{smcl}
{* *! version 1.0.1 Quezada-Sanchez AD 10nov2015}{...}
{* *! version 1.0.0 Quezada-Sanchez AD 02dec2010}{...}
{cmd:help lbpower}
{hline}

{title:Title}


{p2colset 5 18 20 2}{...}
{p2col: {hi: lbpower} {hline 2}} Calculate approximate power (or sample size) for longitudinal studies with binary response 
and two equally sized treatment groups {p_end}
{p2colreset}{...}


{title:Syntax}

{p 8 11 2}
{cmd:lbpower} 
{cmd:,}
{cmdab:nr:ep(}#{cmd:)}
{cmdab:dur(}#{cmd:)}
{cmdab:corr:jk(}#{cmd:)}
{cmdab:d:if(}#{cmd:)}
{cmdab:a:lpha(}#{cmd:)}
[
{cmdab:p:ower(}{it:numlist}{cmd:)}
{cmdab:ns:ize(}#{cmd:)} 
{cmdab:unilateral} 
]


{title:Description}

{pstd}
{opt lbpower} Approximates power (or sample size) for longitudinal studies with a binary
response and two treatment groups with equal size. It should be used if the log odds 
can be assumed to be approximately linear with respect to the probability, this is a
reasonable assumption when response probabilities are between 0.2 and 0.8. Additionally, 
a constant correlation between repeated measurements is assumed and variance of the binary
response variable is set at its maximum value (=0.25, when p=0.5). Note that this is just 
an approximation and should be applied taking into account all these assumptions.


{title:Options}

{phang}{cmdab:nr:ep(}#{cmd:)} Number of repeated mesurements.

{phang}{cmdab:dur:(}#{cmd:)} Duration of the study.

{phang}{cmdab:corr:jk(}#{cmd:)} Correlation between repeated measurements.

{phang}{cmdab:d:if(}#{cmd:)} Difference in the change of response probabilites between groups (from begining to the end of the study).

{phang}{cmdab:a:lpha(}#{cmd:)} Significance level.

{phang}{cmdab:p:ower(}{it:numlist}{cmd:)} Power, sample size is calculated.

{phang}{cmdab:ns:ize(}#{cmd:)}  Sample size, calculate power.

{phang}{cmdab:unilateral} Specify if the test is one sided

{pstd} Either {cmdab:p:ower} or {cmdab:n:size} must be specified


{title:Example}

{pstd} Suppose that subjects are randomly assigned to receive any of two different suplements on a daily basis. There 
is no placebo for ethical reasons but in other contexts may be the case. The duration of the study is two years and 
five measurements will be taken. The researchers would like to detect treatment group differences in the prevalence 
of anemia of at least 6 percentage points (p.p.) per year, that is, 12 p.p. in the course of the whole study. 
The baseline prevalence in this population is about 45% so there is no problem with the linearity assumption for the 
log odds. Correlation between measurements is assumed to be 0.6


{pstd} Calculate sample size for power values between 0.7 and 0.9 :

{p 4 8 2}{cmd:lbpower, nrep(5) dur(2) corrjk(0.6) dif(0.12) alpha(0.05) power(0.7(.05)0.9)  }

{pstd} Calculate power for a sample size of 140 per group:

{p 4 8 2}{cmd:lbpower, nrep(5) dur(2) corrjk(0.6) dif(0.12) alpha(0.05) nsize(140) }

{pstd} Calculate sample size if a power of 80% and a difference of 15 p.p. in the change of prevalences 
(from the beginning to the end of the study) are considered:

{p 4 8 2}{cmd:lbpower, nrep(5) dur(2) corrjk(0.6) dif(0.15) alpha(0.05) power(0.8) }


{title:Saved results}

{pstd} If power is provided, the sample size per group is saved as scalar in {cmd:r(N1)}. In
case a list of power values is given, each sample size value is stored in {cmd:r(N1)},  {cmd:r(N2)}, ...

{pstd} If sample size is specified, power is saved as scalar in {cmd:r(power)}


{title:Author}

{pstd} Amado David Quezada S{c a'}nchez {break}
Center for Research in Nutrition and Health{break}
National Institute of Public Health - Mexico (INSP) {break}
Email {browse "mailto:amado.quezada@insp.mx":amado.quezada@insp.mx}
{p_end}

{title:Reference}

{pstd} Fitzmaurice/Laird/Ware (2004) Applied Longitudinal Analysis, 411-413.