# Questions tagged [survival]

Survival analysis models time to event data, typically time to death or failure time. Censored data are a common problem for survival analyses.

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### Additive hazard model: Estimating a martingale residual process

Consider an additive hazard model with a single categorical covariate $$\alpha(t | x_i) = \beta_0(t) + \beta_1(t) x_i,$$ where e.g., $x_i \in \{0, 1\}$. To assess the goodness-of-fit of this model, ...
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### Survival analysis: tstop is greater that tstart

If tstop in a multistate model for an event of interest is day zero and tstart must be less than tstop (day 0). Where should I move cases that experienced an event at day 0? I am using mstate package
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### Expected winning prize of 95% of total prize amount based on Probability of not winning and Probability of winning for each individual

For this probability model, As I am new to probability, I am looking for an approach of the underlying probability concept to work on the calculation in arriving at the expected winning prize of the ...
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### Testing the validity of a Cox Time-Varying regression model in Python Lifelines

Using the lifelines library for python, I've fitted a Cox Time-varying regression to some customer data, to see which coefficients have an effect on customer churn. The dataset is a combination of ...
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### 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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### Survival analysis for different diseases on same patients

I want to apply survival analysis on UFC-fights. Each fighter represents a "disease" and each knock-out is a "death". Each UFC fight consists of a number of rounds and the number ...
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### Proportional Hazards Model and EM Algorithm

I am working with the standard proportional hazards model given by $\lambda(t|Z) = \lambda_0(t)e^{Z\beta}$ for a special type of data that requires an EM algorithm to estimate a discretized version of ...
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### Given median survival and CI, and assuming an exponential distribution, can one predict survival and CI at a time point?

I have access to a manuscript where the median survival and CI are reported. The shape of the curve approximately takes the shape expected for an exponential distributed failure time. I don't know the ...
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### Survival analysis: using time varying covariates for resolving violated PH

p1 is a factor p2 is a continuous variable Model m = Survival_function ~ p1 + p2 Both covariates - p1 and p2 - violate the proportional hazards assumption. I am ...
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### Customized concordance index for survival analysis in python

I am trying to build a two-stage model where I classify my data and split it into two datasets. I then fit a Cox Proportional Hazard model to each dataset and make predictions and can calculate the C-...
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### Kaplan Meier Curve (right censored data)

I have to draw the Kaplan meier curve to show the proportion of clinical trials with and without results (on y-axis) and their time (which is the difference between trials completion and result ...
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### Is it possible to test what is the type of censoring (or if it is informative/non-informative/etc) when doing survival analysis?

(considering right-censoring) Without knowing the experimental design, is there any conclusion/idea about the type of censoring I have just with the data? I was googling and looking around in ...
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### 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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### Likelihood term in Cox Proportional Hazards Model

I have just started learning on the Cox proportional hazards model. I understand that the hazard function is the multiplicative of the baseline hazard rate $h_0(t)$ and the hazard rates dependence on ...
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### Centered Cox survival and Kaplan Meier interpretation with 2 groups

While trying to interpret some of the results I got from the Cox model, I've read that the centered survival curves where you calculate the mean value of each variable is pretty useless but wouldn't ...
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### Explanation of differential equation solution in survival analysis proof

I follow all the steps in the below derivation until the third to last line, "solving this differential equation for the survival analysis function shows that..." Questions I never took ...
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### Time-varying coefficients in coxph

I'm trying to understand time-varying coefficients in survival::coxph and the tt notation. I found this paper, which clarified ...
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### No observations for specific group - group comparison still possible?

I am conducting a Weibull Survival analysis (recurrent event) with the time-frame between 1970 and 2010. One question is the difference in survival time between gender. However in the earlier years ...
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### Can coxph() from the R survival package be used to fit bidirectional multistate survival models

I am trying to design an illness-death multistate model (see image below) for survival type data in R. This data is more suited for a Markov model, but the investigator I am working with prefers to ...
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### Why are survival outcomes reported using Kaplan-Meier curves and Cox proportional hazards models together in academic papers?

I am relatively new to survival analysis and have seen survival outcomes often being reported using both progression-free survival/overall survival Kaplan-Meier curves in months, as well as hazard ...
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### Would you choose a joint frailty model or a multi-state model for survival analysis with recurrent events and competing risks?

I am going to analyse data with multiple recurring events and additional terminal event. The recurrent events are of the same kind, no hierarchy in them (like in the Prentice-Williams-Petersen). The ...
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### Which frailty model is better for survival analysis with recurrent events and competing (teminal) risks: joint or shared?

I am going to analyse data with multiple recurring events and additional terminal event. The recurrent events are of the same kind, no hierarchy in them (like in the Prentice-Williams-Petersen). The ...
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### Why do we need Fine-Gray, Andersen-Gill, joint fraily and multiple-state model to model complex survival if basic tools (Cox) can handle it?

The basic methods statistical packages, using K-M or Cox regression, are both to handle both recurrent events and competing risks. This setting is very common in medicine, where we have recurring ...
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### Cross-validation for survival analysis

In my problem I am trying to predict the time from a vehicle leaves a charging station until the next one arrives using various techniques, of which Cox Proportional Hazard and DeepSurv are some of ...
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### R: Survfit function - getting p value when specifying start.time

I would like to make a Kaplan-Meier curve for data on an alternate timescale. I'm interested only on events happening after 6months followup, so I use the ...
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### Time to event analysis

If we want to study about how many times of silicone vessel model for arterial blood gas simulator that can be punctured until they have structure failure such as hole or fluid leak.Can we use ...
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### average event time if event did not occur to everyone

How to determine the average or expected time duration of an event to a group statistically correct, if this event has not happened to everybody yet? One could consider only those to whom the event ...
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### Interpretation of an output from a SURVIVAL ANALYSIS - COX

I am struggling to understand the output of my survival analysis. These are the following codes and outputs: ...
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### Survival analysis: How to handle data where I know the event occurred, but I don't know when it occurred?

I am trying to do a survival analysis on some cancer data. I plan on doing Kaplan-Meier and Cox proportional hazards regression. I am interested in looking at the impact of various variables on ...
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### Survival analysis for an event that can influence death on its vecinity (both post and pre)

Is there a survival analysis methodology that can model the time till event (death by x), given another event that can (assumption) trigger death on the days nearby it? I am thinking of a pregnancy, ...
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### Best method for paired survival/time-to-event non-inferiority sample size calculation (using median survival time)?

I am trying to design a theoretical study in which one group of patients uses two wearable devices (i.e., every participant uses both devices) that gather information about their vitals, which is then ...
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### Remaining useful life for Weibull distributed lifetimes

Suppose we model component lifetimes with a two-parameter Weibull distribution. With $\alpha$ as the scale parameter and $\beta$ as the shape parameter, the component's mean survival time is known to ...
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### Allow for non-linear relationship between continuous independent variable and binary outcome in Cox regression

One thing that is not clear to me if how one can model non-linear relationship between continuous independent variables and binary outcome (i.e. dependent variable) in a Cox regression model. Suppose ...
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### Right censoring with recurrent events

I am dealing with retrospective survival data covering 60 years. Some people start their first spell in 1960, others start their first spell in 2000 (they are never left truncated). People can ...
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### Survival analysis for predictive maintenance on one machine

I have date for failures on one engine, 10 failures in total over a several years period, does it makes sense to split the data at each failure event and use the data with 10 failures as if I have ten ...
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### If I want to adjust survival analysis for a covariate, like age, should I add it "smth+age" or add an interaction with it "smth*age"?

I have a survival analysis with a categorical predictor called "smth". I want to adjust it for age. I don't have any idea if they can interact or not but I guess they can. Now, about the the ...