Which software are you using for your analysis? ...R.gui can be quite useful in this analysis. the survfit function may help ...

Hi, you may know now that you need 24 tanks (1 animal in each tank) to avoid pseudoreplication if you want to run Kaplan-Meier. If you use mean to compare survival among treatments, you can only report 1 point of time or 1 event. Since an event is affected by another, an event is not independent anymore if you have two events in your analysis. Another solution, I can think of, is that you treat your tank as a treatment unit where 50% mortality is considered as an event. By doing so, you will have maximum 3 events. This might just be enough for stats but you must be caution when interpreting the result and open about the limitations.  An often suggestion for pseudoreplication is to consider the study as preliminary.  Please note that the log-rank test is used to test whether the difference between survival times between two groups is statistically different or not, and Cox allows to test the effect of the other independent variables. Cheers.      

Per treatment you have 3x8 = 24 animals. Since you do not measure one of these animals several times, I do not see where you should have pseudo-replication.

Due to the fact that groups of 8 of them live together in the same tank, you might get systematic differences between the tanks (sonetimes expressed as "the data from the anuimals within a tank is not independent"). However, in your experiment you actually have two "layers of replication": (a) animals within tank, and (b) tanks within your treatment.

The key question is how large these systematic differences between the tanks are. When they are large, they might prevent you from seeing (systematic) differences between your treatments. When they are small they may not matter at all.

So if your analysis shows clear treatment-effects without considering the tank-to-tank variability (i.e. when all 24 animals per treatment are used as a single group with n=24), then everything is fine. If not, the statistical consideration of the tank-to-tank variability might help. The ideal approch to do this is by a mixed-mode approach where the "tank" is the random factor. I am not sure if there is a Cox model that allows for random factors (survival analysis is not my topic). If this is not available or possible I also see the brute-force method suggested by Dung as a possible work-around: use each tank as the experimental unit to get a single value per tank. This value could be the "half-life" of the animals in the tank. This is worth only when there are drastic differences between the tanks.

Hi Tracy,

I'm not familiar with the specific tests you're trying to apply (do they calculate the % survival data? or do they provide between-treatment comparisons like a general linear model/ANOVA). Here's my two cents anyway.

Individuals within a tank can't be assumed to be independent unless you have a very high flow-through rate or water:biomass ratio such that interactions between individuals are negligible. Your design has an 'n' of 3 independent replicates per treatment (assuming water in each tank isn't drawn from the same sump, which is a whole other argument in itself!). This makes sense if your data are % mortality based on the proportional survival of eight individuals per tank, since you obviously can't have a % survival value for a single animal (so an 'n' of 8 or 24 is not really tenable). Furthermore, the data for each tank are obviously not independent over time, since what happens in a tank on Day 2 affects the data for that tank on Day 3. The most conservative approach, in my mind, would be to calculate % survival for each tank on each day, then use those values in a repeated-measures GLM (one "within subjects" factor: Day, one "between-subjects" factor: Treatment). This analysis only assumes independence between replicates (which you have, because you've got three tanks) and between treatments. Importantly, it doesn't assume independence between time-points, so you can use data taken from the same tank on multiple occasions.

As you said, a lot of the time you'll end up with the same outcome regardless of your statistical approach. It's just about knowing what your level of replication is before you crunch the numbers.

I hope some of this is helpful (and that I understood your question!).

T

If You use R:

package survival

function frailty()

allows  to add a simple random effects term to a Cox or survreg model

function cluster()

This is a special function used in the context of survival models. It identifies correlated groups of observations. Using cluster() in a formula implies that robust sandwich variance estimators are desired.

The first is a mixed-effects approach to correlation and the second a GEE approach, and these don't mix.

when using kepler meir shoold we use each replicate alone or all individuals in same time? (4 replicate each with 20 individual and 5 doses tested).thanks