Distributional comparison of synthesised and observed data

Distributional comparison of synthesised data set with the original (observed) data set using propensity scores.

This function can be also used with synthetic data NOT created by syn(), but then additional parameters not.synthesised and cont.na might need to be provided.

Usage

# S3 method for synds
utility.gen(object, data,
            method = "cart", maxorder = 1, k.syn = FALSE, tree.method = "rpart",
            max.params = 400, print.stats = c("pMSE", "S_pMSE"), resamp.method = NULL,
            nperms = 50, cp = 1e-3, minbucket = 5, mincriterion = 0, vars = NULL,
            aggregate = FALSE, maxit = 200, ngroups = NULL, print.flag = TRUE,
            print.every = 10, digits = 6, print.zscores = FALSE, zthresh = 1.6,
            print.ind.results = FALSE, print.variable.importance = FALSE, ...)

# S3 method for data.frame
utility.gen(object, data, not.synthesised = NULL, cont.na = NULL,
            method = "cart", maxorder = 1, k.syn = FALSE, tree.method = "rpart",
            max.params = 400, print.stats = c("pMSE", "S_pMSE"), resamp.method = NULL,
            nperms = 50, cp = 1e-3, minbucket = 5, mincriterion = 0, vars = NULL,
            aggregate = FALSE, maxit = 200, ngroups = NULL, print.flag = TRUE,
            print.every = 10, digits = 6, print.zscores = FALSE, zthresh = 1.6,
            print.ind.results = FALSE, print.variable.importance = FALSE, ...)

# S3 method for list
utility.gen(object, data, not.synthesised = NULL, cont.na = NULL,
            method = "cart", maxorder = 1, k.syn = FALSE, tree.method = "rpart",
            max.params = 400, print.stats = c("pMSE", "S_pMSE"), resamp.method = NULL,
            nperms = 50, cp = 1e-3, minbucket = 5, mincriterion = 0, vars = NULL,
            aggregate = FALSE, maxit = 200, ngroups = NULL, print.flag = TRUE,
            print.every = 10, digits = 6, print.zscores = FALSE, zthresh = 1.6,
            print.ind.results = FALSE, print.variable.importance = FALSE, ...)


# S3 method for utility.gen
print(x, digits = NULL, zthresh = NULL,
               print.zscores = NULL, print.stats = NULL,
               print.ind.results = NULL, print.variable.importance = NULL, ...)

Arguments

object: it can be an object of class synds, which stands for 'synthesised data set'. It is typically created by function syn() and it includes object$m synthesised data set(s) as object$syn. This a single data set when object$m = 1 or a list of length object$m when object$m > 1. Alternatively, when data are synthesised not using syn(), it can be a data frame with a synthetic data set or a list of data frames with synthetic data sets, all created from the same original data with the same variables and the same method.
data: the original (observed) data set.
not.synthesised: a vector of variable names for any variables that has been left unchanged in the synthetic data. Not required if oject is of class synds
cont.na: a named list of codes for missing values for continuous variables if different from the R missing data code NA. The names of the list elements must correspond to the variables names for which the missing data codes need to be specified. Not required if oject is of class synds
method: a single string specifying the method for modeling the propensity scores. Method can be selected from "logit" and "cart".
maxorder: maximum order of interactions to be considered in "logit" method. For model without interactions 0 should be provided.
k.syn: a logical indicator as to whether the sample size itself has been synthesised.
tree.method: implementation of "cart" method that is used when method = "cart". It can be "rpart" or "ctree".
max.params: the maximum number of parameters for a "logit" model which alerts the user to possible fitting failure.
print.stats: statistics to be printed must be a selection from "pMSE", "SPECKS", "PO50", "S_pMSE", "S_SPECKS", "S_PO50". If print.stats = "all", all of the measures mentioned above will be printed.
resamp.method: method used for resampling estimates of standardized measures can be "perm", "pairs" or "none". Defaults to "pairs" if print.stats includes "S_SPECKS" or "S_PO50" or synthesis is incomplete else defaults to "perm" if method is "cart" or to NULL, no resampling needed, if method is "logit". "none" can be used to get results without standardized measures e.g. in simulations.
nperms: number of permutations for the permutation test to obtain the null distribution of the utility measure when resamp.method = "perm".
cp: complexity parameter for classification with tree.method "rpart". Small values grow bigger trees.
minbucket: minimum number of observations allowed in a leaf for classification when method = "cart".
mincriterion: criterion between 0 and 1 to use to control tree.method = "ctree" when the tree will not be allowed to split further. A value of 0.95 would be equivalent to a 5% significance test. Here we set it to 0 to effectively disable this test and grow large trees.
vars: variables to be included in the utility comparison. It can be a character vector of names of variables or an integer vector of their column indices. If none are specified all the variables in the synthesised data will be included.
aggregate: logical flag as to whether the data should be aggregated by collapsing identical rows before computation. This can lead to much faster computation when all the variables are categorical. Only works for method = "logit".
maxit: maximum iterations to use when method = "logit". If the model does not converge in this number a warning will suggest increasing it.
ngroups: target number of groups for categorisation of each numeric variable: final number may differ if there are many repeated values. If NULL (default) variables are not categorised into groups.
print.flag: TRUE/FALSE to indicate if any messages should be printed during calculations. Change to FALSE for simulations.
print.every: controls the printing of progress of resampling when resamp.method is not NULL. When print.every = 0 no progress is reported, otherwise the resample number is printed every print.every.
...: additional parameters passed to glm, rpart, or ctree.
x: an object of class utility.gen.
digits: number of digits to print in the default output values.
zthresh: threshold value to use to suppress the printing of z-scores under +/- this value for method = "logit". If set to NA all z-scores are printed.
print.zscores: logical value as to whether z-scores for coefficients of the logit model should be printed.
print.ind.results: logical value as to whether utility score results from individual syntheses should be printed.
print.variable.importance: logical value as to whether the variable importance measure should be printed when tree.method = "rpart".

Details

This function follows the method for evaluating the utility of masked data as given in Snoke et al. (2018) and originally proposed by Woo et al. (2009). The original and synthetic data are combined into one dataset and propensity scores, as detailed in Rosenbaum and Rubin (1983), are calculated to estimate the probability of membership in the synthetic data set. The utility measure is based on the mean squared difference between these probabilities and the probability expected if the data did not distinguish the synthetic data from the original.

If k.syn = FALSE the expected probability is just the proportion of synthetic data in the combined data set, 0.5 when the original and synthetic data have the same number of records. Setting k.syn = TRUE indicates that the numbers of observations in the synthetic data was synthesised and not fixed by the synthesiser. In this case the expected probability will be 0.5 in all cases and the model to discriminate between observed and synthetic will include an intercept term. This will usually only apply when the standalone version of this function utility.gen.sa() is used.

Propensity scores can be modeled by logistic regression method = "logit" or by two different implementations of classification and regression trees as method "cart". For logistic regression the predictors are all variables in the data and their interactions up to order maxorder. The default of 1 gives all main effects and first order interactions. For logistic regression the null distribution of the propensity score is derived and is used to calculate ratios and standardised values.

For method = "cart" the expectation and variance of the null distribution is calculated from a permutation test. Our recent work indicates that this method can sometimes give misleading results.

If missing values exist, indicator variables are added and included in the model as recommended by Rosenbaum and Rubin (1984). For categorical variables, NA is treated as a new category.

Value

An object of class utility.gen which is a list including the utility measures their expected null values for each synthetic set with the following components:

call: the call that produced the result.
m: number of synthetic data sets in object.
method: method used to fit propensity score.
tree.method: cart function used to fit propensity score when method = "cart".
resamp.method: type of resampling used to get pMSEExp and pval.
maxorder: see above.
vars: see above.
nfix: see above.
aggregate: see above.
maxit: see above.
ngroups: see above.
df: degrees of freedom for the chi-squared test for logit models derived from the number of non-aliased coefficients in the logistic model, minus 1 for k.syn = FALSE.
mincriterion: see above.
nperms: see above.
incomplete: TRUE/FALSE indicator if any of the variables being compared are not synthesised.
pMSE: propensity score mean square error from the utility model or a vector of these values if object$m > 1.
S_pMSE: ratio(s) of pMSE to its Null expectation.
PO50: percentage over 50% of each synthetic data set where the model used correctly predicts whether real or synthetic.
S_PO50: ratio(s) of PO50 to its Null expectation.
SPECKS: Kolmogorov-Smirnov statistic to compare the propensity scores for the original and synthetic records.
S_SPECKS: ratio(s) of SPECKS to its Null expectation.
print.stats: see above.
fit: the fitted model for the propensity score or a list of fitted models of length m if m > 0.
nosplits: for resampling methods and cart models, a list of the number of times from the total each resampled cart model failed to select any splits to classify the indicator. Indicates that this method is not working correctly and results should not be used but a logit model selected instead.
digits: see above.
print.ind.results: see above.
print.zscores: see above.
zthresh: see above.
print.variable.importance: see above.

References

Woo, M-J., Reiter, J.P., Oganian, A. and Karr, A.F. (2009). Global measures of data utility for microdata masked for disclosure limitation. Journal of Privacy and Confidentiality, 1(1), 111-124.

Rosenbaum, P.R. and Rubin, D.B. (1984). Reducing bias in observational studies using subclassification on the propensity score. Journal of the American Statistical Association, 79(387), 516-524.

Snoke, J., Raab, G.M., Nowok, B., Dibben, C. and Slavkovic, A. (2018). General and specific utility measures for synthetic data. Journal of the Royal Statistical Society: Series A, 181, Part 3, 663-688.

Examples

if (FALSE) {
  ods <- SD2011[1:1000, c("age", "bmi", "depress", "alcabuse", "nofriend")]
  s1 <- syn(ods, m = 5, method = "parametric",
            cont.na = list(nofriend = -8))

  ### synthetic data provided as a 'synds' object
  u1 <- utility.gen(s1, ods)
  print(u1, print.zscores = TRUE, zthresh = 1, digits = 6)
  u2 <- utility.gen(s1, ods, ngroups = 3, print.flag = FALSE)
  print(u2, print.zscores = TRUE)
  u3 <- utility.gen(s1, ods, method = "cart", nperms = 20)
  print(u3, print.variable.importance = TRUE)

  ### synthetic data provided as 'list'
  utility.gen(s1$syn, ods, cont.na = list(nofriend = -8))
  }