Growth Curve Clause Samples

Growth Curve. The growth curve is a great tool for statisticians who would like to analyze rate of change over time. In order to use this method, the clinician must first plot the data and make sure a linear or curvilinear trend is a reasonable summary of the data. If time has a linear trend, then the clinician can use the group by time interaction model shown below. For subject i: yijk = β0 + β0i + β1 ∗ time + b1i ∗ time + β2 ∗ group + β3 ∗ time ∗ group + ejk where j=time from start of study, k=arm, the β′s are parameter estimates, and ejk~N(0, σ2) The growth curve method treats the time variable as continuous. This approach is very different from the ANOVA models previously discussed where time was treated as a categorical variable. Since time is a continuous variable, the test for the significance of the time variable only involves one degree of freedom. Here time does not need to be equally spaced, but should represent the time it is suppose to represent accurately. This allows the results to be easily interpreted. For example, if visits occur at months two, four, six, and eight, then time should be two, four, six, and eight for those visits. This is simpler than the ANOVA models because there are no extra tests needed to determine the difference between multiple groups. If the data correctly fits a linear trend, a growth curve model may be a better approach to the problem and simpler to understand. Sometimes a simple linear trend is not enough to model a complex data set. There are many growth curve adaptations that allow the researcher to create more complex models. One method is treating time not as a linear trend but as a parabolic or cubic trend. This requires modeling the time variable as 2 or 3respectively. The benefit of modeling time as non-linear is that it may be able to capture the trend of the data more accurately which leads to increased precision and decreased residual error.