Time-Dependent Greedy Selection of Controls
method_greedy.RdThis documentation page describes the matching process used when setting method="greedy" in the match_time function and gives a explanation on which arguments may still be used in this case. No additional arguments are currently supported when using this method.
Details
Due to the nature of this approach, almost none of the arguments of the match_time function may be used when using method="greedy", because they do not make sense in the context of greedy selection of controls. More specifically, only the arguments formula, data, id, inclusion, start, stop, method, replace_cases and verbose can be used with this method.
How it works:
All other methods implemented in this package use some sort of matching to select a pre-specified number of controls from the pool of available data. When using method="greedy", this is not the case. Instead of performing a selection, every single individual that is eligible to be a control at the point in time at which "matching" occurs is selected as control. For example, suppose that at \(t = 10\) there are 100 individuals in the dataset. Of these individuals, 20 receive the treatment for the first time at \(t\) and 10 already have received the treatment before \(t\). The remaining 70 individuals are all eligible to be sampled as controls at this point in time (if they fufill the inclusion criteria) and are thus all used as controls.
This process is repeated at each point in time at which at least one individual switches from the control to the treated condition. The selection of controls proceeds as if replace_at_t=TRUE, regardless of the value supplied to the argument. Replacement of controls over time is neccessary, because otherwise there woule be no controls left after the first time at which an individual receives treatment.
This method might seem odd at first, but as Gran et al. (2010) have shown, it does work quite well for some estimands of interest if the analysis is done in an appropriate manner. These authors propose the following three step analysis: (1) censoring the controls whenever they later receive treatment (as implemented in the argument censor_at_treat of the add_outcome function), (2) calculating inverse probability of censoring weights for each "trial" (each .treat_time), and (3) using a stratified weighted Cox model to perform the actual confounder adjustment.
References
Gran, Jon Michael, Kjetil Røysland, Marcel Wolbers, Vanessa Didelez, Jonathan A. C. Sterne, Bruno Ledergerber, Hansjakob Furrer, Viktor von Wyl, and Odd O. Aalen (2010). "A Sequential Cox Approach for Estimating the Causal Effect of Treatment in the Presence of Time-Dependent Confounding Applied to Data from the Swiss HIV Cohort Study". In: Statistics in Medicine 29, pp. 2757-2768.
Karim, Mohammad Ehsanul, John Petkau, Paul Gustafson, Robert W. Platt, and Helen Tremlett (2018). "Comparison of Statistical Approaches Dealing with Time-Dependent Confounding in Drug Effectiveness Studies". In: Statistical Methods in Medical Research 27.6, pp. 1709-1722.
Examples
library(data.table)
library(MatchTime)
if (requireNamespace("survival")) {
library(survival)
# load some example data from the survival package
data("heart", package="survival")
## time-dependent greedy matching
## there does not have to be anything on the RHS of formula, because no
## actual matching is performed
m.obj <- match_time(transplant ~ 1, data=heart, id="id",
method="greedy")
}