*! version 1.1 28May2015

Title

icet -- Imputation for degree-one fractional polynomial (FP1) functions

Syntax

icet incomplete_vars [ weight] [, options]

options

Main
add(#) Specifies number of imputations. Default is 5.

bootstrap(#) Uses the bootstrap to draw parameters.

comp(complete_vars) Specifies fully observed variables to be included as covariates in the imputation models.

cycles(#) Specifies number of cycles of chained equations before imputations are stored. Default is 10.

eqdisplay Displays the equations used for the univariate imputation models.

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

method(pmm/truncreg) Specifies the method by which x^p* will be imputed. Only pmm and truncreg are valid.

noisily Displays the draw of p* for each imputation.

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

truncval(#) Specifies the lower limit value at which imputed values of incomplete_var are to be truncated. Default is 0.1.

Data should be mi set before using icet; see [MI] mi set. However, variables
do not need to be mi registered; see [MI] mi register.

incomplete_vars must take strictly positive values. If there are negative or zero values, icet
will return an error and requst that you choose a preliminary transformation (e.g. add a constant to all values).

Description

icet multiply imputes missing values of incomplete_vars using chained equations,
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; the imputation model allows for this uncertainty via the approximate Bayesian bootstrap.

icet works by repeatedly calling the tuni command. Technically, the imputation process used by
tuni involves drawing a bootstrap sample of the data before fitting models for a series of Box-Tidwell
power transformations of x, denoted 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* in preparation for analysis.

Options

comp(complete_varlist) gives the names of fully observed variables to be included as covariates in the

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

knn(#) specifies the number of donors if the pmm method is used, as described in
mi impute pmm. Do not use knn(1); this caution is not specific to
use with icet.

add(#) specifies the number of imputations to create. Any existing imputations are replaced. The
total number of imputations must not exceed 1,000.

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 can be problematic when used in conjunction with method(truncreg); take care to inspect
imputed values properly after using it.

Remarks

icet multiply imputes missing values of an incomplete variable which is to be included in the analysis
as a one-dimensional fractional polynomial function. For two or more dimensions, there will be a degree of bias
induced by PMM, though of the current methods PMM is less biased than any other.

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.

icet works with Stata's mi formats; data must be mi set before using icet.

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