{smcl}
{* *! version 1.01.0  27june2008}{...}
{cmd:help xtlogitods} 
{hline}

{title:Title}

{phang}
{bf:xtlogitods -- Population averaged logit models for longitudinal data with outcome-dependent (case-control) sampling}


{title:Syntax}

{phang2}
{cmd:xtlogitods}
{depvar}
[{indepvars}]
{ifin}
{weight}
{cmd: ,} 
{cmd:case(}{varname}{cmd:)}
{break}
[
	{cmdab:samplerat:io(}{it:num} |{varname}{cmd:)}
	{cmd:caseeq1(}{varlist}{cmd:)}
	{cmd:caseeq2(}{varlist}{cmd:)}
	{break}
	{cmdab:caseoff:set(}{varname}{cmd:)}
	{cmdab:c:orr(}{it:string}{cmd:)}
	{cmdab:off:set(}{varname}{cmd:)}
	{cmdab:printint:}
	{it:gee_options}
	]

{phang} {it:depvar} is a longitudinal binary response variable and
{it:indepvars} are the predictors in the longitudinal model.

{phang} A panel variable must be specified. Correlation structures other
than exchangeable and independent require that a time variable also be
specified.  See {manhelp xtset XT}.

{phang} {it:depvar} and {it:indepvars} may contain time-series operators;
see {manhelp tsvarlist TS}.

{phang} {cmd:iweight}s, {cmd:fweight}s, and {cmd:pweight}s are allowed.
See {cmd:weight}.  Weights must be constant within panel.


{title:Description}

{pstd} {bf:xtlogitods} performs outcome-dependent (case-control) sampling
analysis of longitudinal binary outcomes according to the method of
Schildcrout and Rathouz (2009).


{title:Options}

{phang} {cmd:case(}{it:varname}{cmd:)} is required.  {it:varname} specifies
the binary case-control variable on which sampling is based.

{phang} {cmd:sampleratio(}{it:num} |{it:varname}{cmd:)} is either a number or
a variable giving the sampling ratio.  It should be constant within panel.
Specifying sampleratio as a variable allows for sampling to be stratified
on predictor variables.  Default value is 1 (sampling is independent of
case).

{phang} {cmd:caseeq1(}{it:varlist}{cmd:)} is the list of predictors, if any,
besides the response variable ({it:depvar}) to be used in the case model.
A constant term is added.

{phang} {cmd:caseeq2(}{it:varlist}{cmd:)} is the list of predictors, if any,
to be interacted with the response variable ({it:depvar}) to be used in
the case model. No constant is required, as {it:depvar} is always included
in the case model.

{phang}
{cmd:caseoffset(}{it:varname}{cmd:)} includes {it:varname} in the case model with coefficient constrained to 1.

{phang} {cmd:corr(}{it:string}{cmd:)} specifies the gee within-group
correlation structure for the response model.  See {manhelp xtgee XT} for
correlation structure options.

{phang}
{cmd:offset(}{it:varname}{cmd:)} includes {it:varname} in the response model with coefficient constrained to 1.

{phang} {cmd:printint} print intermediate modeling output for gee logit
model for case-control status and for longitudinal gee model for binary
outcome.

{phang} {it:gee_options} include any additional options for {hi:xtgee
... , family(binomial)} (i.e., {cmd:xtgee} for binary outcome data), except
{cmd:corr} or {cmd:offset}.  These options will be applied to both estimation of the case model and estimation of the response model.  See {manhelp xtgee XT}.


{title:Remarks}

{pstd} The method of Schildcrout and Rathouz applies to longitudinal study
designs with binary outcomes, where interest lies in fitting a population
average (PA) or "gee" model to the response.  Sampling is based on a
case-control design, wherein the case-variable is related to the response
series.  The method involves fitting an offsetted logistic regression
model to the case-variable, as a function of user-specified covariates and
the response variable, where the offset is given by log(sampling ratio).
This fitted model is used in turn to compute another offset for the PA gee
model of interest.

{pstd} The program generates a new variable _Iy which is the case
variable, and, for each variable {it:var} in {it:caseeq2}, an interaction
variable given by _IyX{it:var}.  The program deletes all existing variables with
prefix _Iy before generating these new variables.

{pstd}
Consider use of
{cmd:xtgee} option {cmd:force} for observations unequally-spaced  in time.


{title:Author}

{phang} Paul Rathouz, Department of Health Studies, University of
Chicago. {break} Email: prathouz@uchicago.edu.


{title:Also see}

{psee}
Manual:  {bf:[XT]}

{psee}
Online:  {manhelp xtgee XT}, {manhelp xtlogit XT}