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

1 vote

Proportional hazards assumption meaning

The hazard function isn't the same for everyone. The hazard functions for each covariate need to be proportional - hence the name. So, regardless of how h(t) bounces around, the ratio of the hazard fu …
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4 votes
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survival analysis without enough data

It is still useful - I wouldn't make really bold claims about what happens past 600 days if I were you, but seeing a clear departure in one category or the other, even if they don't eventually hit zer …
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5 votes
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Is this a problem for Survival analysis?

However…you said you do care, so turning to survival analysis: Yes, "time to event" questions are survival analysis questions, and this looks like a pretty clear one. … You're now in the domain of competing risks survival analysis, of which the cure models suggested in the comments are a sub-set. …
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13 votes

Finding median survival time from survival function

Assuming your survival curve is the basic Kaplan-Meier type survival curve, this is a way to obtain the median survival time. From Machin et al. … Survival Analysis: A Practical Approach: If there are no censored observations (...) the median survival time, $M$, is estimated by the middle observation of the ranked survival times $t_{(1)}, t_{ …
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10 votes
3 answers
3k views

Mean survival time for a log-normal survival function

I've found plenty of formulas showing how to find the mean survival time for an exponential or Weibull distribution, but I'm having considerably less luck for log-normal survival functions. … Given the following survival function: $$S(t) = 1 - \phi \left[ {{{\ln (t) - \mu } \over \sigma }} \right]$$ How does one find the mean survival time. …
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How should I interpret the exp(coef) hazard ratio in Cox regression?

Alright, a couple things. First: The hazard is defined as the instantaneous probability of an event at time t, conditional on it not having occured in any previous time. So yes, the hazard ratio is …
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3 votes

Survival analysis with categorical variable

You then use a robust variance estimator that takes care of the fact that you have some non-independence in your data, and you can run any survival analysis you want. … I suspect if you're looking for a 1 year probability of failure, you'd use some parametric estimator of the survival curve, or a Kaplan-Meyer type analysis. …
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5 votes
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Does the 'reference group' in a Cox proportional hazards model have to exist?

Most regression models can smooth over areas where there are no data. This is not necessarily a feature - if there is a reason they don't exist in your data (notably, that there is some reason they ca …
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3 votes
2 answers
843 views

Absolute vs. Relative Difference in Survival Time - Is this possible?

I suspect there isn't, because these models assume proportional survival times, so the relative measure will be constant, but the absolute measure will vary over time, but I wanted to make sure before …
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23 votes

In survival analysis, why do we use semi-parametric models (Cox proportional hazards) instea...

The range of survival analysis tools ranges from the fully non-parametric, like the Kaplan-Meier method, to fully parametric models where you specify the distribution of the underlying hazard. …
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6 votes
1 answer
8k views

Mean survival time of a Weibull distribution

I'm trying to calculate the mean survival time of a Weibull distribution, and am getting what feels like an errant estimate of the mean--and each source I look up for how to calculate the mean gives a … Thus, for a model with two $\beta$ terms, $\beta_0 = 2.18$ and $\beta_1 = 0.66$ along with an $\alpha$ of 0.88, is the mean survival time, as evaluated by R for a non-integer Gamma function as follows: …
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5 votes

Survival analysis: continuous vs discrete time

There will be tied survival times in most analysis, but big, clear chunks of ties at particular events is troubling. I would think long and hard about the study itself, how its collecting data, etc. … Because, outside of some methodological needs to use one type of time or the other, how you model survival should depend on whether or not the underlying process is discrete or continuous in the world. …
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5 votes

Are survivor functions meaningful with proportional hazards models?

From that, I've asserted that that means you can't use the Cox model to generate estimates of the survival function, only the differences between them, in front of people who should know better and been …
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10 votes

How to report hazard ratios from a Cox proportional hazards model in English?

To a pure lay-audience, I'd go with "Cat owners are 1.2 times as likely to purchase a couch than non-cat owners." Things like "at any point t during the study period", or trying to define the idea of …
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5 votes
1 answer
2k views

PROC NLMIXED and PROC LIFEREG not arriving at the same answer for Log-normal survival function

Related question I have a project where, despite being able to implement some parametric models in LIFEREG, it is somewhat more convenient to do it in NLMIXED. Verifying that this technique works, I …
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