*! version 1.1 28may2015

Title

tuni -- Univariate imputation of one-dimensional fractional polynomial (FP1) functions

Syntax

tuni incomplete_var [complete_vars] [ weight] [, options]

options

Main
method(pmm/truncreg) Specifies the method by which x^p* will be imputed. Only pmm and truncreg are valid; method() is a required option

knn(#) Specifies the number of donors to be used by pmm. knn can only be used with method(pmm). Default is 10

truncval(#) Specifies the lower limit value at which imputed values of incomplete_var are to be truncated. truncval can only be used with method(truncreg). Default is 0.1

powers(#(#)#) Candidate powers of incomplete_var to be considered; must be specified using the #(#)# syntax; default is -2(0.2)3

bootstrap(#) Uses the bootstrap option of mi impute chained to draw parameters; this may cause problems when used with method(truncreg)

noisily Displays the draw of p* for each imputation

* add(#) Specify number of imputations to add; required with
no imputations

* replace Replace imputed values in existing
imputations

* add(#) is required when no imputations exist;
add(#) or replace is required if imputations exist.

Data must be mi set before using tuni;
see [MI] mi set. Note that incomplete_var must be registered as passive.

Description

tuni multiply imputes missing values of incomplete_var allowing for an analysis model that
includes first-dimension fractional polynomial functions of incomplete_var. Denote
incomplete_var x. The analysis model will consider various power transformations x^p, usually
p = -2, -1, -.5, log(x), .5, 1, 2 or 3. The value of p is an unknown parameter and therefore the imputation
model allows for this uncertainty via the approximate Bayesian bootstrap when imputing x.

Technically, the imputation process involves drawing a bootstrap sample of the data before fitting models
for a series of Box-Tidwell power transformations of x, x^p, for p = -2(.2)3. The value of p, denoted p*,
which provides the best fit in the boostrap sample is used for imputation, and x (or rather x^1) is
passively imputed from x^p*.

Options

method(pmm/truncreg) defines the method for imputing x^p* before passively imputing x*.

add(#) specifies the number of imputations to add to mi data.
This option is required if there are no imputations in the data. If
imputations exist, then add() is optional. The total number of
imputations must not exceed 1,000.

replace specifies to replace existing imputed values with new ones. One
of replace or add() must be specified when mi data already
have imputations.

truncval specifies the lower limit for left truncation. Fractional polynomial functions can only be calculated from
positive values, it is therefore important that negative values are not imputed. The value specified is transformed to the
scale of x^p before mi impute truncreg is invoked.

noisily specifies that draws of p* be displayed for each imputation.

bootstrap specifies that posterior estimates of model parameters in mi impute truncreg
be obtained using sampling with replacement; that is, posterior estimates are estimated from a bootstrap sample. The
default is to sample the estimates from the posterior distribution of model parameters or from the large-sample normal
approximation of the posterior distribution. This option is useful when asymptotic normality of parameter estimates is
suspect. CAUTION: the option is currently problematic; inspect imputed values carefully after using it.

Remarks

tuni multiply imputes missing values of an incomplete variable which is to be included in the analysis
as a one-dimensional fractional polynomial function.

This is achieved by using the approximate Bayesian bootstrap to draw a value of p, denoted p* before
imputing x^p* and passively imputing x^1.

tuni works with Stata's mi formats; data must be mi set before using tuni.
In particular, incomplete_var must be registered as passive. It is good practice to register
complete_vars as regular.

References

Morris TP, White IR, Carpenter JR, Stanworth SJ, Royston P.
Combining fractional polynomial model building with multiple imputation.
Statistics in Medicine, 2015.

Author

Tim Morris, MRC Clinical Trials Unit at UCL, London UK

tim.morris@ucl.ac.uk

Acknowledgement

I am grateful to Ian White. This idea was his as well as mine.

Also see

mi impute
mi impute pmm
mi impute truncreg
mi estimate