Matching controls with time-dependent covariates to treated cases with varying treatment time without replacement

In this article, we will explore the problem of matching controls with time-dependent covariates to treated cases with varying treatment times while ensuring that each control unit is matched to only one treated unit. This problem arises in various fields such as economics, public health, and social sciences where the goal is to compare the outcomes of a treatment or intervention between groups.

We will discuss how to achieve this using R and the MatchIt package, which provides an easy-to-use interface for matching data.

Background

The problem can be described as follows: we have two datasets, one containing treated cases (df_treated) and another containing control units (df_control). The treatment time is represented by a variable in the dataset. We want to match each control unit to the closest treated case based on a set of covariates (e.g., age, sex, income). However, we also want to ensure that no control unit is matched to more than one treated unit.

The answer provided suggests using the unit.id argument in the matchit function to declare no replacement all across strata. This approach ensures that each control unit is matched to only one treated unit.

However, this solution may not be sufficient if we have multiple strata (i.e., groups of treated cases with similar treatment times). In such cases, we need to match the control units within each stratum individually and then combine the results.

In this article, we will discuss how to achieve matching without replacement for both simple and complex strata structures.

Matching Without Replacement

To match controls without replacement, we can use the matchit function with the replace = FALSE argument. This tells R not to replace any matched units (i.e., control units) if a better match is found in the same stratum or another stratum.

Here’s an example:

MatchIt::matchit(MATCHING_CASE ~ COV_A + COV_B, 
                 data = df, 
                 method = "nearest",
                 exact="MATCHING_STRATA",
                 unit.id="ID",
                 replace = FALSE)

This will match each control unit to the closest treated case based on the specified covariates without replacing any matched units.

However, if we have multiple strata and want to ensure that no control unit is matched to more than one treated unit across all strata, we need a more complex solution.

Matching Within Each Stratum

One approach is to match control units within each stratum individually using the matchit function with the replace = FALSE argument. We then combine the results by matching the matched units across all strata.

Here’s an example:

# Split the data into strata based on treatment time
df_strat <- df %>% 
  group_by(TREATMENT_TIME) %>%
  mutate(MATCHING_STRATA = row_number())

# Match control units within each stratum individually
df_matched <- lapply(df_strat$MATCHING_STRATA, function(x) {
  MatchIt::matchit(x ~ COV_A + COV_B, 
                   data = df_control %>% filter(MATCHING_STRATA == x),
                   method = "nearest",
                   exact="MATCHING_STRATA",
                   unit.id="ID",
                   replace = FALSE)
})

# Combine the results by matching the matched units across all strata
df_matched_combined <- Reduce(rbind, lapply(df_matched, function(x) {
  MatchIt::matchit(MATCHING_STRATA ~ MATCHING_STRATA,
                    data = rbind(x, df_treated),
                    method = "nearest",
                    exact="MATCHING_STRATA",
                    unit.id="ID",
                    replace = FALSE)
}))

This approach ensures that each control unit is matched to only one treated unit across all strata.

Matching with 1:k Ratio

Another important consideration is the matching ratio, which specifies the number of matches per unit. In our example, we used a simple matchit function without specifying a matching ratio.

If we want to use a 1:1 matching ratio (i.e., one control unit matched to one treated unit), we can modify the matchit function as follows:

MatchIt::matchit(MATCHING_CASE ~ COV_A + COV_B, 
                 data = df, 
                 method = "nearest",
                 exact="MATCHING_STRATA",
                 unit.id="ID",
                 replace = FALSE,
                 ratio = 1)

This will match each control unit to the closest treated case with a matching ratio of 1:1.

Conclusion

Matching controls without replacement is an important problem in data analysis, particularly when working with time-dependent covariates. In this article, we discussed how to achieve matching without replacement using the MatchIt package in R. We covered two main approaches: simple matching and complex strata matching. We also provided examples of how to use a 1:k ratio for matching.

By following these steps and considering the complexities of your data, you can ensure that each control unit is matched to only one treated unit while achieving optimal matching with minimal bias.

Last modified on 2024-07-18