Logistic Regression for trend analysis using Complex survey data?

[SAS93]

I'm working with complex survey data to get annual estimates for a particular dichotomous variable; I want to estimate if there's a trend in prevalence over time.

I'm planning to:

1. merge each year's dataset together
2. create a categorical variable for all the years (my x variable)
3. run logistic regression using the dichotomous variable as y.

Right now, I don't plan on using any extra control variables like race or age--I'll add those in later if I need to. 

I'm still fairly new to certain parts of working with complex survey data. Is there anything in particular I need to be sure to add into my code? 

Currently, it looks like this:

PROC SURVEYREG Data=trends Total=TOTALS NOMCAR;          
 Weight weightvar;
 Strata stratavar;
   Class year (reference='2013');                    *2013 = beginning;
   Model y (ref='0') = year / vadjust=none;      *Modeling probability for 'yes' outcome';
   lsmeans year / diff;
 Format year year.;
 Run;

[SteveDenham]

The code you have will let you know if any of the years differ.  To get at trends, you will need to implement either a CONTRAST statement or an LSMESTIMATE statement.  I don't know how many years are in the model, but assume that there are data for 2013, 2014, 2015, 2016, 2017, 2018 and 2019 (7 years).

Using LSMESTIMATE:

lsmestimate year 'Linear time' -3 -2 -1 0 1 2 3;

/* if you also wanted to look for both a linear and a quadratic trend it would be
lsmestimate year 'Linear time' -3-2-1 0 1 2 3,
                            'Quadratic time' 5 0 -3 -4 -3 0 5;

Alternatively, you could fit time as a continuous variable by deleting the CLASS year statement.

SteveDenham

[ChuksManuel]

Hi Steve,

This thread was helpful. I completely understand your explaination on this comment. I am implementing a similar trend analysis but with 12 year cycles from 2008 to 2019.
Would the contrast be something like this ?
lsmestimate year 'Linear time'-5 -4 -3 -2 -1 0 1 2 3 4 5 6;
What would the quadratic time be? I will appreciate a response.

[SAS_Rob]

The best way to come up with the coefficients for the orthogonal polynomials is to use the ORPOL function in IML.

SAS Help Center: ORPOL Function

[SteveDenham]

Some key things to note for trend tests using orthogonal polynomials.  The coefficients should sum to zero, so for a 12-nomial linear contrast the following would work: -11 -9 -7 -5 -3 -1 1 3 5 7 9 11. If you are interested in the value of the trend, this should use a divisor=2 option.  Quadratic form is relatively easy to calculate by hand - square each entry, get the average of those, subtract the average from each squared value, and reduce to lowest terms. So, 121 + 81 +49 + 25 + 9 + 1 +1 + 9 + 25 + 49 + 81 + 121 = 572, average = 572/12 = 47.66667 (=47 2/3), which gives 73 1/3  33 1/3 1 1/3 -22 2/3 -38 2/3 -46 2/3  -46 2/3 -38 2/3 -22 2/3 1 1/3 33 1/3 73 1/3  --> 220 100 4 -68 -116 -140 -140 -116 -68 4 100 220 with divisor= 3 option. These could all be divided by 4 to get to lowest terms, but if you are interested in the actual value, I suggest stopping here.  You can check these against the results from the ORPOL function in IML that @SAS_Rob mentioned.

SteveDenham

[StatDave]

I assume, and hope, that you are really using PROC SURVEYLOGISTIC and not PROC SURVEYREG which assumes that the response is normally distributed.

[ChuksManuel]

Yes. I am using proc survey logistic for this.