How to analyze data which has varying amounts of measurements recorded?

Question

I'm doing research which involves data pertaining to the physical characteristics, recorded at consistent intervals, of mice, with the mice's time at death being recorded as well. As such, some mice have more timepoints recorded than others. How should I approach modelling this?

I've considered using a hierarchical linear model, but I admittedly am not especially knowledgeable about this sort of analysis and was curious if anyone had suggestions. There are a large number of total datapoints for several hundred individual mice, so I had initially planned on using a neural network before I saw the variety of recorded data. Is there a way I could implement this approach in these circumstances? Or would this be unnecessary? Thanks for any help.

Edit: Basically, I have information pertaining to these mice over time, with data being collected every 4 weeks or so, and including blood glucose levels, food intake, and other similar metrics. There is also discrete information, such as the genetic strand of the mice, and lastly a "time of death" value. Because the mice died at very different times, certain things, such as food intake, have data corresponding to shorter or longer time periods (so every 4 weeks for 18 months versus every 4 weeks for 5 months depending on how long it lived). I'd like to make a model to determine which of these factors are most significant in how long these mice lived for, i.e. which provides the best information for predicting how long these mice will live. Hope this clears things up.

Answer 1

In principle, you could use a Cox survival regression with time-varying covariate values. The process, using the "counting process" data format, is explained in a vignette of the R survival package.

You set up a separate row for each time interval over which an individual has a constant set of measured values (e.g., each 4 weeks or so in your data). Each row contains the start and stop times of the interval, the covariate values in place during the interval, and an event indicator of whether the individual was alive or dead at the end of the interval.

The problem is defining useful values of time-varying covariates. A typical survival model assumes that the current risk of an event (death in your data) is related to the current values of the covariates. In this type of study, some aspect of the history of covariate values might be better associated with the current risk. You would have to apply your understanding of the subject matter to come up with a way to incorporate that history into the time-varying variables you supply as predictors to the model.

You might also consider a "joint model", combining a model of the longitudinally observed covariates along with a model of time to death. There are several packages available for such modeling noted in the R Survival Task View. A vignette in one of those packages, rstanarm, explains the approach:

Joint modelling can be broadly defined as the simultaneous estimation of two or more statistical models which traditionally would have been separately estimated. When we refer to a shared parameter joint model for longitudinal and time-to-event data, we generally mean the joint estimation of: 1) a longitudinal mixed effects model which analyses patterns of change in an outcome variable that has been measured repeatedly over time (for example, a clinical biomarker) and 2) a survival or time-to-event model which analyses the time until an event of interest occurs (for example, death or disease progression). Joint estimation of these so-called “submodels” is achieved by assuming they are correlated via individual-specific parameters (i.e. individual-level random effects).

That differs from the approach in the Cox model, which simply takes the covariate values as given and doesn't try to model the trajectories of their values over time. A joint model thus provides information about the covariates that a Cox model doesn't.