statistical cosinor analysis,

Question

Hey i am trying to calculate a cosinor analysis in statistica but am at a loss as to how to do so. I need to calculate the MESOR, AMPLITUDE, and ACROPHASE of ciracadian rhythm data.

http://www.wepapers.com/Papers/73565/Cosinor_analysis_of_accident_risk_using__SPSS%27s_regression_procedures.ppt

there is a link that shows how to do it, the formulas and such, but it has not given me much help. Does anyone know the code for it, either in statistica or SPSS??

I really need to get this done because it is for an important paper

Answer 1

I don't have SPSS or Statistica, so I can't tell you the exact "push-this-button" kind of steps, but perhaps this will help.

Cosinor analysis is fitting a cosine (or sine) curve with a known period. The main idea is that the non-linear problem of fitting a cosine function can be reduced to a problem that is linear in its parameters if the period is known. I will assume that your period T=24 hours.

1. You should already have two variables: Time at which the measurement is taken, and Value of the measurement (these, of course, might be called something else).
2. Now create two new variables: SinTime = sin(2 x pi x Time / 24) and CosTime = cos(2 x pi x Time / 24) - this is desribed on p.11 of the presentation you linked (x is multiplication). Use pi=3.1415 if the exact value is not built-in.
3. Run multiple linear regression with Value as outcome and SinTime and CosTime as two predictors. You should get estimates of their coefficients, which we will call A and B.
4. The intercept term of the regression model is the MESOR.
5. The AMPLITUDE is sqrt(A^2 + B^2) [square root of A squared plus B squared]
6. The ACROPHASE is arctan(- B / A), where arctan is the inverse function of tan. The last two formulas are from p.14 of the presentation.
7. The regression model should also give you an R-squared value to see how well the 24 hour circadian pattern fits the data, and an overall p-value that tests for the presence of a circadian component with period 24 hrs.
8. One can get standard errors on amplitude and phase using standard error propogation formulas, but that is not included in the presentation.