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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Trying to understand formula for the Survival Function (survival analysis)

I'm trying to learn the Cox Proportional Hazards Model on my own, and found this link that describes it in clear terms. But when I get to Formula (5) ($S(t) = \exp(−H(t))$) I can't figure out where ...
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1answer
155 views

Relationship between sample mean and sample survival probability

I am not sure if this question is very naive, but I was wondering if there is a relationship between sample mean and sample survival probability. For an exponential distribution with mean $\mu$, $$S(...
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1answer
1k views

interval censored survival analysis with time dependent covariates

I'm working on a long-term, large tree data set from Africa. I have data on the same set of individuals from year 2006, 2008, 2011 and 2015. The data consist of tree status (alive/dead) at each time ...
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1answer
948 views

Time varying coefficient in Cox model

I have a model for survival after an injury that is borderline passing the Schoenfeld test for the proportional hazards assumption (cox.zph() in R). However, ...
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1answer
3k 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 ...
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1answer
189 views

Time-wise treatment effect / survival analysis

Let's say I have some kind of survival data - i.e. I'm giving a drug that may cause mortality. So I have three patients: A, B and C. All are given the drug at Time t1. Let's say patient A dies at ...
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1answer
593 views

How to select the best classification scheme in survival analysis (SurvivalROC, R2, Concordance, AIC)?

I'm studying several schemes on classifying patients about their survival time. Let me illustrate the problem with supposing I have just two schemes. Let's suppose that Scheme 1 put the patients in 5 ...
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1answer
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How to simulate a Cox proportional hazards model with change point and code it in R

I have a model that has the following characteristics: The covariate $X$ follows a $Be(1/3)$. If $X=0$, survival time $Y$ follows an $E=Exponential (1)$. If $X=1$, survival time $Y$ is generated as $...
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Adding high-dimensional data to mutivariate Cox model

I have a survival cancer clinical trials dataset from which I have generated Cox models using forward likelihood ratio testing within R. These models are based on 'traditional' cancer variables (eg. ...
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Do Oscar winners live longer? How account for length and time-dependent bias

I read a bunch of references on the bias that one should beware of when analyzing survival times. One classic example is the one of Oscar winners: a miss-specification of the model leads to two kind ...
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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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Confidence interval for the restricted mean in survival analysis

What is the recommended way of calculating confidence intervals for the restricted mean in survival analysis? Here are some example data, taken from the paper Chris Barker (2009), The Mean, Median, ...
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How to simplify coxme survival models?

I have some questions about specifying a coxme (mixed-effects Cox proportional hazards) model in R and then simplifying it after reading the ...
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Analysis of survival data using binomial GLM with offset

We are interested in determining whether there's an association between frequency of screening visits and cancer outcomes and whether that differs by race. We have Medicare data to analyze this. ...
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Machine learning methods which takes time-to-event into account?

My vague understanding is that machine learning methods are based on classification labels. How about a survival type of problem? That is to say, not only "have event" or "have no event", but also "...
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why there is no “error” term in survival analysis?

Where is the error term behind the following model: $$h_i(t) = h_0(t) \exp \left ( \sum_{k = 1}^p \beta_k z_{ik} \right )$$
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321 views

Is the use of cutoffs for dichotomisation of biomarkers really that bad?

Tissue microarrays are commonly used to assess potential prognostic biomarkers. For decades now, many authors (I would even say the majority) feel the need to categorise their continuous predictors, ...
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2answers
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Proportionality assumption in Cox Regression Model

When dealing with a Cox regression model, we have to assume that the proportionality assumption holds. I have read about a lot of methods to check if this assumption holds or not but I have not ...
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4answers
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Start time requirements or assumptions for survival analysis

We have prospective data from an observational registry and wish to consider the affects of a gene on time to cardiovascular events. The data includes standard data like age, gender, ... and also the ...
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495 views

Does the Cox proportional hazards model process past values for time-varying covariates?

I am currently working on a survival analysis project and am struggling regarding the inner workings of the coxph function of the ...
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1answer
3k views

Time to event with no censoring - use survival or normal regression?

I have some time to event data, but the population is only those who had the event (specifically, my cohort is all kidney tx recipients who were readmitted within one year of discharge for a specific ...
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1answer
160 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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3answers
251 views

Survival Analysis or Not?

I am conducting an analysis where the outcome is time to an event in minutes, with no censoring of the event, and in this situation the event always occurs. The distribution of the outcome variable ...
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1answer
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How does lifelines calculate baseline hazard in CoxPHFitter?

I have learnt that the baseline hazard function in the Cox PH Model is unspecified. Does it mean that I can specify it as any functions and select the best one during experiments? I also see that the ...
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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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3answers
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Cumulative Incidence vs. Kaplan Meier to estimate probability of failure

To estimate the probability failure in medical sciences, it is not atypical to use 1-KM. However this does not account for competing risks, such as death by natural causes or causes unrelated with the ...
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How to estimate the Poisson distribution with one event occurrence?

Let us say we observed one event on 1 Jan 2005, and we were observing the events since 2000. What's the best estimate of Poisson distribution? One approach is to set intensity $\lambda=1/18$ per year....
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1answer
309 views

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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1answer
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Handling borderline cases of the proportional hazards assumption

In order to verify the assumption of proportional hazards, I plotted the following: $$\log(-\log(S(t))) = \log(\Lambda(t))$$ If the hazards are indeed proportional for two groups, these curves should ...
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3answers
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Values for integral of square of standard Brownian process

I am trying to generate values in a table for the following function: $$ W = \int_0^1 [B(t)]^2 dt $$ Where $B(t)$ is a standard Brownian motion. Example: $W_{0.05} = 1.656$, $W_{0.025} = 2.135$. ...
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2answers
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Change-point in Cox survival model

I am looking to fit a Cox proportional hazard survival model. Looking at the K-M curve (below) for one variable (with 2 categories) it appears there is a change in hazard ratios at around day 110. I ...
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1answer
571 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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2answers
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Proportional hazards vs proportional odds for modeling ordinal data

When working with ordinal response data, we can use a proportional odds model to calculate the log odds in favor of one category over another. Often we use a logit link yielding the following model: $$...
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1answer
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Can survival models be used for modeling progression along a sequence of events?

I am wondering whether survival analysis can be used to model situations where the subject progresses through stages. Here is an example of what I mean: Suppose I want to track the progress of ...
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Determining sample size for proportional hazard

I am in the design phase for a longitudinal study examining the effect of a predictor (neighborhood risk score) on time to an outcome (re-arrest), as well as whether or not the variation explained by ...
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Logrank test for trend (proportional hazards)

How one can create a logrank test for trend and does it differ from normal logrank test? Any suggestions or literature? Maybe some R examples and functions?
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Inference with only left-censored data

Suppose I have a data set that is only left-censored data, ex: <5, <5, <5, <10, <10, <10 A technique to handle left-censored data is the Kaplan Meier estimate, see page 5 of this ...
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1answer
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Discrete Time Survival Analysis - Correct Way to Write Survival Function

I have seen several ways to write (and calculate and interpret) a survivor function in discrete time survival analysis and I wonder which is correct or if they both are, but the interpretation and/or ...
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3answers
569 views

Understanding survival at time function

This question is related to a few others (Here,Here) on the topic as I have been searching for information. Hopefully this one is sufficient. 1) I am seeing differences in the relationship between ...
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2answers
165 views

Left censoring with time-varying covariates

I have a data with some participants entering the study with a disease of interest already present. For others, I have several points of observation where different factors were measured (such as ...
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1answer
276 views

Survival analysis when exact time to event unknown?

My dataset (example here) represents a long-term capture-mark-recapture study, approximately 20 years duration. I am interested in looking at how the survival of animals is influenced by their sex and ...
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1answer
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Interpretation of Weibull Accelerated Failure Time Model Output

In this case study I have to assume a baseline Weibull distribution, and I'm fitting an Accelerated Failure Time model, which will be interpreted by me later on regarding both hazard ratio and ...
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1answer
382 views

Must the hazard function integrate to infinity?

Consider a non-negative random variable $T$ arising in the context of survival/reliability analysis (usually representing the time until some event occurs). It is well-known that the survival ...
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1answer
502 views

Predict when a user logins next

I am building a user login prediction system. This is my first time building any prediction system. Main aim is to predict when a user might login next in future. That is i need to predict "Time". I ...
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1answer
12k views

Estimating median survival times from Kaplan-Meier plot inspection

I've gone through the various questions relating to Kaplan-Meier plots and survival estimates, but I haven't really been able to find anything to help with this specific scenario. Sometimes, when ...
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3answers
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Hazard function of a gamma distribution

The system we are working on is biological, more specifically the distribution of specific events across a chromosome. This can be thought of as 1D array (the chromosome) across which points can be ...
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1answer
719 views

Schoenfeld residual independent of time?

I've seen it claimed (e.g. in these notes ) that "Schoenfeld residuals are, in principle, independent of time." Can this be right? Consider the following situation: You are using a Cox model to ...
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1answer
7k views

Impute missing values using aregImpute

I have a data frame with 61 columns. Some data is missing. I read in Steyerberg's book about aregImpute in Hmisc. I used it with ...
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1answer
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In which situation does the log-rank test have low power?

This question is complementary to question 1 asked by @Jesse here. It is about the case when we don't find a significant result when performing the log-rank test and when the proportional hazard ...
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2answers
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Can survival analysis be used to predict earthquakes?

Given survival analysis relates to an analysis/prediction of time to an event, I was wondering if it was possible to be used to predict eathquakes. If so, how would one go about carrying out that ...

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