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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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49 views

Expressing a hazard function with a Cox proportional hazards model

I'm trying to wrap my head around Cox models as well as how to express them in the form of hazard functions when you have both categorical AND numeric covariates. I need some assistance with this ...
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20 views

Predicting hazard in an AFT Weibull model

I have fitted a Weibull Accelerated Failure Time model and my question is how to obtain the hazard. For example in Stata, after fitting a model with streg, typing predict newvar, hazard obtains the ...
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1answer
46 views

Calculating the Expected life of network with hazard functions

I have been asked to solve some questions in the statistical program R. First, I want to find the expected life length (by numeric integration) of a network with 3 parallel components (T1,T2,T3) and ...
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116 views

Is there an S-shaped (like sigmoid function) probability distribution? [closed]

Suppose there is a disease whose likelihood of occurring increases with age. But this increase is not linear, in fact it is at a certain age (e.g. 50) that the risk starts growing rapidly. But at some ...
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6 views

unknown parameters α0 and co-variance matrix Q using EM Algorithm for ddhazard model

I am working on panel data with catagorical variable as independent and 6 explanatory variables. sample years are 1992-2018(27).total number of firm-year observations are 33946. I want to know the ...
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15 views

time varying covariates, ddhazard, bankruptcy prediction, shumway

I want to use shumway simple hazard model to predict bankruptcy. I am trying to use ddhazard to fit my data which includes time varying covariates. This is how my ...
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2answers
67 views

Hypothesis test for Poisson process failure rates stays just as powerful for Compound Poisson

The book "Testing Statistical Hypotheses" by Lehman describes in section 4.5, a test for comparing the rates of two Poisson point-processes. This is the "uniformly most powerful" (UMP) test for this ...
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0answers
18 views

Hazard ratio endpoint vs Odds ratio

This study (https://academic.oup.com/cid/article/65/1/100/3097834) seems to conduct a cox proportional hazard regression on survival data, but reports hazard ratios for 30- and 90-day mortality: ...
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1answer
44 views

What are the hazard ratios in this plot referring to?

With the following code in R, I created this graph: ...
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0answers
12 views

piecewise constant hazard survival analysis with time-dependent covariates and frailty

I have data (repeated measures) of organizations over time, and I want to predict organization dissolution, the rates of which differ quite a lot over time. Is my understanding correct that this is ...
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0answers
17 views

Proof of likelihood ratio ordering implying hazard rate ordering

I'm studying stochastic orders and am stuck in the proof of likelihood ratio ordering implying hazard rate ordering. Definitions: Let $X$ and $Y$ be two random variables with respective densities $f(...
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0answers
30 views

Testing for Constant Hazard Function

My colleagues and I have some unemployment data, and we'd like to test the hypothesis that it's drawn from a memoryless distribution (= constant hazard function). Is there a standard test for this? (...
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1answer
26 views

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
60 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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1answer
34 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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27 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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0answers
28 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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0answers
25 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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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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0answers
32 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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0answers
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
95 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
17 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
85 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
290 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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14 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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0answers
58 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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14 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
82 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
109 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
76 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
35 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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0answers
96 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
97 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
57 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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34 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
35 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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38 views

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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0answers
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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0answers
51 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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30 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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0answers
53 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 ...
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1answer
137 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
27 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, ...