In the psrwe, PS-integrated matching method (Chen, et al., 2021) is also implemented for leveraging real-world evidence in evaluation of diagnostic tests for low prevalence diseases. This example is based on PS matching and stratification on an important baseline covariate (e.g., disease stage) which may have major impact on the sensitivity of diagnostic.
Not that this example is only for demonstrating PS matching on low prevalent disease and when the resource may be very limited. For different scenarios, other PS-integrated approaches may be more appropriate.
data(ex_dta)
dta_ps <- psrwe_est(ex_dta,
v_covs = paste("V", 1:7, sep = ""),
v_grp = "Group",
cur_grp_level = "current",
ps_method = "logistic")
dta_ps## This is a sing-arm study. A total of 1031 RWD subjects and
## 200 current study subjects are used to estimate propensity
## scores by logistic model. A total of 5 RWD subjects are
## trimmed and excluded from the final analysis. The following
## covariates are adjusted in the propensity score model: V1,
## V2, V3, V4, V5, V6, V7.
##
## The following table summarizes the number of subjects in
## each stratum, and the distance in PS distributions
## calculated by overlapping area:
##
## Stratum N_RWD N_Current Distance
## 1 Stratum 1 729 40 0.561
## 2 Stratum 2 156 40 0.721
## 3 Stratum 3 78 40 0.804
## 4 Stratum 4 50 40 0.810
## 5 Stratum 5 13 40 0.796The propensity score (PS) estimation above based on psrwe_est() may provide stratification. This matching example psrwe_match() below will match the RWD (real-world data) to the current study with \(2:1\) ratio (ratio = 2) based on the covariate V1 (strata_covs = "V1"). The (categorical) covariate V1 will be used to create strata, then the data will be matched within each stratum based on PS values based on the nearest neighbor algorithm.
Please see Section of Demo example below for the other option using different matching algorithm and package.
dta_ps_match <- psrwe_match(dta_ps,
ratio = 2,
strata_covs = "V1")
dta_ps_match## This is a sing-arm study. A total of 1031 RWD subjects and
## 200 current study subjects are used to estimate propensity
## scores by logistic model. A total of 631 RWD subjects are
## trimmed and excluded from the final analysis. The following
## covariates are adjusted in the propensity score model: V1,
## V2, V3, V4, V5, V6, V7.
##
## The matching is stratified by the following covariate(s):
## V1. A total of 0 current study subjects are matched by less
## than 2 RWD subjects. Please note unequal matching may cause
## unbalance in covariate distributions of the current and
## matched RWD subjects.
##
## The following table summarizes the number of subjects in
## each stratum:
##
## Stratum N_RWD N_Current
## 1 V1=0 108 54
## 2 V1=1 292 146The returned object dta_ps_match will be used to calculate discounting parameters for the study design. Note that the results are based on two stages indicated by V1 rather than five strata originally set by dta_ps above.
ps_bor_match <- psrwe_borrow(dta_ps_match,
total_borrow = 30)
ps_bor_match## A total of 30 subjects will be borrowed from the RWD. The
## number 30 is split proportional to the number of current
## control subjects in each stratum. The following table
## summarizes the number of subjects to be borrowed and the
## weight parameter in each stratum:
##
## Stratum N_RWD N_Current Proportion N_Borrow Alpha
## 1 V1=0 108 54 0.27 8.1 0.075
## 2 V1=1 292 146 0.73 21.9 0.075The PSCL analysis (Wang, et al., 2020) can be done below with the same step as other PSCL examples.
rst_cl <- psrwe_compl(ps_bor_match,
outcome_type = "binary",
v_outcome = "Y_Bin")
rst_cl## With a total of 30 subject borrowed from the RWD, the point
## estimate is 0.303 with standard error 0.029.The outcome analysis can be done in the same way. Note that typically the Wilson score method will be used for constructing confidence intervals.
oa_cl <- psrwe_outana(rst_cl, method_ci = "wilson", mu = 0.40)
oa_cl## - Method: ps_cl, Outcome Type: binary, Study Type: single-arm
## - StdErr Method: jk
## - Confidence Interval: wilson, Level: 0.95
## - Test Method: p_value
## H0: theta >= 0.400 vs. Ha: theta < 0.400
## - Analysis Results:
## Stratum Mean StdErr Lower Upper p-value
## Overall 0.303 0.0285 0.247 0.365 0.000347The script in “psrwe/demo/sec_4_3_ex.r” source file has the full example for the PS matching which can be run via the demo("sec_4_3_ex", package = "psrwe").
Note the R package optim may provide other matching algorithms, however, it may need additional license permission. Please check with package announcement if the package is turned on.
Chen, W.-C., Li, H., Wang, C., Lu, N., Song, C., Tiwari, R., Xu, Y., and Yue, L.Q. (2021). Evaluation of Diagnostic Tests for Low Prevalence Diseases: A Statistical Approach for Leveraging Real-World Data to Accelerate the Study. Journal of Biopharmaceutical Statistics, 31(3), 375-390.
Wang, C., Lu, N., Chen, W. C., Li, H., Tiwari, R., Xu, Y., and Yue, L.Q. (2020). Propensity score-integrated composite likelihood approach for incorporating real-world evidence in single-arm clinical studies. Journal of Biopharmaceutical Statistics, 30(3), 495-507.