficient $\beta$, such that the hazard function is given by,
$...
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22 views
“Hazard function” for logistic PDF
Question: Does hazard function
$h(x, \mu, \sigma)=\frac{f(x, \mu, \sigma)}{1-F(x, \mu, \sigma)}$
of logistic PDF $f(x,\mu, \sigma)$ make sense?
The problem is that logistic PDF is defined for ...
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22 views
How is a survival model with constant baseline hazard and time varying covariates called?
The data situation:
Supose in different forests data have been collected. These data include the temperature at different time points, the hours of rain, the type of forest and whether the event (a ...
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30 views
Time and events in a Cox model
I am going to perform survival analysis using the Cox model, but I have some doubts about the input data.
The data have the following structure:
...
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11 views
Likelihood function for a unit $i$ with death at time $t_{i}$ and non - death at time $t_{i}$
The survival function with respect to time is defined to be
$S(t) = 1 - F(T) = \int_{t}^{\infty}f(x)dx$
With a bit of algebraic manipulation, one arrives at the time dependent hazard rate ...
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8 views
It is possible to calculate what the expected hazards ratio would be for a subgroup if I am assuming the subgroup is an independent variable?
I am interpreting a placebo-controlled comparative study. For the primary endpoint:
Overall
n=8179
Hazards ratio: 0.75, 95% CI: 0.68 - 0.83
Gender is assumed to be an independent variable in ...
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0answers
21 views
Does prediction-at-the-means give the correct survival function in the long run?
If you fit a Cox model, it's possible to come up with an estimate of the baseline hazard function using the Breslow step estimator. In R, this is the basehaz ...
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1answer
61 views
What does 'km' transform in cox.zph function mean?
I'm trying to understand how cox.zph function in r programming language works and I find myself not knowing what km transform ...
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0answers
16 views
Hazard ratio for continuous variable
I have a HR of 0.65 (0.46-0.92) and my explanatory variable is age (weeks of age). Time, event ~ age modeled with a flexible semiparametric model.
My interpretation is that for each week elapsed, ...
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2answers
42 views
Interpreting hazard ratios in stratified models
I am unsure how to interpret hazard ratios from cox-proportional hazard models that include 1 or more stratified terms.
For example, say I run a cox regression with treatment as a covariate and ...
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2answers
289 views
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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13 views
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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1answer
28 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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32 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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13 views
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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19 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 $\...
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1answer
80 views
Obtain hazard ratio from other hazard ratios
Given a hazard ratio($HR$) as $$𝐻𝑅_{b}=ℎ𝑎𝑧𝑎𝑟𝑑(b)/ℎ𝑎𝑧𝑎𝑟𝑑(a)$$ and another hazard ratio as $$𝐻𝑅_{c}=ℎ𝑎𝑧𝑎𝑟𝑑(c)/ℎ𝑎𝑧𝑎𝑟𝑑(a)$$ How can we obtain the hazard ratio between $b$ and $c$ ...
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1answer
65 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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2answers
67 views
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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2answers
34 views
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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66 views
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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1answer
87 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
54 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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29 views
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
34 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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17 views
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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25 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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43 views
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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26 views
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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51 views
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 ...
4
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1answer
113 views
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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0answers
24 views
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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1answer
90 views
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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3answers
160 views
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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0answers
31 views
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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25 views
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 ...
6
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1answer
98 views
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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1answer
580 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
39 views
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
40 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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21 views
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
53 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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2answers
373 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
72 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 ...
