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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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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54 views

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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45 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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31 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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1answer
47 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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22 views

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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59 views

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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26 views

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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38 views

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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43 views

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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5 views

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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1answer
147 views

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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1answer
24 views

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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43 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 view 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
48 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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2answers
41 views

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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2answers
130 views

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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1answer
48 views

(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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30 views

Proportional hazard assumption in survival analysis

Which is the best method to check proportional hazard assumption in survival analysis?
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1answer
89 views

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. ...
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59 views

Relation between P value and HR (hazard ratio) [on hold]

I am doing a project on meta-analysis on breast cancer analogues. The clinical trial papers related to my topic contain insufficient statistical data. So, I would like to know the following relations ...
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29 views

chance of death year by year or a hazard function

I have a large birth cohort (about 250K) of firms organised into four size-bands (classified by the number of jobs). There are 15 years of annual observations, and by age 15 about 90% of firms are ...
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21 views

Life table based on age groups

I am working on panel attrition (loss of respondents at each wave of follow-up of a longitudinal survey). A multivariate model (discrete-time event history analysis) to analyse panel attrition is ...
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290 views

Modeling customer churn - Machine learning versus hazard/survival models

Is their any rational (theoretical, substantial, statistical) to opt for either machine learning or hazard models when modeling customer churn (or more general, event occurences)?
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P-value versus Exp(B) value in Cox regression analysis

I performed Cox regression analysis for two Biomarkers. Both were significant (p<0.05). Biomarker 1 showed higher significance but lower Exp(B)=hazard ratio value than Biomarker 2 (see below). ...
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87 views

What is the difference between the “Hazard Rate” and the “Killing Function” of a diffusion model?

I posted the same question in Mathematics. I will update both posts if we get any answers. Link here. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ What is the ...
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36 views

Computing hazard ratio between groups adjusting for other confounding variables

I have groups formed based on BMI; consider the standard Underweight, Normal, Overweight, etc. groupings for BMI as you might see for classification. I'd like to form a hazard ratio for comparing any ...
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120 views

Fluctuations in hazard function at high (x) values

Using a best-fit algorithm, i've obtained gamma-distribution parameter MLEs for my data (scale and shape). When evaluating the hazard function, calculated as the PDF divided by the reciprocal CDF, ...
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38 views

Cox Regression Hazard Ratio in Percentiles

I computed a Cox proportional hazards regression in R. cox.model <- coxph(Surv(time, dead) ~ A + B + C + X, data = df) Now, I got the hazard ratio (HR, or ...
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1answer
45 views

Calculating group size from hazard ratio

I am undertaking a systematic review and as part of the data extraction process I would like to know how many patients were analysed in the treatment and control arm (in a particular subgroup). In one ...
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145 views

Time-dependent coxph output and making predictions in R

I'm trying to use a Cox proportional hazard model to predict the time until an employee terminates from an organization. There are a bunch of covariates (~20), some of them time-dependent. So I've ...
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14 views

Point process models

Two of the popular models for analyzing point process data are Cox and Hawkes processes. My question is how do we compare the statistical properties of these two processes as they both can be ...
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39 views

Cox survival analysis versus multilevel modeling

I'm debating the wisdom of a couple different approaches. I am constructing a model that measures whether the amount of a treatment received leads to a person coming back for another treatment or ...
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20 views

Using Hazard Ratio to predict Population Incidence or Prevalence

The univariate hazard ratio corresponding to a per unit continuous linear increase between a risk score and a disease is 1.04 (literature) . I am interested in using this hazard ratio to predict the ...
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115 views

Calculating constant hazards in exponential survival distributions in R using survreg()

In an ecological seed removal experiment, we have seed removal data from 720 seed plates with 25 seeds each. For each plate, we know the number of "surviving" seeds at several times ti until the end ...
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165 views

Simulate a random variable having piecewise gamma failure rate

I am having trouble in simulating values for a random variable $X$ having a piecewise gamma failure rate: $$ \lambda_X(t) =\lambda_1(t)1\!\!1_{\lbrace t\leq t_0 \rbrace} + \lambda_2(t)1\!\!1_{\lbrace ...
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1answer
54 views

Risk ratios in a Cox hazard model

I'm reading a paper which gives "Risk ratios from Cox hazard models with time-varying covariates". Time-varying covariates just means that, for example if $X_i$ is a covariate for person $i$ then it ...
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1answer
87 views

Survival Analysis Applied when Individuals that “Died” can still Return

I'm running an AB Test and using Survival Analysis to estimate the Return Rate to the website. Each day (in a total of 7 days) I randomly assign 100 users to group A and 100 users to group B and ...
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2answers
191 views

What is the right way of computing baseline hazard rate

What is the right way of computing baseline hazard rate? To my understanding hazard rate at time t is simply #events / #AtRisk ...
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1answer
102 views

Intuitive meaning of the limit of the hazard rate of a gamma distribution

For a Gamma distribution with shape parameter $\alpha >1$ and scale parameter $\beta > 1$, one can show that its hazard rate function $h$ is increasing and satisfies \begin{equation} ...
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57 views

Tail problem with hazard function

Before doing a more advanced survival analysis, I generated an exponentially distributed variable in Stata and used the following code to get a constant hazard rate graph: "sts graph, hazard" I get ...
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1answer
292 views

Comparing failure rates between 2 products with different number of deployed equipment

I have the following scenario, which I am trying to better understand. There are 2 different brands or groups of devices performing the same functionality as such: - Product/Brand 1 has 4,323 devices ...
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1answer
467 views

Interpretation of the hazard ratio in a spline model on continuous exposures

I am having trouble interpreting the output from a Cox proportion hazard model with a spline term on a continuous exposure. In the below example (pseudo-code from ...
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27 views

Cox PH Modelling: How important are ties to the end result?

I am working on create a survival model using Cox PH, but am concerned with the limitation of the continuous time requirement. In my dataset there are often ties. For example, out of 35000 records, ...
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0answers
61 views

How to demonstrate biased estimates of linear regression vs cox proportional hazard survival analysis in R?

I want to perform a really simple simulation of right censored data. Then I want to draw a kaplan meir survival curve and do a cox proportional hazards test. Then I also want to perform a simple ...
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2answers
157 views

Hazard function, survival function, and retention rate

What is the difference between the hazard function, survival function, and retention rate in survival analysis?
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24 views

Are there any possibilities to check model assumptions or any diagnostic for the proportional hazards model with correlated times?

As far as I know, regular proportional hazards model have assumptions that times have to be independent, hazards for each variables should be proportional and there should be noninformative censoring. ...
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50 views

Can proportional hazard regression predict the S(t) of subjects?

In my understanding, cox PH model can only give estimates of coeffs of regressors and then interpretations can be drawn. Since it does not assume a base hazard function, it cannot give an estimated ...
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1answer
58 views

Some doubts about survival analysis

I'm struggling to perform a correct and unbiased survival analysis, but I have some doubts. Data I observe a population of posts on a blog within a temporal window $[T_{0}, T_{final}]$. Each post ...