Hi Shelley,
Time-varying covariates can occur both naturally and by experimental design. My background is in biomedical research so I'll give a couple examples of each.
Naturally occurring:
1. Suppose you are trying to model the trajectory of systolic blood pressure in children through adolescence. The rate of increase may change with onset of puberty in girls. So you'd have an indicator for puberty, that takes effect only at puberty, and might affect both the absolute level of puberty (a jump?) and the rate of change after (slows the rate of increase, starting then.)
2. Cognitive performance trajectories in the elderly typically show a gradual decline in performance with age, but a stroke might lead to a drop in function, followed by a slow recovery (if not to baseline), so the "rate of decline" might actually turn into improvement.
In both cases, you'd need to include in the model a "main effect" for the event (puberty, stroke) that would be time varying, would not click in until the event happened, and then you'd have to include an interaction that would incorporate time since event (would not affect the slope before event.)
Experimental: Mainly cross-over designs.
- You are treating ovarihysterectomized female mice and measuring bone loss from the time of surgery. Outcome is a bone density measure. The introduction (or cessation) of drug treatment would change the trajectory of bone loss.
- You are considering the effect of a community intervention, and one set of communities starts right away and the other set has a delayed introduction (for ethical reasons, you can't have a strict control group that never gets the intervention.) For the delayed-start group, there's a time-varying treatment.
Hope this helps!
Laurel A. Beckett, Ph.D.
Professor and Chief, Division of Biostatistics
Department of Public Health Sciences
School of Medicine
University of California, Davis
Mailing address: Division of Biostatistics, MS1C
University of California
One Shields Avenue
Davis, CA 95616
Phone: (530) 754-7161
Fax: (530) 752-3239
Original Message------
Shelley-
I am relatively new to this forum but did an extensive amount of reliability work in the high tech industry so I thought I should chime in here. It would help to have a little more info here. Are there two datasets, one for each product? If so, I am imaging two survival curves that "cross" each other at some point. I am a little concerned that you may be reading more into the data post hoc than is justified. Focussing on the "mid-point" after seeing the data seems a little arbitrary unless there is strong physical knowledge a priori that this might be the mechanism.
In my experience, I would view this as a problem of fitting and comparing two distributions. In other words, we want to see if the two products generate the same life distribution. And if different, how do they differ. The fact that the curves "cross" might suggest the distributions are different; but it could just be natural variation.
So I would use JMP (or some other software with strong survival stats apps) to find a life distribution like lognormal or Weibull that fits each dataset reasonably well and then do some tests to see if we can consider the distribution parameters to be the same. And if not, which are different; for example, shape, scale, location. This might also help to understand and quanitfy the mechanism.
Hope this helps!
-Walt
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Walter Flom
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Original Message:
Sent: 09-19-2015 08:12
From: Stephen Simon
Subject: Splitting the survival curve
I've never done this, but when I listened to a talk about time-varying covariates, the speaker asked, rhetorically, what some examples of time-varying covariates are? The fist example, ironically, was time itself. Have you considered a time varying covariate model with a time by treatment interaction?
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Stephen Simon
Independent Statistical Consultant
P. Mean Consulting
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Original Message:
Sent: 09-18-2015 16:58
From: Shelley-Ann Walters
Subject: Splitting the survival curve
Hello.
Does anyone have any experience (or references to share) on how to analyze survival data which shows separation after a certain time point. I have a dataset which shows survival curves crossing at roughly the mid-time point (log rank and Wilcoxon-Gehan tests are all non-significant), and wonder if I can analyze the data to help support a conclusion that once survival is reached at the mid time-point, there is a benefit with one product over another?
Would it be acceptable to partition the time axis somehow and re-run the non-parametric tests?
Much thanks in advance.
Shelley
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Shelley-Ann Walters
3M
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