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I am a student, working with a team on a large-scale ecological experiment. We want to analyze survival data which has been derived from an experimental design with some pseudo-replication. This pseudo-replication was not discovered, unfortunately, until the middle of the experiment, at which point the design could not be altered.

The experimental design involves comparing the survival data of several treatment groups, each comprised of 10 replicates (aquaria) with 10 individuals in each tank. We have measured mortality as a response variable, in response to different environmental stressors. The trouble is that we cannot say that each of the deaths that occurred, have occurred independently since each tank has many individuals. We would like to acknowledge this problem and address it in our analysis.

All of the survival analysis tools we are aware of, assume independence between replicates. We are considering using Kaplan-Meier curves, Cox proportional hazard, or even a glm with Gamma error distributions.

Any ideas about how we can properly address this problem in order to detect a difference in survivorship between the treatment groups?

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  • $\begingroup$ Roughly what proportion of the individuals died by the end of the experiment? If it's reasonably low there may be little advantage of survival analysis over ignoring the time to death and treating died/survived as a binary outcome, which could be considerably simpler. $\endgroup$
    – onestop
    Nov 11 '10 at 23:46
  • $\begingroup$ A more complex option is frailty models - i'm too tired to attempt say any more now but i've added the 'frailty' tag above so you can click that and look at the answers to the other q with this tag. $\endgroup$
    – onestop
    Nov 11 '10 at 23:53
  • $\begingroup$ @onestop- Thanks for contributing some perspective and ideas! I will look into the frailty model option. We had about 20 to 40% mortality in the treatment levels. After some discussion, we are now considering analyzing the replicates, not the individual deaths, since the replicates are independent from one another. Using this perspective, maybe we can arrive with a mean mortality value for each replicate and compare them (accounting for censoring also). Another option could be to compare the chance to survive in each replicate, then compare replicates to each other. $\endgroup$ Nov 12 '10 at 11:02
  • $\begingroup$ ...maybe Repeated Measures ANOVA could be an option, using replicate level information. We would need to use something that would allow for non-normal data distribution. $\endgroup$ Nov 12 '10 at 11:02
  • $\begingroup$ Any thoughts on these ideas? (thanks!) $\endgroup$ Nov 12 '10 at 11:03
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Here's some thoughts on what I'd do using relatively simple methods (i.e. avoiding frailty models, which I admit I've never used and don't really understand, so someone else may like to provide an answer involving them). I'm assuming you don't have other forms of censoring apart from the end of the experiment and that there are no time-dependent exposures (i.e. the treatment is either constant or applied only at the start before any deaths have taken place)

  • Do some descriptive statistics and Kaplan-Meier plots ignoring the issue of dependence and therefore without reporting or displaying standard errors, confidence intervals or p-values.
  • Ignore the time component and just count the number of deaths out of the total starting number in each aquarium. Fit a generalized linear model with a binomial distribution to these counts, using either a logistic link function (to give odds ratios) or a log link function (giving easier-to-interpret risk ratios at the price of potential problems with fitting the model). I think this is along the same lines as the analysis you said you're considering in the first comment to the question. As your mortalities are reasonably low, the loss in power over a full survival analysis with frailty modelling will probably be modest. This overcomes the dependence issue as you are using each aquarium as the unit of analysis instead of each individual.
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  • $\begingroup$ Thanks onestop! We are definitely going to use each aquarium as the unit of analysis so we will not have dependent data. We are still formulating the best approach. I will post the final decision once it is made. $\endgroup$ Nov 14 '10 at 19:45

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