Polynomial regression: Fitting the curve

[rogersaj]

Hi, I have a dataset of women in labor. We have a repeated measure, cervical dilation for each woman, as well as the time between cervical dilation measurements. My goal is repeat what a similar paper did to find how the rate of cervical dilation differs with different patient characteristics. One prior study used Proc Mixed to model increasing cervical dilation parameter over time using an eighth-degree polynomial model. I'd like to:

1) Fit the data to the correct polynomial model

2) Impute the value of 6cm (clinically significant) for all women for whom that value was not recorded

3) Find out the average time taken to traverse from the first recorded cervical dilation to 6cm (eg. took 120 minutes to go from 3cm to 6cm).

Here is a sample of my data;

Patient ID	Cervical dilation	Difference in time between two consecutive cervical dilation checks (Minutes)
1	1
1	2	60
1	3	30
1	5	60
1	6	30
1	7	45
1	10	30

Thanks in advance!

[SteveDenham]

I wish that the journal that published the paper you are working from had sent the paper for a proper statistical review.  An eighth degree polynomial has some drawbacks that may (or may not) affect your analysis. First, for the sample data, there are only seven observations. You can't fit an eighth degree polynomial to only seven observations. Second, there is very little likelihood that you can attribute the higher order terms to anything biological - as a result, those terms are being driven by noise in the data.  If someone can point to a biological or physical process that operates in nine-dimensional space, then I am willing to retract that statement.

But all is not lost. A semi-parametric method that fits a spline to the data avoids both of those issues. Check the use of the EFFECT statement in PROC GLIMMIX https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_glimmix_examples20.htm  or PROC ORTHOREG followed by PROC PLM https://documentation.sas.com/doc/en/pgmsascdc/9.4_3.4/statug/statug_plm_examples06.htm  for fitting a spline. If the reason for using PROC MIXED is to incorporate various random effects, PROC GLIMMIX is a better effect.  Using ORTHOREG might be a good way to comparing the fit of that eighth degree polynomial to the spline fit.

SteveDenham

[StatsMan]

PROC ADAPTIVEREG can be helpful in situations where you do not fully understand the nature of the relationship between the predictor(s) and the response.