Survival analysis interpretation
MANOJ KUMAR
Marc Schwartz
Hi Manoj,
Two questions:
- Can you clarify if this is a Kaplan-Meier analysis or a Cox regression analysis?
- Have you created a plot of the survival curves for your groups? If not, you should do so and share it here if you can.
The plot visualization may give some insights here as to what is happening, especially if the proportional hazard assumption has been violated, which would be my initial guess here. That would be inferred from crossing survival curves in the plot. The plot would also give us some indication of median survival in your groups, presuming that the survival curves cross 0.5.
Giving us some details on your dataset such as the sample size per group, the unit of time being used, perhaps the code being used, would be helpful as well.
Regards,
Marc Schwartz
Tzippy Shochat
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MANOJ KUMAR
| trans | var (risk factor) | hr | cil | ciu | p | sig | |
| 1 | W -- W+I | Female | 1.03 | 1.01 | 1.06 | 0.014 | 1 |
| 2 | W -- W+I | Age of Patients | 0.99 | 0.99 | 1 | 0 | 1 |
| 3 | W -- W+I | race1 White | 1.13 | 1 | 1.28 | 0.051 | 0 |
| 4 | W -- W+I | race2 Black | 1.23 | 1.09 | 1.4 | 0.001 | 1 |
| 5 | W -- W+I | race3 ASIAN | 0.87 | 0.66 | 1.15 | 0.327 | 0 |
| 6 | W -- W+I | race4 NHPI | 0.73 | 0.49 | 1.08 | 0.112 | 0 |
| 7 | W -- W+I | race5 AIAN | 1.04 | 0.68 | 1.58 | 0.85 | 0 |
| 8 | W -- W+I | NonHispanic | 0.97 | 0.91 | 1.03 | 0.281 | 0 |
| 9 | W -- W+I | Hispanic | 1.07 | 0.99 | 1.17 | 0.086 | 0 |
| 10 | W -- W+I | Diabetes | 1.11 | 1.07 | 1.15 | 0 | 1 |
| 11 | W -- W+I | A1C value | 1.01 | 1 | 1.03 | 0.087 | 0 |
| 12 | W -- W+I | A1C Well Controlled | 0.96 | 0.92 | 1.01 | 0.124 | 0 |
| 13 | W -- W+I | A1C Moderately controlled | 0.96 | 0.94 | 0.98 | 0.001 | 1 |
| 14 | W -- W+I | Age at Wound | 1 | 1 | 1.01 | 0.033 | 1 |
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Assistant Professor
Centre for Economic Studies & Planning (CESP), School of Social Sciences (SSS-II),
Jawaharlal Nehru University, New Delhi-110067, India.
Stephen Simon, P.Mean Consulting
This is almost certainly a units conversion problem. If you were looking at mortality risk and the independent variable was birth weight in grams, then the hazard ratio increases by a small amount that is lost when you round. You're comparing the risk of mortality for a 1500 gram baby to a 1501 gram baby. If you instead use birth weight in kilograms, the problem disappears. You are looking at the risk of mortality for a 1.5 kilogram baby compared to a 2.5 kilogram baby.
I'm not sure what your independent variable is, but check out and
possibly convert the units of measure.
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MANOJ KUMAR
| Female | Age of Patients | race1 White | race2 Black | race3 ASIAN | race4 NHPI | race5 AIAN | NonHispanic | Hispanic | Diabetes | A1C value | A1C Well Controlled | A1C Moderately controlled | Age at Wound |
| Cat(2 | Cont. | Cat(6 | Cat(3 | Cat(2 | Cont. | Cat(3 | Cont. | ||||||
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Marc Schwartz
Hi Manoj,
Thanks for the additional information.
As Tzippy and Stephen noted, especially considering the 50k sample size, the HR for age, which is presumably in years as a continuous variable, is significant for a one-year increase in age.
The likelihood is that if you were to print out the CIs for age for that transition state to a greater level of precision, you would likely find that the upper bound is slightly less than 1, whereas the rounding for the output function that you are using is displaying the value of 1, thus seems to be artificially in conflict with the p value.
Bear in mind, as often pointed out, that statistical significance and clinical relevance are not synonymous. So even though the p value for a one-year increase in age is significant, the relative clinical impact of a one-year increase on the probability of the outcome(s) of interest over time is minimal.
Looking at your truncated multi-column figure, it would seem that for other transition states, you have a similar phenomenon, with the HR for age being very slightly less than or very slightly more than 1, presumably differentiated by the green versus red colors, respectively.
Your A1C covariate appears to have a similar situation.
Thus, you might consider plotting the impact of age over time, on the probability of your outcome event of interest, selecting specific relevant ages to generate multiple predicted probability curves, which can be more insightful in terms of showing clinically meaningful differences between the ages over time, as opposed to having a fixed number in a table. For example, visually compare 50 to 60 or 70, while holding other variables constant, if those ages make sense here.
Also, among other things, you might want to consider using a spline function on age to allow it to be non-linear, as opposed to presuming a linear (straight-line) relationship to your outcome(s). The same consideration for A1C and any other continuous covariates that may be present.
I might also offer some other thoughts, based upon your figures, which is that you appear to have a rather large number of outcome states, transitions and covariates. On the face of it, given your large sample size, this would perhaps seem reasonable, albeit, in this setting, it is the number of events, not patients, that is ultimately relevant.
Thus, you may presumably have low event counts in at least some of the combinations, leading to low precision in the estimates. That may give you pause to consider whether they should be included in your overall analysis, or even collapsed into larger aggregate groups if that makes clinical sense in your context.
Visually, there are notable differences across many of the curves, with good separation in some, material overlap in others, and differences in early versus late events, all of which may raise other issues pertaining to relevant underlying assumptions for the analysis.
Since you are using R, you might also want to review the several vignettes for the survival package by Therneau et al, if you have not already:
https://cran.r-project.org/web/packages/survival/index.html
These might give you some other insights as well, and there is content across multiple vignettes there that cover multi-state models, the use of the ridge() function and related topics.
Regards,
Marc
On Mon, Jan 8, 2024 at 12:07 PM Marc Schwartz <wdwg...@gmail.com> wrote:
Hi Manoj,
Two questions:
1. Can you clarify if this is a Kaplan-Meier analysis or a Cox regression analysis?
2. Have you created a plot of the survival curves for your groups? If not, you should do so and share it here if you can.
Abhaya Indrayan
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MANOJ KUMAR
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Marc Schwartz
Hi Manoj,
Please review the multi-state models and competing risks vignette for the survival package:
https://cran.r-project.org/web/packages/survival/vignettes/compete.pdf
which as I noted yesterday, has worked examples for several scenarios, including the multi-state transition type of model that you have.
For example, using the “mfit3” model that they create, which begins on the bottom of page 9, starting below with the model creation, after they create the required dataset:
mfit3 <- survfit(Surv(tstart, tstop, event) ~ sex, data=data3, id=id)
> print(mfit3, rmean=240, digits=2)
Call: survfit(formula = Surv(tstart, tstop, event) ~ sex, data = data3,
id = id)
n nevent rmean*
sex=F, (s0) 690 0 118.2
sex=M, (s0) 809 0 104.1
sex=F, pcm 690 59 3.2
sex=M, pcm 809 56 2.7
sex=F, death 690 423 118.6
sex=M, death 809 540 133.2
*restricted mean time in state (max time = 240 )
Note that the output presents a summary of the restricted mean times in each state for each gender, given the model specification above. There are various options that can adjust the output as well, including the max time as a cutoff, which they set above to be 240 months, and where months is the time unit for the example dataset. You can adjust that output as you may require, and can review the help pages for the relevant R functions in the survival package.
You can also display the transition states by printing out the ‘transitions’ part of the mfit3 model object:
> mfit3$transitions
to
from pcm death (censored)
(s0) 115 860 409
pcm 0 103 12
death 0 0 0
Finally, you can generate estimates of the probabilities for each state for each gender at specific time points, using the following basic approach with the summary() function. If you do not specify the times vector, for example just using summary(mfit3), you will get a much larger table output with a series of times for each state depending upon your dataset.
> summary(mfit3, times = c(12, 36, 60, 96), scale = 12)
Call: survfit(formula = Surv(tstart, tstop, event) ~ sex, data = data3,
id = id)
sex=F
time n.risk n.event Pr((s0)) Pr(pcm) Pr(death)
1 569 69 0.894 0.00953 0.0968
3 504 73 0.786 0.01430 0.2001
5 442 62 0.696 0.01913 0.2846
8 310 107 0.540 0.01558 0.4448
sex=M
time n.risk n.event Pr((s0)) Pr(pcm) Pr(death)
1 646 117 0.847 0.00398 0.149
3 559 94 0.729 0.01064 0.260
5 453 99 0.603 0.01339 0.384
8 293 113 0.455 0.01184 0.533
Note that because the data being used for the example has months for the time unit, I used a vector of months for the time argument, and combined that with the scale argument to convert the output to years, giving 1, 3, 5, and 8 year estimates for each of the event types in the dataset.
Your model is more complex, given the larger set of transition states and covariates, so you will need to play around with the output as you may require to obtain the results you need.
Regards,
Marc
From:
meds...@googlegroups.com <meds...@googlegroups.com> on behalf of MANOJ KUMAR <manoj...@jnu.ac.in>
Date: Monday, January 8, 2024 at 10:44 PM
To: meds...@googlegroups.com <meds...@googlegroups.com>
Subject: Re: {MEDSTATS} Survival analysis interpretation
Rajeev Kumar
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MANOJ KUMAR
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