Bioengineering & Chronobiology Laboratory

Departamento de Teoría de la Señal y Telecomunicaciones

Universidad de Vigo

ChronoLab documentation 3/6

3. Example: Two subjects, multiple components

3.1 Introduction

In this example, more elaborate than the preceding, we show how ChronoLab adjusts several components on series from several subjects. In this case we analyze blood pressure series from two subjects (one healthy young woman and one healthy young man) that you can find in the files "Woman" and "Man", respectively. For each series we fit one composite cosine model with periods of 24 and 12 hours, so we will obtain the parameters and the results of the tests associated to this model. For the two series we will also obtain a chronogram that will be saved in a graphic file (PICT type).

3.2 Parameter file

If you need to analyze several subjects (files), as in this case, you must create a parameter file before using ChronoLab which must be a text file (ASCII, as generated with TeachText, Edit or similar text program). In order to illustrate the construction of this kind of file we repeat the first three lines of the data files:

ETV,AAA,2,002,198902041850,110, 70, 89
ETV,AAA,2,002,198902041900, 98, 63, 78         Extract from file "Woman"
ETV,AAA,2,002,198902041930, 93, 55, 73
...
 
ETV,MOA,1,014,198902061842,120, 70, 71
ETV,MOA,1,014,198902061900,131, 72, 72         Extract from file "Man"
ETV,MOA,1,014,198902061930,134, 77, 67
...

The parameter file must have as many lines as the number of subjects you want to analyze (one for each subject). Each of these lines must have four pieces of information (delimited by blanks):

Key: is text code (up to 6 characters, without blanks), that identifies subjects in the tables of results.
File name: is the file name (without blanks) where the data of one subject is located.
Field of date: identifies the field for the time code, as in the example of the preceding chapter (fig. 2.3).
Field(s) of variable(s): identifies the field(s) for each variable to be read in, as in the example of the preceding chapter (fig. 2.3). Later, ChronoLab will ask for the number of variables to be analyzed.

In our example, the parameter file (file "Setup") could be as follows:

AAA Woman 5 6 7 8
MOA Man 5 6 7 8

AAA and MOA are the initials for these subjects. Woman and Man are the data files. 5 is the field of date. 6 7 8 are the fields of systolic blood pressure, diastolic blood pressure and heart rate. In this case the two files exhibit a similar structure, but it is not necessary.

Important!

The parameter file must be in the same folder as the data files.

3.3 Read several subjects to analyze

After opening ChronoLab, select several subjects..., as follows:

Fig. 3.1

A dialog box appears. Choose the file Setup and hit Open. You will see a new dialog box:

Fig. 3.2

With Number of subjects we tell ChronoLab how many subjects will be read using the parameter file. All other items in this dialog are similar to those in figure 2.3 in the previous chapter.

Complete the dialog like in figure 3.2 and hit OK.

3.4 Analysis

After the data are read in, transform v0 (systolic blood pressure) removing those values that are three or more standard deviations apart from the mean of its series. A new variable, v3 (transformed systolic blood pressure), appears. Check it and write s as the code for this variable. Then select Multiple components... in the menu Methods.

Fig. 3.3

A dialog box like this appears:

Fig. 3.4

This dialog is very similar to the one in figure 2.8. The differences arise in the model definition. Here you can adjust up to ten sinusoidal components at a time. You can fit linear, cuadratic an/or cubic trends, too (check the desired box(es) in Trend:). ChronoLab offers three ways to select the sinusoidal components:

Adjust of the n first harmonics: adjust the n first harmonics of the fundamental period (Fundamental period (hours)). Note that the fundamental period itself is considered as the first harmonic. For example, in figure 3.4 the fundamental period is 24 hours and n is 2, ChronoLab will fit components with periods of 24 and 12 hours.
Adjust of n selected harmonics: adjust n selected harmonics (integers) of the fundamental period. To do it you must write in the lower box the number for each desired harmonic (delimited with blanks). For example, to adjust components with period of 24 and 8 hours, you can write 24 as fundamental period, 2 as value for n and 1 3 as numbers of the desired harmonics.
Adjust of n selected components: you can fit n sinusoidal components that are not harmonics of a known period. In order to do it you must write the desired periods (delimited with blanks and expressed in hours) in the lower box.

In this example we wish to obtain a chronogram, so you must check the box Chronogram.... When you do it, the following dialog box appears:

Fig. 3.5

In the left upper corner you can tell ChronoLab the number of intervals (Number:) considered for the calculation of the means (Means) to be computed and displayed in the chronogram. If you check Centered means will be drawn in the center of the corresponding time interval. Otherwise, means will be drawn at the beginning of the intervals.
With the box Standard error checked ChronoLab draws the standard error of the estimation of the mean for each time interval. If the option unilateral (only available with two subjects) is selected, this standard error will be drawn only on one side of the corresponding mean. Otherwise, it will be drawn in both sides.
Manual adjust...: with this option, through an appropriate dialog box, you can provide upper and lower limits for the ordinate axis. Remember that there are always 6 divisions and 7 tick marks on the vertical axis. If these limits become very restrictive when ChronoLab presents the chronogram, they will be scaled to the minimum possible range.
Show isolated points...: in some cases you may want to represent individual values over your chronogram, which is accomplished via an appropriate dialog box that appears when ChronoLab is drawing the chronogram. These values must be in a file with the same characteristics of a data file and are not taken into account for the scaling of the upper and lower limits of the chronogram (so you may need to manually adjust the vertical scale for this plot).
Parameters for each subject...: with this button you can, through dialog boxes like in figure 3.6 (one for each subject), provide several attributes for the chronogram of each subject (hit this button):
- Identificative character: with this character you can distinguish each subject in the table that completes the chronogram.
- Legend: This text, that appears in the header of the chronogram, has also an identificative function (ie. name of variable, units, Mean±SE, etc).
- Level: it tells ChronoLab that you want a horizontal line drawn to represent the MESOR of the fitted model, the global mean of all the data for this subject (Mean) or that you do not want to represent any level (Nothing).
- Adjusted curve: if this option is checked, ChronoLab will draw the fitted curve (single or multiple cosine model). Remember that each model was fitted to the data for each subject. In addition, there are three more options:
- Arrow at maximum and Arrow at minimum: with these boxes checked ChronoLab draws vertical arrow(s) from the time axis to indicate the maximum and the minimum of the fitted curve. The corresponding phases for the high values are known as the acrophase (single period) or orthophase (multiple periods) and bathyphase for the lowest value.
- Thick line: if this option is checked, ChronoLab will draw the fitted curve and the level associated with a model in a pen size one pixel thicker than the previous model. This option may be useful to distinguish between different models if you have a black and white monitor. If your Macintosh has a color monitor, ChronoLab uses a different color for each subject.

Fig. 3.6

Fill the dialog boxes like in figure 3.6 and hit OK. When you finish (in this example we use only two subjects) the frontmost window must be the dialog of the figure 3.5. The last button is referred to time axis:

Time axis...: hit this button and you will see a new dialog (figure 3.7). Here you can control some aspects of the time axis representation:
- Title: is the title of the time axis.
- Units: are the possible units to express the time axis.
- Periodic: if this option is not checked the time axis will be labeled with respect to the reference date, otherwise the units will be labeled with respect to the period. For example: the file "Man" has about 48 hours of data; if you check this box when you are fitting a model with fundamental period of 24 hours and you are representing two periods (see below), the chronogram will show two idealized periods with the time axis labeled in clock hours (00:00 to 00:00); but, if you do not select this option, the time axis will show time from the reference date (0.0 to 48.0).
- Data span...: you can, through an appropriate dialog box, select a temporal window to visualize the chronogram. In this case, ChronoLab does not consider an idealized period to do the calculation of the means, and the time axis is labeled in absolute time as the difference from the reference date.
- ... periods starting from ... units: if the model you are fitting has no trends and has an explicit fundamental period (not selected components), you can represent as many periods as you want, starting with a certain shift with the origin (reference date). With this option on, ChronoLab considers an idealized interval of n periods to calculate the means; i.e., if the fundamental period is 24 hours and you want to represent two periods, a value at 2.0 hours from reference is in the same group that other values at 50.0 hours from reference, but a value at 26 hours from reference is in a different group.
- Dark axis: permits selection of any part of the time axis to be darkened. This may be useful to mark a season, darkness, sleeping time or any other interval of interest.

Fig. 3.7

Complete the dialog box as in figure 3.7 and hit OK. The dialog of figure 3.5 must be the frontmost window. Fill it as in the figure and hit OK. You have again the dialog box of the figure 3.4. Fill it as in the figure and hit OK and the analysis will begin.

3.5 Results

When the analysis ends, you can see the results in appropriate Macintosh windows. In this example, there will be three windows:

The first of them, named Untitled, contains the desired chronogram (figure 3.8). At the bottom of this window you can find (depending on the fitted model) a table with information about the parameters of the model, too.
In the second window, named ChrL.Test_t_table, there are, for each subject, one table with as many lines as intervals you have requested. Each record contains: the time associated with the corresponding mean in the chronogram, the number of values used to compute this mean, its calculated value, its standard deviation and its standard error. Moreover, if you are analyzing two subjects (as in this case), ChronoLab performs a t-test to compare the means of the two subjects in each interval (not adjusted for multiple testing). The results of these tests are summarized in an additional table that, for each interval, presents: the time associated with the corresponding interval, degrees of freedom, t statistic, p-value and, with a confidence level of 95%, the test significance. If any interval shows a statistically significant difference (with a confidence level of 95%), ChronoLab draws an asterisk (*) in this interval just above the time axis in the chronogram. In this example, all the intervals show statistically significant differences between means, as you can see in the tables:

PROGRAM ChronoLab 2.2     Mon Oct 19 19:30:58 1992
 
 
Variation of systolic blood pressure in a young woman and in a young man
 
     AAA
________________________________________
    time     #pts    mean    s.d.   s.e.
________________________________________
     1.500     10    93.2     8.7    2.7
     4.500     12    85.5     8.2    2.4
     7.500     12    88.1     6.9    2.0
    10.500     12    90.9     9.0    2.6
    13.500     12    98.3     8.0    2.3
    16.500     12   100.8     8.1    2.3
    19.500     11   103.4    11.8    3.5
    22.500     10   102.8     8.2    2.6
________________________________________
 
 
 
 
     MOA
________________________________________
    time     #pts    mean    s.d.   s.e.
________________________________________
     1.500     12   112.2    13.4    3.9
     4.500      9   104.0    17.2    5.7
     7.500     12   107.2    12.3    3.6
    10.500     12   115.2    13.9    4.0
    13.500     12   125.5     8.4    2.4
    16.500     12   122.3    11.5    3.3
    19.500     12   127.4    13.1    3.8
    22.500     10   128.2    14.4    4.5
________________________________________
 
 
 
Comparison of mean for both individuals at each interval
_______________________________________________
    time     d.f.     t       p    significance
_______________________________________________
     1.500    20   -3.840   0.001       yes
     4.500    19   -3.281   0.004       yes
     7.500    22   -4.702   0.000       yes
    10.500    22   -5.086   0.000       yes
    13.500    22   -8.098   0.000       yes
    16.500    22   -5.297   0.000       yes
    19.500    21   -4.612   0.000       yes
    22.500    18   -4.851   0.000       yes
_______________________________________________

At the bottom of the third window, named ChrL.Chronobiologic_table, there is a descriptive table similar to that which has been explained in the previous chapter. The results for the multiple component analysis are in another table at the top of the window. The fields for each period are similar to those explained in the previous chapter for one component. For the complete model, you can obtain: the value of PR (percent of variability explained by the model), the p-value for the model tested [Weisberg, 1985] (H0: the series is better fitted by a constant flat line than by the model tested), point estimates for the MESOR, Amplitude (half of the difference between the maximum and the minimum of the model), Orthophase (phase where the model reaches its maximum) and Bathyphase (phase where the model reaches its minimum). If the model does not have a fundamental period, then Amplitude, Orthophase and Bathyphase are marked as 0. If the option to perform the regression tests is "on", ChronoLab appends to this table the p-values from the tests for lack of fit and normality, variance homogeneity and independence of the residuals (see Section 2.5 for explanation).

PROGRAM ChronoLab 2.2     Mon Oct 19 19:30:57 1992
 
 
Variation of systolic blood pressure in a young woman and in a  young man
 
_________________________________________________________________________________________________________________________________________
 Sub.  Var    Period   PR      p     MESOR   s.e.    Amp.   s.e.    C.I. Amp.      Acr.   s.e.   C.I. Acr.     lof    norm  homog  indep
_________________________________________________________________________________________________________________________________________
AAA     s
              24.000  36.7  <0.001                   8.92   1.25  (  6.4, 11.4)  -274.6    8.2  (-258,-291)
              12.000   1.3   0.422                   1.67   1.27  (  0.0,  0.0)  -325.9   43.0  (   0,   0)
             Overall  38.0  <0.001   95.36   0.89    9.26            Orthophase = -297    Bathyphase =  -85   0.893  0.234  0.177  0.729
MOA     s
              24.000  30.5  <0.001                  12.10   1.84  (  8.4, 15.8)  -267.7    8.7  (-250,-285)
              12.000   6.5   0.006                   6.19   1.80  (  2.6,  9.8)  -303.9   17.3  (-269,-338)
             Overall  37.1  <0.001  117.67   1.30   15.44            Orthophase = -311    Bathyphase =  -70   0.385  0.408  0.512  0.477
_________________________________________________________________________________________________________________________________________
 
 
 
__________________________________________________________________________
 Sub.  Var  #pts    min   max    mean    dev   err  median   rng50  rng90
__________________________________________________________________________
AAA     s     91   72.0  132.0   95.2   10.6   1.1    95.0    15.0   32.0
MOA     s     91   84.0  155.0  118.0   15.2   1.6   117.0    21.0   51.0
_________________________________________________________________________

Fig. 3.8

3.6 More analysis

Close the window with the chronogram. An alert like this appears:

Fig. 3.9

Hit Save and complete the process as was explained in the previous chapter. The type of the saved file is PICT and can be opened and modified with applications like Canvas or MacDraw, for example.

Try to analyze the rest of the variables and change some options to see their effects.

To do any new analysis using another data file without quitting ChronoLab, you must close the window of variables (Figure 2.4).

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