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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Discrete survivor function expressed in terms of hazard

Let $T$ can take on values $t_1,t_2,\ldots,$ with $0\le t_1\le t_2,\ldots,$ and let the probability function be $$f(t_j)=Pr(T=t_j),\quad j=1,2,\ldots$$ The survivor function is then $$S(t)=Pr(T\ge ...
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Fractional polynomials in PHREG procedure

For regression analysis by fractional polynomials i used the PHREG procedure in SAS. But it didn't give any Hazard Ratio values. Is it normal or any mistake in my code? ...
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26 views

Age-matching for 2 samples in Cox Regression

I have 2 samples with a very significant mean age difference: Sample0: less-invasive,lower-risk surgery. mean age = 70. n=159 , deaths = 24 Sample1: higher-risk surgery. mean age = 60. n=86, deaths ...
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42 views

Which model to use for survival analysis when there are different times of entry into the sample?

I have a data set containing the trades executed by many traders as follows: ...
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Differences between logistic regression parameter estimates and Cox-proportional hazard parameters

We have been working on a survival analysis. We are examining tree seedling survival over a decade with annual to biannual census intervals. We have been using the package coxme in R for a mixed ...
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18 views

Bivariate gamma distribution with one parameter marginal

Suppose two random variables X,Y>0, have a joint gamma distribution. Its marginal for X is G(a,b) and that for Y is G(a,c). For identification purposes, normalization is needed.does anyone know if ...
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Hazard ratio can be computed from shrinkage estimators?

I am using LASSO in survival analysis. I wonder if it is valid to compute a hazard ratio (HR) from a lasso coefficient, that is, $\text{HR} = \exp(\text{lasso coef})$? Thank you for any help!
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Average hazard rate with Cox proportional hazard model always larger than the hazard rate without any explanatory variables?

I am estimating a Cox proportional hazard model with and without explanatory variables. Without explanatory variables, the hazard rate is just the proportion of all individuals that failed at time ...
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25 views

How to calculate Hazard Ratio from Kaplan Meier curve

Is it possible to calculate the Hazard Ratio, Log[HR], and SE for overall survival (OS) using data from a manuscript that presents Kaplan Meier curve for OS? Usually these manuscripts present the ...
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27 views

Implication of Hazard Rate?

So from my understanding, the hazard rate is not a probability but a rate of an event happening at any one period of time. Can someone please tell me the implications of a hazard rate value. Would ...
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How to show that the cumulative hazard function is equal to the formula below?

I need help to show the equation below. $$H(t)=ln[\frac{mrl(t)}{mrl(0)}]+\int_{0}^{t}\frac{1}{mrl(u)}du$$ where mrl is the mean residual life using $$h(t)=\frac{\frac{d}{dt}mrl(t)+1}{mrl(t)}$$
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Is the magnitude of the hazard ratio change reflective of survival function change?

I need to know the change in survival caused by increasing inbreeding in my study group. As my model has random effects, and as coxme has no easy ...
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72 views

How to conduct Cox PH stratisified by matched pair in R

I am wanting to calculate hazard ratio in a matched cohort design. For such I am using the coxph() function in R. But I have been recommended to stratify by matched ...
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1answer
305 views

Find the mode of a probability distribution function

I am trying the find mode of a probability distribution function given by \begin{equation} g(x/\alpha,\beta,\sigma)=\frac{1}{\Gamma \left( \alpha ...
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131 views

Cox discrete time regression model question

Cox's 1972 publication Regression Models and Life Tables links logistic regression to an extension of the discrete time proportional hazard model. I do not understand how Equation (21) in the ...
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1answer
31 views

Study Length Over-Estimating Hazard Ratio?

Are cox model studies over too long a time-scale at risk of over estimating (or under estimating) a covariate's effect on hazard? I'm studying inbreeding in a captive animal population. Some ...
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89 views

What does muhaz return?

A pretty basic question. I have read somewhere that the muhaz function in muhaz package will return the baseline hazard rate for COX model. The muhaz document states that it "Estimates the hazard ...
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1answer
49 views

Estimating mortality using Cox model with baseline

I have been reading online notes and papers on how to build survival models using CPH, and I think I've a good idea how things work. However, there are two questions I still have in mind: 1) let's ...
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2answers
202 views

How to calculate the HR and 95%CI using the log-rank test in R?

The R survival package is very useful to do survival analysis. And I know the survdiff function can be used to compare the difference of survival time in two or more groups. And the p-value number can ...
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Hazard ratios for three groups - does deleting one group affect the remaining ratio?

My study originally had 3 groups, x , y and z. Hazard ratios were reported for x vs y, x vs z and y vs z. If we remove group z from the study, would the x vs y hazard ratio change? If someone can ...
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72 views

Survival analysis where P(event) < 1

Suppose you are interested in analyzing time to event data for a sample of patients. You are interested in the time elapsed until a patient contracts an illness. However, a majority of patients will ...
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1answer
73 views

different HRs and corresponding CIs with cph and coxph

I tried a model using cph and coxph: ...
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Is it possible to add 2 ore more Hazard factors?

I'm a general practicioner and I'm trying to estabilish a conection between interarm sistolic blood pressure difference with cardiovascular disease but i dont have time to wait 10 years or more to ...
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1answer
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Compute the cumulative hazard of a time interval

I'm a little confused in calculating the cumulative hazard within a time interval. We know that $H(t)=\int^{t}_{0}h(u)du$, if I have $\Delta t=t_1-t_0$ (1) $H(\Delta t)=\int^{\Delta t}_{0}h(u)du$ ...
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151 views

Is it possible to construct a discrete-time multilevel hazard model in R?

I'm trying to run a discrete-time multilevel hazard analysis comparable to the model proposed by Barber et al. I am attempting to model the hazard of migrating internationally using predictors at the ...
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It it possible in R to specify a regression formula for the hazard rate for a survival analysis model?

I am currently trying to fit a survival analysis model which has the following survival function: $S(t) = \lambda_i e^{-\lambda_i t}$ but with $\lambda_i = e^{\beta_0 +\beta_1 log(1+X_i)}$ where ...
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29 views

Calculate Hazard Ratio Manually for Continous Covariate

I found an example for manually calculating the hazard ratio when there are two groups. ...
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Outliers in proportional hazards model

How can one easily found an outlier in PH model and why are they so important? Can anybody give me some advice or suggest which R function may I use? Thanks for comments and help.
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Using two hazard ratios to make third comparison

I have two sets of hazard ratios (with confidence intervals), one comparing risk of developing a cancer between current smokers and never smokers, and another comparing former smokers to never ...
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estimate conditional time-to-event for recurring event history model

I have a sample of individuals for whom I have measured the time at which they display a particular behavior. This behavior is recurrent (it is not fatal). I have modeled these events with ...
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Negative Regression Coefficent (Cox Regression)

I'm doing a Cox regression analysis in order to verify the role of two variables on the prediction of disease conversion. Previously, I did a ROC analysis and a logistic regression. All these methods ...
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Showing $ λ_V(x) \leq min\{λ_1(x),\cdots,λ_n(x)\}$ Hazard function

Suppose $X_1, \cdots, X_n$ are independent, nonnegative continuous functions, each $X_i$ has hazard function $\lambda_i(x)$. If $V=\max\{X_1, \cdots, X_n\}$, I need to show that ...
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Evaluating Proportional Hazards with time-dependent variables

I'm doing survival analysis and using the survival package from R to do it. I have 7 variables, 5 of which are time-dependent (all except sexo and peso). Here is my model: ...
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predicting manufacturing survival time

My task is to improve widget quality from a high volume manufacturing process. The survival data is 99% right censored, since most products do not fail, and rapid analysis long before failure is ...
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How to reconcile SAS hazard ratio standard error with actual value

I am trying to replicate the "C3 Contrast" (Output 66.3.7) at the bottom of: http://support.sas.com/documentation/cdl/en/statug/63962/HTML/default/viewer.htm#statug_phreg_sect048.htm I am able to ...
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Violation Proportionality Cox model - Repeat analysis?

I'm new to survival analysis, but I've been reading some papers and books and I got a nice model. However, one of the variables (Sit) does not met the proportionality assumption for the Cox model. ...
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159 views

Hazard and density function in survival analysis with discrete time

I am running a survival analysis with descrete time. For that purpose I use the R package survival with this function ...
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Selection correction variable (non-randomly selected sample / bias) and Cox regression

I found an approach to calculate a selection correction variable for a Cox regression (Lee 1983. Generalized econometric models with selectivity. Econometrica 51: 507–512.): $$ λ = \phi \frac{ ...
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Difference between hazard function and intensity function?

I'm reviewing a paper whereby the nonhomogeneous poisson process is explored. I'm familiar with the intensity function, but the idea of the hazard function is throwing me off. Especially, I cannot ...
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Difference in Effect for Time-Varying Covariate in Survival Analysis

I am analyzing offender recidivism data using survival analysis. In particular, I am looking at the risk of getting arrested as a function of employment. When I treat employment as a time-varying ...
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Converting a parametric survival model to a cash flow model. How do I account for aging in the population?

I'm building a survival model for time to failure of widgets. Other members of the team want to convert the model to a cost flow model. The basic idea is that we can use the functional form of the ...
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How to interpret standard errors in a Cox model?

I am running a multi-variate Cox regression and Stata provides the standard errors for each hazard ratio. How are theses to be interpreted? I know that I want my coefficients to be large compared to ...
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Is there any functional difference between an odds ratio and hazard ratio?

In logistic regression, an odds ratio of 2 means that the event is 2 time more probable given a one-unit increase in the predictor. In Cox regression, a hazard ratio of 2 means the event will occur ...
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185 views

Meta-analysis Hazard Ratio

I need to explain the calculations involved in a meta-analysis with Hazard ratios (random effects) for programming in a tool. It is not possible to use statistical softtware neither webpages where ...
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Generating cumulative incidence curve for competing risk model - assuming changing covariates

I am implementing a Fine & Gray competing risk model. The model includes covariates that are static for each person (e.g. location) as well as covariates that change over time (such as local ...
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119 views

Kernel estimation of hazard or density function

I am working with R package "muhaz" to get the kernel estimate of the hazard function. If we have the following example which is the sample of uncensored data: ...
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1answer
236 views

Calculating discrete hazard rates problem

I am working on an assignment for a Stochastic Modeling class and am stuck on the following question: Let $X$ have probability mass function $p_j = P \lbrace X = j \rbrace $ for $j \geq 1$. Let ...
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Hazard Function - Survival Analysis

I just started taking survival analysis class and I'm stumped on this question. Let $T_1,...,T_n$ random independent continuous variables, with hazard function of $h_1(t),...,h_n(t)$. ...
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Survival regression and prediction using median

I'm using artificially generated hazard curves (that is, I know the true hazard curve) and Aalen's additive model to fit the covariates. For example, below is an individual's hazard curve and my ...
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398 views

Can I perform Cox regression on left truncated records?

Is a Cox proportional hazards regression model appropriate for records which are left truncated? I'm developing a model that predicts risk of hospitalization during a two year time period. Some ...