ps.balance: Statistical tests and standardized differences for balance...
In nonrandom: Stratification and matching by the propensity score

Description Usage Arguments Details Value Author(s) Examples

Apply statistical tests or calculate standardized differences for balance checks of covariate distributions between treatment groups

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  ps.balance(object, sel=NULL, treat=NULL, stratum.index=NULL,
  match.index=NULL,method="classical", cat.levels=2, alpha=5,
  equal=TRUE)

`object`	an object of class 'stratified.pscore', 'stratified.data.frame', 'matched.pscore', 'matched.data.frame', 'matched.data.frames' or a data frame.
`sel`	a data frame or a vector of integers or strings indicating covariates to be checked. The default is 'NULL', i.e. all variables in the data are selected.
`treat`	an integer or a string indicating the treatment variable in the data (and in the matched data if `ps.match()` is previously used). If the class of the input object is 'stratified.pscore' or 'matched.pscore', no specification is needed.
`stratum.index`	an integer or a string indicating the vector containing the stratum indices in the stratified data. No specification is needed if `ps.makestrata()` is previously used.
`match.index`	an integer or a string indicating the vector containing matching indices in data and in matched data. No specification is needed if `ps.match()` is previously used.
`method`	a string indicating the method used to decide about covariate balance between treatment groups. The default is 'classical', i.e., `ttest()` for continuous and `chisq.test()` for categorical covariates are applied, both in original data and in stratified or matched data. If 'stand.diff', standardized differences are calculated for covariates before and after stratification or matching (formulas are nicely explaind in: D. Yang and J.E. Dalton: 'A unified approach to measuring the effect size between two groups using SAS', Paper 335-2012, SAS Global Forum 2012: Statistics and Data Analysis).
`cat.levels`	an integer indicating the maximal number of levels of selected categorical covariates to consider them as categorical. The default is '2', i.e., covariates with more than two different values are considered as continuous. For example, cov1 and cov2 has three and four levels, respectively. `cat.levels` should be set to 4 to consider both as categorical. Caution: If covariates are factors and `cat.levels` is not appropriately chosen, errors can occur since `t.test` can not be performed!
`alpha`	an integer indicating the significance level (per cent) or the cutpoint at which the decision about balance or imbalance is made in case of standardized differences.
`equal`	a logical value. The default is 'TRUE', i.e. equally-sized weights are used to combine standard deviations of covariates in treatment groups for calculating standardized differences. If 'FALSE', weights are proportions of observations in treatment groups within data, matched data and strata.

Propensity score methods aims to eliminate imbalances in covariate distributions between treatment groups. An important issue is to check those after stratification or matching. Statistical tests or standardized differences can be used for those balance checks.

The usage of ps.balance() depends on the class of the input object. If either ps.makestrata() or ps.match() are previously used, treat, match.index and stratum.index are not needed, contrary to the case where the input object is a data frame.

ps.balance() returns an object of the same class as the input object. The number and the manner of the values depends on the used method:

`data`	a data frame containing the input data.
`data.matched`	a data frame limiting 'data' only to matched observations. It is only available if `ps.match()` is previously used.
`name.stratum.index`	a string indicating the name of the selected stratum variable. It is only available if `ps.makestrata()` is previously used.
`stratum.index`	a numeric vector containing stratum indices labeled by 'name.stratum.index'. It is only available if `ps.makestrata()` is previously used.
`intervals`	a vector of characters indicating intervals. It is only available if `ps.makestrata()` is previously used.
`stratified.by`	a string indicating the name of stratification variable. It is only available if `ps.makestrata()` is previously used.
`formula.pscore`	a formula describing formally the propensity score model fitted at last in `pscore()` .
`model.pscore`	an object of class `glm` containing information about the propensity score model fitted at last in `pscore()`.
`name.pscore`	a string indicating the name of propensity score at last estimated via `pscore()` and saved in the data.
`pscore`	a numeric vector containing the estimated propensity score labeled by 'name.pscore'.
`name.treat`	a string indicating the name of the treatment variable.
`treat`	a numeric vector containing the treatment variable labeled by 'name.treat'.
`matched.by`	a string indicating the name of the matching variable. It is only available if `ps.match()` is previously used.
`name.match.index`	a string indicating the name of the selected matching variable. It is only available if `ps.match()` is previously used.
`match.index`	a numeric vector containing the matching indices labeled by 'name.match.index' whereas '0' indicates 'no matching partner found'. It is only available if `ps.match()` is previously used.
`match.parameters`	a list of matching parameters including `caliper`, `ratio`, `who.treated`, `givenTmatchingC` and `bestmatch.first`. It is only available if `ps.match()` is previously used.
`bal.test`	a list of elements describing the results for the performed balance checks. balance.table a 2xK table describing the balance of K covariate distributions between treatment groups. The first/second row presents results from balance checks before/after stratification or matching. '0'/'1' indicates significant/non-significant differences between treatment groups. balance.table.summary a 2x2 table summarizing balance information from 'balance.table' across all K covariates. Only variables with balance tests done correctly are accounted for this table. covariates.NA a vector of strings indicating the names of covariates for which balance checks could not be done correctly. covariates.bal.before a vector of strings indicating the names of covariates balanced before stratification or matching. covariates.bal.after a vector of strings indicating the names of covariates balanced after stratification or matching. p.value a (s+1)xK table containing p-values from statistical tests for K covariates before (first row) and after (2nd, ..., (s+1)st row) stratification or matching (s is the number of defined strata; if matching, s=1). It is only available if `method`='classical'. Stand.diff a 2xK or (s+1)xK table containing standardized differences for K covariates before (first row) and after matching (2nd row) or stratification (2nd, ..., (s+1)st row). It is only available if `method`='stand.diff'. method a vector of strings indicating the scale of covariates assumed for balance checks ('none', 'bin', 'cat' or 'num'). The value 'none' means that no balance check was performed and 'bin', 'cat' and 'num' indicate binary, categorical and continuous. alpha a numeric value defining the significance level or the cut point at which the decision about balance or imbalance is made.

Susanne Stampf susanne.stampf@usb.ch

## STU1
data(stu1)
stu1.ps <- pscore(data    = stu1, 
                  formula = therapie~tgr+age)
stu1.match <- ps.match(object          = stu1.ps,
                       ratio           = 2,
                       caliper         = 0.5,
                       givenTmatchingC = FALSE,
                       matched.by      = "pscore",
                       setseed         = 38902)
stu1.balance <- ps.balance(object  = stu1.match,
                           sel     = c("tgr","age"),
                           method  = "stand.diff",    
                           alpha   =  20) 

## PRIDE
data(pride)
pride.ps <- pscore(data        = pride,
                   formula     = PCR_RSV~SEX+RSVINF+REGION+
                                 AGE+ELTATOP+EINZ+EXT,
                   name.pscore = "ps")
pride.strata <- ps.makestrata(object = pride.ps,
                              breaks = quantile(pride.ps$pscore,  
                                                seq(0,1,0.2)),
                              stratified.ps = "ps")
pride.balance <- ps.balance(object     = pride.strata,
                            sel        = c(2:6),
                            method     = "classical",
                            cat.levels = 4, 
                            alpha      = 5)