library(psborrow2)
library(cmdstanr)Propensity scores (PS) methods offer various ways to adjust analyses for differences in groups of patients. Austin (2013) discusses various approaches for using PS with survival analyses to obtain effect measures similar to randomized controlled trials. Wang et al. (2021) discuss using PS for IPTW, matching and stratification in combination with a Bayesian analysis. These methods allow for the separation of the design and analysis into two stages, which may be attractive in a regulatory setting. Another approach is the direct inclusion of the PS as a covariate in the outcome model.
WeightItThe WeightIt
package can calculate PS and other balancing weights with a number of
different methods, such as generalized boosted modeling
(method = "gbm"). In addition, weights can be calculated
differently for different estimands. Here, we specifying
estimand = "ATT", to calculate weights for estimating the
average treatment effect among the treated (ATT).
library(WeightIt)
#> Error in `library()`:
#> ! there is no package called 'WeightIt'
example_dataframe <- as.data.frame(example_matrix)
example_dataframe$int <- 1 - example_dataframe$ext
weightit_model <- weightit(
int ~ cov1 + cov2 + cov3 + cov4,
data = example_dataframe,
method = "gbm",
estimand = "ATT"
)
#> Error in `weightit()`:
#> ! could not find function "weightit"
summary(weightit_model)
#> Error:
#> ! object 'weightit_model' not foundAnother useful package is cobalt, which
provides tools for assessing balance between groups after weighting or
matching. It is compatible with many matching and weighting packages.
See the vignette
for more details. We can use the cobalt package to assess
balance with bal.plot().
library(cobalt)
#> Error in `library()`:
#> ! there is no package called 'cobalt'
bal.plot(weightit_model)
#> Error in `bal.plot()`:
#> ! could not find function "bal.plot"“Love plots” can also be generated that compare the populations before and after weighting:
love.plot(weightit_model, stars = "std")
#> Error in `love.plot()`:
#> ! could not find function "love.plot"The PS values can be copied into the data set and the analysis object can be constructed as before.
example_dataframe$att <- weightit_model$weights
#> Error:
#> ! object 'weightit_model' not found
example_matrix_att <- create_data_matrix(
example_dataframe,
ext_flag_col = "ext",
outcome = c("time", "cnsr"),
trt_flag_col = "trt",
weight_var = "att"
)
#> Error in `create_data_matrix()`:
#> ! Assertion on 'weight_var' failed: Must be a subset of {'id','ext','trt','cov4','cov3','cov2','cov1','time','status','cnsr','resp','int'}, but has additional elements {'att'}.
analysis_att <- create_analysis_obj(
data_matrix = example_matrix_att,
outcome = outcome_surv_exponential("time", "cnsr", prior_normal(0, 10000), weight_var = "att"),
borrowing = borrowing_full("ext"),
treatment = treatment_details("trt", prior_normal(0, 10000)),
quiet = TRUE
)
#> Error:
#> ! object 'example_matrix_att' not found
result_att <- mcmc_sample(analysis_att, seed = 123)
#> Error in `h()`:
#> ! error in evaluating the argument 'x' in selecting a method for function 'mcmc_sample': object 'analysis_att' not foundMatchItA variety of matching methods, including PS matching are implemented in the MatchIt package.
As described in the Getting Started vignette, it can be useful to check the imbalance before matching.
library(MatchIt)
#> Error in `library()`:
#> ! there is no package called 'MatchIt'
# No matching; constructing a pre-match matchit object
no_match <- matchit(trt ~ cov1 + cov2 + cov3 + cov4,
data = example_dataframe,
method = NULL, distance = "glm"
)
#> Error in `matchit()`:
#> ! could not find function "matchit"
summary(no_match)
#> Error:
#> ! object 'no_match' not foundHere we are matching treated to untreated to select the most comparable control group, regardless of whether they are internal or external. For simplicity let’s try a 1:1 nearest matching approach.
match_11 <- matchit(trt ~ cov1 + cov2 + cov3 + cov4,
data = example_dataframe,
method = "nearest", distance = "glm"
)
#> Error in `matchit()`:
#> ! could not find function "matchit"
summary(match_11)
#> Error:
#> ! object 'match_11' not foundset.seed(123)
plot(match_11, type = "jitter", interactive = FALSE)
#> Error in `h()`:
#> ! error in evaluating the argument 'x' in selecting a method for function 'plot': object 'match_11' not foundDetermining whether the balance after matching is appropriate is
beyond the scope of this vignette. You can read more in the MatchIt
Assessing Balance vignette. Again the cobalt package
can be useful here.
However, if you are happy with the results of the matching procedure,
you can extract the data for use in psborrow2.
example_matrix_match <- create_data_matrix(
data = example_dataframe[match_11$weights == 1, ],
ext_flag_col = "ext",
outcome = c("time", "cnsr"),
trt_flag_col = "trt"
)
#> Error:
#> ! object 'match_11' not foundanalysis_match <- create_analysis_obj(
data_matrix = example_matrix_match,
outcome = outcome_surv_exponential("time", "cnsr", prior_normal(0, 10000)),
borrowing = borrowing_full("ext"),
treatment = treatment_details("trt", prior_normal(0, 10000)),
quiet = TRUE
)
#> Error:
#> ! object 'example_matrix_match' not found
result_match <- mcmc_sample(analysis_match, seed = 123)
#> Error in `h()`:
#> ! error in evaluating the argument 'x' in selecting a method for function 'mcmc_sample': object 'analysis_match' not foundThe models also support fixed weights on the likelihood contributions from each observation. This is equivalent to fixed power prior weights. This allows for the combination of models, such as an IPTW + commensurate prior approach.
analysis_iptw_bdb <- create_analysis_obj(
data_matrix = example_matrix_att,
outcome = outcome_surv_exponential("time", "cnsr", prior_normal(0, 10000), weight_var = "att"),
borrowing = borrowing_hierarchical_commensurate("ext", prior_gamma(0.01, 0.01)),
treatment = treatment_details("trt", prior_normal(0, 10000)),
quiet = TRUE
)
#> Error:
#> ! object 'example_matrix_att' not found
result_iptw_bdb <- mcmc_sample(analysis_iptw_bdb, seed = 123)
#> Error in `h()`:
#> ! error in evaluating the argument 'x' in selecting a method for function 'mcmc_sample': object 'analysis_iptw_bdb' not foundWe can also use weights to specify a fixed power prior model. Here we set the power parameter \(\alpha = 0.1\) for the external controls.
example_matrix_pp01 <- cbind(example_matrix, pp_alpha = ifelse(example_matrix[, "ext"] == 1, 0.1, 1))
analysis_pp01 <- create_analysis_obj(
data_matrix = example_matrix_pp01,
outcome = outcome_surv_exponential("time", "cnsr", prior_normal(0, 10000), weight_var = "pp_alpha"),
borrowing = borrowing_full("ext"),
treatment = treatment_details("trt", prior_normal(0, 10000)),
quiet = TRUE
)
result_pp01 <- mcmc_sample(analysis_pp01, seed = 123)For comparison, we also fit a full borrowing, a no borrowing, and a BDB model without weights.
result_full <- mcmc_sample(
create_analysis_obj(
data_matrix = example_matrix,
outcome = outcome_surv_exponential("time", "cnsr", prior_normal(0, 10000)),
borrowing = borrowing_full("ext"),
treatment = treatment_details("trt", prior_normal(0, 10000)),
quiet = TRUE
),
seed = 123
)
result_none <- mcmc_sample(
create_analysis_obj(
data_matrix = example_matrix,
outcome = outcome_surv_exponential("time", "cnsr", prior_normal(0, 10000)),
borrowing = borrowing_none("ext"),
treatment = treatment_details("trt", prior_normal(0, 10000)),
quiet = TRUE
),
seed = 123
)
result_bdb <- mcmc_sample(
create_analysis_obj(
data_matrix = example_matrix_att,
outcome = outcome_surv_exponential("time", "cnsr", prior_normal(0, 10000)),
borrowing = borrowing_hierarchical_commensurate("ext", prior_gamma(0.01, 0.01)),
treatment = treatment_details("trt", prior_normal(0, 10000)),
quiet = TRUE
),
seed = 123
)
#> Error in `h()`:
#> ! error in evaluating the argument 'x' in selecting a method for function 'mcmc_sample': object 'example_matrix_att' not foundmodels <- list(
"No borrowing" = result_none,
"Full borrowing" = result_full,
"Power Prior 01" = result_pp01,
"ATT Weights" = result_att,
"IPTW + BDB" = result_iptw_bdb,
"Matching 1:1" = result_match,
"BDB" = result_bdb
)
#> Error:
#> ! object 'result_att' not foundWe can use summary() to extract the variable of interest
and specify summary statistics.
results_table <- do.call(rbind, lapply(
models,
function(i) i$summary("HR_trt", c("mean", "median", "sd", "quantile2"))
))
#> Error:
#> ! object 'models' not found
knitr::kable(cbind(models = names(models), results_table), digits = 3)
#> Error:
#> ! object 'models' not foundWe can extract a draws object from each model and plot
the posterior distribution of the treatment hazard ratio.
plot(density(models[[1]]$draws("HR_trt")),
col = 1, xlim = c(0, 2), ylim = c(0, 9), lwd = 2,
xlab = "HR_trt",
main = "Posterior Hazard Ratio"
)
#> Error in `h()`:
#> ! error in evaluating the argument 'x' in selecting a method for function 'plot': object 'models' not found
for (i in 2:7) {
lines(density(models[[i]]$draws("HR_trt")), col = i, lty = i, lwd = 2)
}
#> Error:
#> ! object 'models' not found
legend("topright", col = seq_along(models), lty = seq_along(models), legend = names(models))
#> Error:
#> ! object 'models' not foundHere we see no borrowing and full borrowing at the extremes and the other methods in between.