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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10 views

How do I change the reference group for hazard ratio for SAS? [closed]

I am running a survival analysis. Let's say SAS uses 0 as the reference group for all of my variables. However, I want to use 1 instead as I want the inverse of the HR and CI. If I want to change the ...
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13 views

How to simulate a time dependent variable on a existing dataset?

I made a coursera course abouth survival analysis. It uses a heart failure dataset for the examples. (That same dataset can be found on Kaggle https://www.kaggle.com/jackleenrasmybareh/heart-failure) ...
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Combining Time-Defined Hazard Ratios and Odds Ratios in Meta-Analysis

I am attempting to complete a meta-analysis of studies that variously report Odds Ratio of death at 30 days, and Hazard Ratios for death at 30 days. All are reported as being close to 1 (range 1.2-1....
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Is it possible to calculate conditional PD / unconditional PD from Hazard Rate?

I'm just wondering that can I convert hazard rate to probability of default? Suppose I have the lifetime table data as per below: Time Total Default Non-Default At Risk 0 - - - 356,335 1 5,587 1,...
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35 views

I cannot match the results of KaplanMeier and Nelson Aalen by hand

I have fitted both models by using lifelines python library. The results of .event_table from both models are identically matched. However, when I try to ...
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32 views

Survival function of accumulated hazard in Cox model

I have this setup: Independent subjects following a Cox model $$\lambda_i(t,X_i) = \lambda_0(t) \exp(X_i^T \beta ) $$ the observed right censored survival data $(T_i, \delta_i, X_i)$ are i.i.d. and $...
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33 views

Cumulative Incidence function and competing risks

Let $R_1,...,R_K$ be competing risks and put $T=\min(R_1,...,R_K)$ and $\delta = i$ if $T=R_i$. The cumulative incidence function is then defined as $F_i(t):=P(T\le t,\delta = i)$. The cause-specific ...
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Connecting Survival Analysis to Overall Predicted Survival Probabilities

I've got a question on combining survival analysis with predicted survival probabilities that I'm sure someone must have thought about, but I just can't find anything out there. Imagine I have a good ...
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1answer
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How does the hazard ratio change when the exposure is doubled?

I am a medical student who somehow ended up having to do a meta-analysis. I have no knowledge about statistics. For example, if the cardiovascular mortality hazard ratio associated with a 5μg/m3 ...
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19 views

Survival data simulation based on confidence interval of Hazard ratio

I got a published hazard ratio (HR) of 0.464 with 95%CI as (0.337, 0.639) from a paper. My question is How can I get the distribution of the HR, so that I can check the different quantiles? is that ...
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In Survival Analysis, does "Non - Cumulative" Hazard Exist?

In the context of Survival Analysis, I have seen that the standard (non-parametric) estimate of the Hazard Function is through the Nelson-Aalen Estimator : As seen from this formula, the Nelson-Aalen ...
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Distance between hazard functions? [closed]

Let $F$ and $G$ two cumulative distribution functions with support on $(0,\infty)$. I know of many distances between distributions: Total Variation, Wasserstein, Hellinger, Kullback Liebler (...
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34 views

Plot of hazard ratio for primary endpoint and continuous covariate

Good morning, I wonder if you could tell me the R code to use to obtain a graph similar to the one below. (from: https://www.nejm.org/doi/full/10.1056/NEJMoa1215740) That is, I would like to graph ...
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How do you interpret outputs of Cox regression based on data type of an independent categorical variable?

I have the following data frame which consists of a grouping variable, as well as time ans status variables for survival analysis: ...
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Cumulative incidence vs Cumulative hazard: What's the difference?

Does anyone know what he difference between the 2 is? I want to calculate the cumulative incidence, but all I see is cumulative hazard in SAS.
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Hazard function of a simple system of components

I have been asked to complete these tasks, and a few more, but I am stuck somehow: Figure 6 is the simple system above. For task number 1: [DONE] I started by recognizing that the total survival time ...
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Cox Proportional Hazards Interaction Hazard Ratios

I am looking at the interaction of dose (continuous with mean=2241 and sd=949.4) and cause of death (values of 0 or 1) in a survival analysis. The interaction is tending towards significance, and ...
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Why are confidence intervals of hazard ratios not symmetric?

My understanding is that the confidence interval for a hazard ratio should be symmetrical about the mean (the distance between the lower limit and the mean is the same as the distance between the mean ...
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185 views

Calculate the standard deviation from a hazard ratio's confidence interval

I often come across hazard ratios and their confidence intervals in the published literature on clinical trials. I would like to calculate the standard deviation from these confidence intervals for ...
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Meta analysis Hazard Ratio with small number of studies (n=2)

I am doing a fixed effect meta-analysis pooling hazard ratios from 2 very similar cohorts. I understand that the inverse variance method is most commonly used to pool HR, however I also read that this ...
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Mathematical connection between hazard functions for e.g. Cox models and expected values in GLMs

I intuitively understand why the hazard function is interesting to link to patient attributes, as explained in this answer. However, is there a mathematical reason this is done? I'm particularly ...
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74 views

Why does random survival forest use Cumulative Hazard Function to calculate C Index?

I am working with Random Survival Forests and I found out in the documentation that it uses Sum of Cumulative Hazard Function to define a worse predicted outcome, which is subsequently used to compute ...
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Presenting raw hazard ratios, not log(hazard ratio), in forest plot for meta-analysis using metafor

I'm trying to perform a meta-analysis in R with metafor of trials for which the hazard ratios(HR) and 95% CI are available as outcomes. I am aware that I have to use log(HR) for calculation, but I ...
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75 views

How to get beta coefficients for reference group in Cox proportional hazards regression model survival analysis (R or other)?

The model was calculated using the coxph and survival functions from the survival package (R). Each of nine variables was set as categorical with a reference strata.The criterion was the survival ...
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35 views

How to find hazard function from a survival curve

I have just started learning survival analysis. And i came across the survival curves and graphs and hazard function. Help me answer with the following question: Given a well structured graph of ...
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53 views

Merging survival data with time varying covariates

In merging the data in R the censored observations are merged well but the observed subjects are not. For example, the second subject had an event at time 0.546. How can I merge the time varying ...
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56 views

How to find out hazard ratio and confidence interval from LASSO cox regression ans plot momogram in R?

I am working on a prognostic model based on time to event endpoint. The training data consists of 800 participants and test data around 400. The number of variables is 21. I was using glmnet package. ...
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How to plot the hazard ratio of a categorised variable in its original continuous scale? take BMI for an example

I have BMI divided into quartiles. I fitted two cox regression models that included BMI as a categorical and continuous variable respectively. Now I want to plot the hazard ratio of categorical BMI ...
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Network meta-analysis with trials of different follow-up time [closed]

0 I am trying to do a network meta-analysis, and calculating anticipated absolute differences, I have seen other papers generating anticipated absolute differences for treatment for x number of years. ...
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1answer
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Regression on time passed until certain threshold is "re-reached"

I would like to test the time/duration it takes for a certain variable to reach a certain level (e.g. time passed after companies reach a pre-crisis level at point x again in their recovery process ...
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1answer
48 views

Can one compare Hazard Ratio and Average Hazard Ratio?

I would like to compare three predictors of survival by comparing three cox regression models. One model violates the PH assumption which brought me to weighted cox regression as implemented by ...
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37 views

How to sample non-event data for survival analysis

I am building a model to predict customer churn using survival analysis, COX regression in particular. While it is pretty straight forward to collect churn events, it is a little tricky to sample for ...
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Effect of mean to power transformation on standard deviation

For a meta-analysis, I am converting hazard ratios per log base 2/log base 10 increase, to SD increase (of the ln-transformed normal distribution). I am doing this by raising the HR to the power of, ...
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174 views

Cox PH model and regression with log-log link function: is there a connection?

In this post: interpreting estimates of cloglog logistic regression, I read that when interpreting the results of a regression with a log-log link function, the exponent of the estimated coefficient ...
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1answer
75 views

Computing Chi-square values from Schoenfeld residuals

Based on page 164-165 of [Collett:Modelling Survival data in medical research (Third edition-2014)] the Schoenfeld for individual test and for global test can be obtained as follows[1]. However, ...
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1answer
109 views

Hazard function to PDF computation [closed]

I am trying to formulate the computation between the Hazard function and probability density function. Given an example: pdf_arr = [0.2, 0.2, 0.2, 0.2, 0.2]. My ...
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Conversion from hazard function to probability density function

While following this conversion follow: https://lifelines.readthedocs.io/en/latest/_images/map.png I am unable to convert from PDF to hazard function and vice versa. ...
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225 views

Intuition behind Weibull distribution?

I don't understand the physical meaning of Weibull distribution's $k$ parameter. Here is a simplified formula of cumulative probability function of Weibull in the simplest form: $$p(\xi \geq x) = e^{-(...
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1answer
124 views

Calculate the confidence interval of a Hazard Ratio from the ones of the survival

I have 2 populations with their survival at n years and their 95% confidence interval. Under the assumption of exponential distribution, the hazard ratio can be ...
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Improved/novel/useful Hazard Rate Analysis Based on Approximating the Derivative of Log Survival Ratio?

Those acquainted with the Hazard Function Analysis are likely familiar with the literature which notes that a hazard ratio can be expressed as the derivative of the log of the survival function (which ...
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41 views

Stratified KM curve plot for estimation of proportional hazards assumption violation

I am reading a paper that attempts to investigate time varying covariates in Cox proportional hazard model for breast cancer patients. I read that we can plot stratified KM curves for two groups of ...
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What is the difference between finding the hazard function by using an NHPP and fitting a Weibull curve to the data for a repairable system?

When modelling a repairable system, one should use a non-homogeneous Poisson Process (NHPP). E.g., the moment the hazard function I use in the NHPP is a Weibull function. However, I have difficulty ...
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1answer
108 views

Pooling different effect sizes in meta-analysis with metafor

Simple question here. Suppose that I have 20 papers to be included in a meta-analysis, which compare the risk of death with 2 treatments, A vs. B. For 15 of them, I only have number of events and ...
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1answer
108 views

How do I calculate the probability that some system will survive for some years before some event will occur?

I have a failure rate problem involving structural beams. The scenario is that a set of $n$ structural beams are supporting a weight of $W$ kilograms. For the purpose of simplification, we can assume ...
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2answers
29 views

Failure Rate of a Sum of i.i.d Random Variables

Suppose that $X_1, X_2, \ldots, X_n$ are i.i.d. random variables, with failure rate $r(t)$. Suppose $r(t)$ is increasing. Is it true that the sum $X_1 + X_2 + \ldots + X_n$ also has an increasing ...
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54 views

Would you used prediction from Cox or stratified KM for drawing survival curves and testing them?

Let's assume I have an experiment, where I track some event. I want to analyse the time to this event between two levels of a group G: g1 and g2 I want to do the comparative analysis in sub groups, ...
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54 views

Is it possible to convert the hazard difference of an Aalen additive model to the hazard ratios that are typically outputted by Cox PH models?

I am comparing the behavior of the survival and hazard function estimates of the two models using the same dataset and the same factors/covariates influencing survival time. I am not sure if it is ...
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2answers
48 views

Why doesn't simulation show KM estimators approach the true survival function?

I'm trying to simulate a survival data with very large sample size and show that the KM estimators approach the true survival function, however it ends up that the two are visually quite different. I ...
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2answers
110 views

Can it be said, that in case of non-proportional hazards, Cox returns average hazard ratio over the entire period?

I have read two opposite statements about the hazard ratios obtained from the Cox procedure in presence of non-proportional hazards. One is that the HR for a certain covariate, that fails this ...
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302 views

Survival analysis with repeated measures

I've recently started working on survival analysis, but I'm still new to the field. My dataset consists of a cohort of 50 individuals with advanced cancer for whom I have some blood quantitative ...

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