# Approach to a complex survival analysis

I'm a student who has unfortunately 'designed' quite a complicated experiment which I'm struggling to analyse statistically. I do like statistics but my experience is limited and I think there is great potential for error in the current datasets I have!

I'm looking at the survival of neurons from different patients in cultures with variable doses of a drug called tunicamycin which it was hypotheised would decrease survival. The dataset is very large and quite complicated so I've created two mock datasets available at https://docs.google.com/spreadsheets/d/168VVI4L36MYqnKrUAv4IiiPenkgWSCVySMUlGIYIip0/edit?usp=sharing

In brief, the experiment is as follows:

1. Cells are cultured from healthy patients (Patient 1 in the mock dataset) or from those with a disease caused by a genetic mutation (Patient 2, Mutation = 1)
2. Cells from patients with the mutation are 'gene corrected' repairing the mutation (Patient 2, Mutation = 0). Doing this allows the contribution of the genetic mutation to any phenomena observed to be assessed.
3. Cells are grown until the ages of 1 week or 3 weeks old (Age of first treatment (Weeks) = 1 or 3)
4. 1 week and 3 week old cells are imaged using a dye which makes live cells glow green (0h imaging to define baseline survival)
5. Cells are subject to a control treatment (Tunicamycin Dose = 0) or varying doses of tunicamycin (Tunicamycin Dose = 5 or 10)
6. At 24h (S(24h)) and 48h (S(48h)) post treatment, more of the live cell dye is added and cells which are still glowing green are counted as alive (0) or dead (1)
7. Each experiment was repeated three times (Experiment = A,B or C)

The data was analysed in two ways - both of which have limitations! The first way data was analysed is termed manual cell tracking (Sheet 1 of the Mock Dataset). Five cells from each condition were randomly selected from the 0h images. (I have tracked 49 cells from each experiment but data from only 5 cells is included in the mock dataset for user friendliness). The survival of these cells at 24h and 48h. Each cell is defined using Cell ID (Column 1 in the mock data) - e.g. Cell 4, from the first of the three experimental replicates (Experiment A), from healthy patient 1, without the mutation, at 1 week old when the experiment was performed, subject to control conditions (Tunicamycin dose = 0) was alive at 24h but dead at 48h.

It was suggested to me that Cox proportional hazard modelling may be a good way to analyse this dataset with clustering of cells by experiment (A,B or C) addressed by incorporation of random effects into the model. I would be interested to hear if readers feel this would be appropriate though I appreciate this is hard to assess without full access to the data - I have a concern that the assumption of proportionality is violated.

I have some concerns with the approach of manual cell tracking. Firstly, a small proportion of cells are sampled (thousands of cells are captured in each image). Secondly, cells that exist in clumps are censored as it is not possible to determine discrete cells from within the clumps of cells that form in these cultures. Additionally (and importantly), I am concerned my intraobserver reliability is low as the green signal is rarely completely abolished but does decrease in intensity. I think think decrease in intensity is important to consider as it reflects leakage of green dye from cells with compromised membranes. These cells are not as healthy as cells in which the membranes are intact and the green signal stays constant over the course of the experiment or decreases. For that reason, I have also analysed the data using a measure termed normalised mean integrated density (nmID). The logic is that the live cell dye is only green when it exists within cells so multiplying the mean intensity of the green signal in cells by the area provides a surrogate marker of cell viability (Mock Dataset Sheet 2 - nmID). nmID values at 24 and 48 hours have been calculated by dividing the mean integrated density at these time points by that at 0h and multiplying by 100 to give each answer as a percentage.

Analysis of the nmID dataset is something I am uncertain about. Presumably, the data is still best considered as right-censored though it is not in the conventional binary form of survival data. Secondly, as the green dye was added before each imaging cycle, the nmID can increase whereas by definition survival should only ever decrease. I have been experimenting with some mixed linear regression models with random effects to account for the clustering by Experiment (A,B or C) - I'm concerned about assumptions of linearity and uneven residual error distribution though I know very little about these modelling techniques and am learning on the go! I think some kind of regression may be the way to go though rather than a survival technique.

A number of questions can be addressed using this data - primarily though I would like to know if survival following treatment with tunicamycin, varies between patients and whether the presence of the mutation is important for any effect observed.

The work I have already done on this dataset focused on mixed linear regression modelling on R.

I'd be massively grateful for guidance as to which of these approaches is best suited to answer the question I have in mind or if there is a completely different set of techniques I should be considering.