Calculate the Fragmented Care Density for all Patients

This function calculates the Fragmented Care Density Index as defined by Engels et al. (2024) for each patient in the supplied dataset. Works well with large patient-sharing networks.

Usage

fragmented_care_density(data, pat_col=1, weights, type,
                        by_connection=FALSE, data_frame=TRUE)

Arguments

data: A data.frame like object containing exactly two columns. One should include only patient IDs and the other one only provider IDs. Each row should denote one patient-provider contact. Multiple contacts (same rows) are allowed but have no effect on the outcome. Both patient and provider IDs should be unique, which means that one ID may not be in both rows.
pat_col: Specifies which column of data includes the patient IDs. If the first column contains the patient IDs this should be kept at 1, if the second column contains the patient IDs it should be set to 2.
weights: A data.frame containing three columns called "from" (character), "to" (character) and "weight" (numeric). The first two columns should contain types of providers, thus defining different provider connections. All possible non-redundant connections need to be specified this way. The "weight" column should include the weight associated with that connection. When using by_connection=TRUE this argument can be set to NULL, because it won't be needed then. See examples for more information.
type: A data.frame containing two columns called "ID" (containing all provider IDs) and "Type" (containing the type of the provider). Both columns should be character vectors.
by_connection: Either TRUE or FALSE (default). If TRUE this function returns the person and connection-specific sums of weights and simple care densities instead of returning the fragmented care density directly. This may be useful to estimate weights for the weights argument.
data_frame: Set this argument to TRUE to return a data.frame instead of the data.table format that is used under the hood.

Details

The Fragmented Care Density is an extension of the classic Care Density (see care_density) and was proposed by Engels et al. (2024). It is also a measure of care coordination, but it allows a lot more flexibility by using different weights for different provider-type connections. For example, it may make sense to weight the amount of patients shared by two general providers differently than the amount of patients shared by a general provider and a specialist. Formally, the fragmented care density is defined as:

$$FC_p = \sum_{j = 1}^{k} w_j \frac{s_j}{n_p(n_p - 1) /2},$$

where $n_p$ is the number of different providers patient $p$ visited and $w_j$ are some connection specific weights. $k$ is defined as:

$$k = {l \choose 2} + l,$$

with $l$ being the number of different provider types. Finally, $s_j$ is the sum of the number of patients shared by all doctors of a specific connection type. See Engels et al. (2024) for more information.

Under the hood, this function uses the igraph package to construct a patient-sharing network from the provided data to calculate the weights. It then uses the data.table package to efficiently calculate the care densities from a resulting edge list with weights.

Value

Returns a single data.frame (or data.table) containing output depending on the specification of the by_connection argument.

When by_connection=FALSE was used the output only includes the patient id ("PatID") and the calculated fragmented care densities ("fragmented_care_density").

When by_connection=TRUE was used instead, the output includes the patient id ("PatID"), the connection-type ("connection") the sum of all weights ("sum_weights"), the number of providers seen by each patient ("n") and the calculated simple care density ("care_density").

References

Pollack, Craig Evan, Gary E. Weissman, Klaus W. Lemke, Peter S. Hussey, and Jonathan P. Weiner. (2013). "Patient Sharing Among Physicians and Costs of Care: A Network Analytic Approach to Care Coordination Using Claims Data". Journal of General Internal Medicine 28 (3), pp. 459-465.

Engels, Alexander, Claudia Konnopka, Espen Henken, Martin Härter, and Hans-Helmut König. (2024). "A Flexible Approach to Measure Care Coordination Based on Patient-Sharing Networks". BMC Medical Research Methodology 24 (1), pp. 1-12.

Author

Robin Denz

Examples

library(CareDensity)
library(data.table)
library(igraph)

# some arbitrary patient-provider contact data
data <- data.frame(PatID=c("1", "1", "1", "2", "2", "3", "3", "4", "5"),
                   ArztID=c("A", "C", "D", "A", "D", "A", "D", "D", "C"))

# defining the provider types
d_type <- data.frame(ID=c("A", "C", "D"),
                     Type=c("GP", "GP", "Psychiatrist"))
                     
# defining the connection-specific weights
d_weights <- data.frame(from=c("GP", "GP", "Psychiatrist"),
                        to=c("GP", "Psychiatrist", "Psychiatrist"),
                        weight=c(1.1, 0.8, 1.3))

# calculate the fragmented care densities
fragmented_care_density(data, type=d_type, weights=d_weights)
#>   PatID fragmented_care_density
#> 1     1                1.433333
#> 2     2                2.400000
#> 3     3                2.400000
#> 4     4                      NA
#> 5     5                      NA

# calculate only the connection-specific sums and care-densities per patient
# NOTE: "weights" can be set to NULL here because they won't be used
fragmented_care_density(data, type=d_type, weights=NULL, by_connection=TRUE)
#>   PatID        connection sum_weights n care_density
#> 1     1           GP - GP           1 3    0.3333333
#> 2     1 Psychiatrist - GP           4 3    1.3333333
#> 3     2 Psychiatrist - GP           3 2    3.0000000
#> 4     3 Psychiatrist - GP           3 2    3.0000000
#> 5     4              <NA>          NA 1           NA
#> 6     5              <NA>          NA 1           NA