Programming the statistical procedures from SAS

Spline Regression, graph interpretation

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Spline Regression, graph interpretation

I am not familliar with spline regression. I have used splines to present probabilities/odd ratios, but that is the limited of my experience.

In the article: http://www.ncbi.nlm.nih.gov/pubmed/22257645 , multiple splines are presented and used. They describe the procedure as the following (and that they used SAS):

The course of each measurement from baseline to 18 months was compared between arms by linear smoothing-spline analysis, a semiparametric regression technique that furnishes a precise estimate of the general time trend in longitudinal data while permitting arbitrary changes of linear direction, both above and below the general trend, at designated junction points [35]. In a 2-arm trial, spline analysis produces a test for the difference in trend between arms (PΔtrend) as well as a test for nonzero trend in each arm (Ptrend). Analyses of aBMD and bone markers were adjusted for time-varying weight and age. Analyses of aBMD z were adjusted for weight only, as age is accounted for in the z score calculation. All other longitudinal analyses were adjusted for age. Variables with skewed distribution were log-transformed for analysis and retransformed for reporting, with linear trend estimates expressed as percentage change per month.

Spline-fitting computations were implemented as a mathematically equivalent linear mixed model, with random effects (Gaussian deviates) serving to express subject-to-subject variation in overall slope and junction-to-junction variation in local slope. The mixed-model formulation accounts for visit-to-visit correlation within subjects and carries the additional advantage of being unbiased in the presence of missing data, so long as the missingness is either random or predictable by available variables [36]."

I understand this description, but get intuitively confused when looking at Figure 3, the top left graph. In this graph both treatment groups start at the same location, one (placebo) gradually (monotonically) increases and is said to have a non-significant positive trend, however the active group dips way down then has a positive increase only to have a final value still lower than the placebo group. I see that the differences in trends are significant, but I don't get how the active group has a significant trend when it changes directions and ends up at a lower value than the placebo group. Both groups have relatively equal sample sizes.  I would imagine the average slope for the active group would be less than placebo group's average slope.  Can someone provide some insight on this result and how it is significant and determined tb be a significant trend (for the active group)?

Thanks in advance for any help!

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Posts: 2,655

Re: Spline Regression, graph interpretation

An example in the PROC GLIMMIX documentation may provide some help on this.  In the SAS/STAT13.1 documentation, read through Example 43.6 Radial Smoothing of Repeated Measures Data.  Another source would be Walt Stroup's Generalized Linear Mixed Models, Chapter 15.4 Spatial Covariance Modeling by Smoothing Spline.  Repeated measures in time can be fit by spatial covariance type covariance structures, and I suspect that is what the authors did here.

Steve Denham

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