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help for ^optbud^                                                  (STB-58: sxd2)
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Optimal sampling design for 2-stage studies with fixed budget
-------------------------------------------------------------

  	^optbud^ depvar [indepvars] [^if^ exp] [^in^ range]  
	[^, first(^varlist^)^ ^prev(^vecname^)^ ^b(^#^)^ ^c1(^#^)^ ^c2(^#^)^ 
	^var(^#^)^ ^coding(^#^)^


Options
-------

^first(^varlist^)^ specifies the first stage variables.

^prev(^vecname^)^ specifies the vector of prevalences for each stratum 
	      formed by different levels of dependent variable and
	      first stage covariates. (See Description on how
     	      to enter the vector.)

^b(^#^)^	specifies the available budget.
^c1(^#^)^	specifies the cost per study subject at the first stage.
^c2(^#^)^	specifies the cost per study subject at the second stage.

^var(^#^)^     	specifies the position in the logistic regression model of the
            covariate whose variance is to be minimized (i.e. optimized). For
            example, in the simple model Y = b0 + b1X1 + b2X2, if we want to
            minimize the variance of X1, then ^var^ = 2.

^coding(^#^)^	is a logical flag; the default of 0 (FALSE) means that prior to
            calling the ^optfixn^ function, you have to run the
            ^coding^ function (help @coding@ for details) to create the
            vector ^grp_yz^, which contains the distinct groups (strata)  
            formed by the different levels of response (Y) and first stage
            covariates (Z). If you have not run ^coding^ and you call the
            ^optbud^ function with ^coding=1^, the ^grp_yz^ vector will be
            created within the ^optbud^ function, but it is imperative that
            the vector vecname is provided to ^optbud^ in the correct
            order! For this reason, we strongly suggest that any call to
            ^optbud^ is preceded by a call to ^coding^.



Description
------------

The ^optbud^ function calculates the total number of study observations
and the second-stage sampling fractions that will maximize precision 
subject to an available budget. The user must also supply the unit cost 
of observations at the first and second stage and the vector of prevalences
in each of the strata defined by different levels of dependent variable and
first stage covariates. 

Before running the ^optbud^ function you should run the ^coding^ function, 
(see help @coding@), to see in which order you must supply the vector of
prevalences. 


Examples
--------

This is an example based on the CASS data (see Reilly, 1996) where the
association between various predictors and operative mortality is of
interest. The objective is to design a two-stage study where only
operative mortality, sex and a categorical weight variable will be 
measured at the first stage and all other covariates (weight, age, 
angina, chf, lvedp, surgery) determined for a sub-sample of subjects 
at the second stage. A pilot sample of 118 second-stage subjects is 
available, the prevalences of the various first-stage stata are known, 
and the budget is assumed to be 10,000. The following commands will 
calculate the optimal sampling design to minimize the variance of LVEDP 
subject to a total cost of 10,000, if the cost per first-stage
observation = 2 and cost per second-stage observation = 15.

 . ^use wtpilot^

 . ^coding mort sex wtcat^	 [get the different strata formed by levels of
		   	        dependent variable (mort) and first stage
		   	        covariates (sex)]

# enter the prevalences in the order suggested
# by @coding@ function

 . ^matrix prev=(0.02,.134,.670,.054,.05,.047,.001,.004,.013,.002,.003,.002)'^

 . ^optbud mort sex-surg,first(sex wtcat) prev(prev) var(7) b(10000) c1(2)i^ 
   ^c2(15)^


Author
------

      	Marie Reilly, Dept. of Epidemiology & Public Health
	and
	Agus Salim, Dept. of Statistics,

	University College Cork, Cork, Ireland
	marie.reilly@@ucc.ie


Also see
--------
    STB:  STB-58: sxd2
Manual :  [R] logit, glm
On-line:  help for @logit@, @glm@, @coding@, @optfixn@, @optprec@