*! version 2 07Oct2015

Title

sk_distdicho -- The distributional method for dichotomizing skewed
outcomes (based on Sauzet et al 2015)

Syntax

Distributional estimates for the comparison of proportions derived from a comparison of means allowing for a perturbation to the normal distribution of var1 .

sk_distdicho
varlist

[if] [in]
[, options] cp(#)

Immediate form of the distributional estimates

sk_distdichoi
#obs1
#mean1
#sd1
#obs2
#mean2
#sd2
#cutpoint
#tail
#alpha

options

Main
twovar if the two group outcome values are provided as two separate
variables

cp(#) value of the cut-point under or over which to compute
proportions

tail(string) provides the tail of the distribution in which the
proportions are computedrequired only for tail("upper")

bootci calculate bootstrap confidence interval

nrep(#) modify number of bootstrap replicates

Description

sk_distdicho returns the results of a two-group unpaired ttest followed
by skew-normal distributional estimates of comparisons of proportions and their standard errors (see also Sauzet et al 2014
and Peacock et al 2012). Estimates are given for a difference in proportions, risk ratio and odds
ratio for the compaison of proportions below or above the given cut-point (Treshold) with the distributional 95% confidence
interval for the statistics estimated. By default the first variable in varlist
is the outcome. The second variable is the group code.
The skew-normal distributional method estimates a third parameter "alpha" and corrects
the estimates when the outcome is skewed and thus allows to use the distributional
approach (distdicho) without having to transform the outcome into a normally distributed variable.
For the option method(var), the first variable is the outcome for
group1 and the second variable is the outcome for group2. It is assumed
that there are only two groups. If there are more than two groups in
var2 then only data for the first and last group is used.
For adjusted distributional estimate see reg_distdicho.

Options

Main

twovar must be specified if the two variables provided are the outcomes
values for each group. By default the first
variable provides the outcome values and the second the group categories:
exposed, unexposed.

cp(#) specifies the cutpoint under which the distributional proportions among the exposed
and the non-exposed (reference) are computed using the distributional method described in
Peacock et al.
cp requires a real number.

tail(string) provides the tail of the distribution in which the proportions are to
be computed. The default is the lower tail, upper will provide estimates
in the upper tail.

bootci Bootstrap bias corrected confidence intervals are calculated instead of
distributional ones using the command bootstrap
with 2000 replicates (default) under the hypothesis that the data is normal distributed
and that the variance is the known and equal to the data variance for the
default version or if the ratio of variances is known for the unequal variance case.

nrep(#) The number of bootstrap replicates can be altered. The default value is 2000.

Remarks

The order in which the variables are given matters. The difference in proportion
in the distributional proportion in group1 minus the distributional proportion
in group2. The risk ratio is the risk of being under cutpoint in group1
over the risk in group2. The odds ratios are the odds of being under the cutpoint
in group1 over the odds in group2.
The function used to calculate the cumulative probabilities of the skew-normal-distribution
was transformed according to the function "psn" of the R package "sn" (Azzalini, A. (2014).
The R 'sn' package: The skew-normal and skew-t distributions (version 1.1-1). URL http://azzalini.stat.unipd.it/SN)

Confidence intervals are returned using the current level in the system. This level can be modified
using the command set level.

Examples

setup

. use bwsmoke

Proportions of low birthweight babies among smoking and non-smoking mothers(Data from Peacock et al 1995).
Returns distributional estimates, standard error and distributional confidence
interval for difference in proportions, RR and OR of babies having a birthweight
under 2500g (low birthweight LBW) for group smoke=1 (mother smokes) over the odds
of LBW in group smoke=0 (mother doesn't smoke))

. sk_distdicho birthwt smoke, cp(2500) tail(lower)

setup

. use bmi

Body Mass Index(BMI) and parity. Returns distributional estimates,
standard error and distributional confidence interval for difference in proportions,
RR and OR of obese mothers (weight of >30 kg/m^2) for group group_par=1 (multipari)
over the odds of obesity in group group_par=0 (primipari)

. sk_distdicho bmi group_par, cp(30) tail(upper)

setup

. use gest

Gestational age and parity. Returns distributional estimates,
standard error and distributional confidence interval for difference in proportions,
RR and OR of preterm babies (< 37 weeks) for group group_par=1 (primipari)
over the odds of preterm babies in group group_par=0 (multipari)

. sk_distdicho gest group_par, cp(37) tail(lower)

setup

Immediate form

. sk_distdichoi 75 3250 450 110 2950 475 2500 lower -2.3

Stored results

sk_distdicho stores the following in r():

Scalars

r(prop1) distributional proportion estimate for the group at risk

r(prop2) distributional proportion estimate for reference group

r(propdiff) distributional estimate for the difference in proportions between the group at risk and the reference group

r(distrr) distributional estimate for risk ratio between the group at risk and the reference group

r(distor) distributional estimate for odds ratio between the group at risk and the reference group

r(sediff) standard error for the distributional estimate of the difference in proportion

r(serr) standard error for the distributional estimate of the risk ratio

r(seor) standard error for the distributional estimate of the odds ratio

r(ciinf) difference in proportions: lower limit of the confidence interval

r(cisup) difference in proportions: upper limit of the confidence interval

r(ciinfrr) risk ratio: lower limit of the confidence interval

r(cisuprr) risk ratio: upper limit of the confidence interval

r(ciinfor) odss ratio: lower limit of the confidence interval

r(cisupor) odds ratio: upper limit of the confidence interval

References

Peacock J.L., Sauzet O., Ewings S.M., Kerry S.M. Dichotomising continuous data while retaining statistical power using a distributional approach. Statist. Med; 2012; 26:3089-3103.

Sauzet, O., Peacock, J. L. Estimating dichotomised outcomes in two groups with unequal variances: a distributional approach. Statist. Med; 2014 33 4547-4559 ;DOI: 10.1002/sim.6255.

Sauzet, O., Ofuya, M., Peacock, J. L. Dichotomisation using a distributional approach when the outcome is skewed BMC Medical Research Methodology 2015, 15:40; doi:10.1186/s12874-015-0028-8.

Peacock, J.L., Bland, J.M., Anderson, H.R.: Preterm delivery: effects of socioeconomic factors, psychological stress, smoking, alcohol, and caffeine. BMJ 311(7004), 531{535 (1995).

Authors

Odile Sauzet, Universität Bielefeld , odile.sauzet@uni-bielefeld.de

Maren Kleine , Universität Bielefeld

07.10.2015