Two-part /hurdle model for healthcare costs/expenditures as dependent variable

[uzma03505621]

For a two-part/hurdle model for costs/expenditures as the dependent variable: Expected expenditures are obtained by multiplying the predictions from the two parts.

My study Model is as follows

cost= x1,x2,x3,x4,x5,x6,x7,x8 (categorical) x9 x10 (continuous)

x1 is my main classification variable that divides my sample into 3 groups; my study purpose is to estimate the healthcare expenditures in these 3 groups and the differences in their healthcare expenditures.

1st part:  logistic regression estimating the probability of positive expenditures

I created an indicator variable ispositive which is 1 for positive expenditure and 0 when no expenditure is incurred.

SAS code:

data data2;
 set data1;
if cost ne . then ispositive=(cost>0);
if ispositive then do;
 logcost=log(cost);
 costp=cost;
 end;
run;

Then the first part of my model, I use LOGIT:

proc logistic data=data2 descending;
 class categ_mdd sex adult povcat inscov marry region cobd1 cobd5 cobd6 cobd7 cobd8 cobd9 cobd2 cobd3 cobd4;/*these are categorical variables */
 model ispositive = categ_mdd adult sex marry povcat inscov region cobd1 cobd5 cobd6 cobd7 cobd8 cobd9 cobd2 cobd3 cobd4 mcs42 pcs42/firth;
 output out=predlogistic pred=phat;
run;

Second part of the model, I use GLM with log link and gamma dist, taking only positive costs (COSTP):

proc genmod data=data2;

class categ_mdd adult sex povcat inscov cobd1 cobd2 cobd3 cobd4 cobd5 cobd6;

 model costp =categ_mdd adult sex marry povcat inscov region cobd1 cobd5 cobd6 cobd7 cobd8 cobd9 cobd2 cobd3 cobd4 mcs42 pcs42  /dist=gamma link=log;

output out= y_hatC pred= condpred ;

run;

My question is now how do I obtain my expected cost = multiplying the predictions from the two parts ?

What should I multiply?

Is the expected cost= phat*condpred ?

[StatDave]

That is probably reasonable, but as I've suggested before, this complication goes away if you fit a Tweedie model. That is a single model and you just ask for the predicted values from the OUTPUT statement in GENMOD as usual.

[uzma03505621]

Yeah, I will be trying Tweedie distribution.
But just to be sure about this two-part, once I have the predicted cost..then to get the mean expenditures of each category, I'll use lsmeans right?

[uzma03505621]

I used the following as the syntax to get mean expenditures

 
 data estimate;
 merge y_hatc predlogistic;
 predcost=phat*condpred;
 run;
 
 
 proc means data=estimate;
 var predcost;
 by categ_mdd;
 run;

categ_mdd=1

Analysis Variable : predcost
N	Mean	Std Dev	Minimum	Maximum
1125	23338.54	13994.49	3179.75	167320.80

categ_mdd=2

Analysis Variable : predcost
N	Mean	Std Dev	Minimum	Maximum
627	20472.25	10540.79	2622.02	65667.96

categ_mdd=3

Analysis Variable : predcost
N	Mean	Std Dev	Minimum	Maximum
5236	13527.46	9546.90	2103.80	183025.71

[Raymond-milan]

Hi can you please let us know how to program a Tweedie distribution and how to get predicted value? 

Thank you!

[StatDave]

Just specify DIST=TWEEDIE in the MODEL statement and the PRED= option in the OUTPUT statement.

proc genmod;
model y = x / dist=tweedie;
output out=twpred pred=p; 
run;