sbdecomp {SBdecomp}

Selection Bias Decomposition

Description

This function decomposes the estimated selection bias to quantify what proportion of the estimated selection bias is explained by each observed confounder used in the propensity score model when estimating propensity score weighted treatment effects. The function offers two approaches - confounder inclusion or removal, and offers two estimation approaches - parametric or nonparametric.

Usage

sbdecomp(outcome, treatment, confounders, data=NULL, type = "inclusion", estimation 
= "parametric", Bonly = T, balance = T, n.trees = 20000, interaction.depth = 4, 
shrinkage = 0.005, verbose = FALSE, stop.method = c("es.max"), cv.folds = 0,
standard.error = F, boot.rep=500)

Arguments

outcome

Continuous outcome; numeric vector or name of the variable in supplied data

treatment

Binary treatment indicator, 0 or 1; numeric vector or name of the variable in supplied data

confounders

a data frame of confounders with names or a vector containing the names of the confounders in supplied data (each confounder must be either numeric or factor)

data

data containing all variables; required if names provided in outcome, treatment, and/or confounders arguments above

type

The type of method for selection bias deocomposition; options are inclusion or removal, default is inclusion

estimation

The type of estimation that should be used; options are parametric (based on logistic regression) or nonparametric (based on generalized boosted models [GBM]), default is parametric

Bonly

TRUE or FALSE; whether the user only wants the quantities B which are the proportions of the selection bias explained by each confounder, default is TRUE

balance

TRUE or FALSE; whether the user wants balance information, default is TRUE

n.trees

The n.trees for the nonparametric GBM approach, if using nonparametric estimation; default is 20000

interaction.depth

The interaction depth for the nonparametric GBM approach, if using nonparametric estimation; default is 4

shrinkage

The shrinkage for the nonparametric GBM approach, if using nonparametric estimation; default is 0.005

verbose

TRUE or FALSE for the nonparametric GBM approach, if using nonparametric estimation; default is FALSE

stop.method

The stopping method for the nonparametric GBM approach, if using nonparametric estimation; default is "es.max"

cv.folds

The cross-validation folds for the nonparametric GBM approach, if using nonparametric estimation; default is 0

standard.error

TRUE or FALSE; whether the user wants standard error estimates for the resulting estimates, obtained using boostrapping; default is FALSE; note that if using nonparametric estimation, obtaining the standard error estimates will be very time-intensive

boot.rep

The number of bootstrap replications to be used when calculating the standard error; default is 500

Details

Details can be found in: Parast, L and Griffin, BA (2020). "Quantifying the Bias due to Observed Individual Confounders in Causal Treatment Effect Estimates". Statistics in Medicine, In press. Please email [e-mail] for a current version.

Value

A list is returned:

delta.naive

Estimated naive treatment effect

p.value.delta.naive

P-value for estimated naive treatment effect

conf.int.delta.naive

95% confidence interval for estimated naive treatment effect

delta.fully.adjusted

Estimated treatment effect after adjusting for all variables

p.value.delta.fully.adjusted

P-value for estimated treatment effect after adjusting for all variables

conf.int.delta.fully.adjusted

95% confidence interval for estimated treatment effect after adjusting for all variables

B

The proportion of the selection bias explained by each variable

estimated.selection.bias

The estimated selection bias, only if Bonly = FALSE

lambda

The defined selection bias movement when including/removing a variable, only if Bonly = FALSE

delta.each

The adjusted delta including only each variable or dropping each variable (depending on type), only if Bonly = FALSE

balance.naive.mean

mean of the standardized effect size differences across all variables between the two groups; only if balance = TRUE

balance.naive.max

max of the standardized effect size differences across all variables between the two groups; only if balance = TRUE

balance.fully.adjusted.mean

mean of the standardized effect size differences across all variables between the two groups, after weighting with propensity score weights calculated using all variables; only if balance = TRUE

balance.fully.adjusted.max

max of the standardized effect size differences across all variables between the two groups, after weighting with propensity score weights calculated using all variables; only if balance = TRUE

balance.mean

mean of the standardized effect size differences across all variables in the relevant propensity score model between the two groups, after weighting with relevant propensity score weights; if using type = "inclusion" and variable included is a factor, output will be the mean effect size difference across all levels; only if balance = TRUE

balance.max

max of the standardized effect size differences across all variables in the relevant propensity score model between the two groups, after weighting with relevant propensity score weights; if using type = "inclusion" and variable included is a factor, output will be the max effect size difference across all levels; only if balance = TRUE

B.standard.error

The estimated standard error for the estimated proportion of the selection bias explained by each variable; only if standard.error = TRUE

lambda.standard.error

The estimated standard error for the estimated selection bias movement when including/removing a variable; only if standard.error = TRUE

Author(s)

Layla Parast

References

Parast, L and Griffin, BA (2020). "Quantifying the Bias due to Observed Individual Confounders in Causal Treatment Effect Estimates". Statistics in Medicine, 39(18): 2447- 2476.

Examples

data(petsdata)
sbdecomp(outcome = petsdata$genhealth, treatment = petsdata$gotdog, confounders = 
as.data.frame(petsdata[,c(2:13)]), type = "inclusion", estimation = "parametric",
balance = FALSE)

sbdecomp(outcome = petsdata$genhealth, treatment = petsdata$gotdog, confounders = 
as.data.frame(petsdata[,c(2:13)]), type = "inclusion", estimation = "parametric", 
Bonly =FALSE, balance = TRUE) 

sbdecomp(outcome = "genhealth", treatment = "gotdog", confounders = c("age",
"ismale", "race_coll","hhsize","ownhome", "married",  "ontanf", "hhincome",
"fulltime","spouse_fulltime" ,"liveinhouse", "ruralurban"), data = petsdata, 
type = "inclusion", estimation = "parametric", Bonly =FALSE, balance = TRUE)