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I have data where different compounds were applied to cells and a numerical readout was measured.

  • Each compound was used at multiple concentrations
  • The readout was measured at multiple points in time.
  • Compound-dose combinations were applied to two types of cells.

The goal is to identify compounds which affect the cell types in very different ways.

My current approach is to use the R package drc to fit 3-parameter log-logistic models to estimate a half-maximal effective concentration (EC50) for each (cell type, time point) combination. Afterward, I use ad hoc methods like examining differences of EC50s to identify compounds which affect the two cell types differently.

Is there a way to fit a dose-response model which accounts for the time variable as well, or ideally both the time variable and the cell type variable? A solution in R is preferred.

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  • $\begingroup$ Make sure that you inspect the quality of the fits by eye, as there are many circumstances where a logistic fit can converge to a nonsense result with concentration-response curve data. You can not rely on the EC50s otherwise. $\endgroup$
    – Michael Lew
    Commented Mar 21, 2018 at 20:08
  • $\begingroup$ @MichaelLew: Yes, I take care to subsequently exclude fits that clearly indicate the concentration range tested didn't actually cover enough of the dynamic range for the fit to make sense at all. $\endgroup$
    – Marcus Emilsson
    Commented Mar 21, 2018 at 20:13
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    $\begingroup$ Two clarification questions: First, ¿do you wish to explore one single model for the two cell types? or ¿are you happy looking at separate models for the different cells? Second, for the different compounds, ¿is the selection of compounds "random" in nature? or ¿where the compounds specifically chosen for specific comparisons? (Essentially, I'm wondering if the different compounds can be treated as random effects or not.) $\endgroup$
    – Gregg H
    Commented Mar 24, 2018 at 13:21
  • $\begingroup$ @GreggH: (1) I suppose separate models for each cell type is appropriate. (2) Yes, the compounds may be considered as "random" in nature. $\endgroup$
    – Marcus Emilsson
    Commented Mar 26, 2018 at 18:06
  • $\begingroup$ Do you have an expectation for how your response changes with time? How does this interact with concentration? $\endgroup$
    – mkt
    Commented Mar 27, 2018 at 12:49

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What you are looking for is a way to characterize dose-response surfaces formed by a series of single-time dose-responses. Sun et al (Risk Analysis 15: 247, 1995) illustrate an approach using maximum-likelihood estimation based on assumptions about "shape factors" for dose-responses and time-responses. In that approach you could compare the parameter values found to characterize the responses of each of the cell lines, but you might be limited by restrictions and assumptions on the forms of the shape factors.

A more recent and more general approach that even allows for evaluation of multiple outcomes is given by Patel et al (Ann Appl Stat. 6: 1707, 2012). They use splines to model the dose- and time-responses and a Bayesian approach with appropriate choices of priors and Markov Chain Monte Carlo sampling to ultimately evaluate dose- and duration-response slopes, maximal safe doses/times, and maximum responses. The approach was apparently developed for high-throughput biologic testing of nanomaterials on a single cell type, but I see no reason why it can't also (a) be used for standard drug testing and (b) be used to compare responses of different cell types to the same drug rather than compare different drugs on the same cell type. Visualization of responses by color over 2-dimensional plots of time by dose seem to more than make up for not having easily interpretable functional forms of the response surfaces. I'm not sure that I can legally copy the image here, but the paper is freely available from the link above; look at Figure 6 for an example of what can be done.

Strictly, this site doesn't deal with implementations in software. Patel et al did use R for at least some of their work, but I'm not aware of a particular package that implements their entire approach. The rsm package in R might give you something close to what you need. It fits response surfaces (not just dose-time response surfaces) but is limited to combinations of first-order, two-way, pure quadratic, and second-order functions to fit the responses in a generalization of linear modeling, so it might not be sufficiently flexible for your purpose.

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