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Visual exploration of a time series uses a graphical presentation of the data, plotted along a time axis. The graph must be as simple as possible to allow a good visual inspection of the data.
Figure 1: Crude data signal
The aim of the descriptive analysis of a time series is to characterize it in term of trend and seasons.
Describing a trend requires that a moving average window encompassing a full year be used (i.e. 52 weeks for weekly data). The shape of the resulting trend line is visually compared to the linear regression line.
Figure 2: Crude data, 52 weeks moving average, and regression line
A moving average window of 15 weeks smoothes the crude series, highlighting the seasonal pattern of the series. The size of the moving average windows depends upon the variance of the series, corresponding to the amount of variability to be smoothed. In general, windows from 5 to 15 weeks result in appropriate smoothing, but visual inspection of the result is required.
Figure 3: Crude data, and 15 weeks moving average
Spreadsheet software such as Microsoft Excel © allows to easily display time series filtered by a moving average window. For description purposes, it is important to display the averaged value in the center of the moving average window. The example below used a five-week moving average window. The first value equals the sum of the first 5 weeks, divided by 5 (5.73). This value is plotted against week 3, which represents the middle week for this first window.
Table 1: Crude series, formulas and smoothed series for calculating moving averages in Excel (5 week window)
A
B
C
D
1
Time
Crude data
Formulas
Smoothed series
2
6.70
3
5.73
4
5.59
= AVERAGE(B2:B6)
5
5.15
= AVERAGE(B3:B7)
6
5.47
= AVERAGE(B4:B8)
5.20
7
6.03
= AVERAGE(B5:B9)
4.93
8
3.75
= AVERAGE(B6:B10)
5.07
Using the median value over the window rather than the mean generates a moving median which is more robust to outliers than the mean. In such case, the Excel © formula should be =MEDIAN(B2:B6) in cell C4 and copied over the range. Note that functions in Excel © may vary according to languages.
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6 Comments
Prattingerova Jana posted on 1/24/2012 8:41:52 AM:
I am a little bit confused. According Czech definition source of infections can be human, animal , or enviromental in origin ( only for legionela or some kind of mycobacterium).
Food , watrer etc are vehicles of infection.
Your example with a chocolate cake .... cake is vehicle, eggs used are vehicles and hen is source.
Who first defined the source of infection?
Jana
Arnold Bosman replied on 1/25/2012 1:21:28 AM:
Good question Jana, thank you. and I believe you are right. I am not completely sure if my interpretation is correct. This is how I understand it:
- Source is a broad concept that could cover people, animals, or inanimate objects.
- the term 'vehicle' is mostly used for specific type of sources in the specific context of indirect transmission routes: the transmission route can be vehicle borne, vector borne or airborne
So indeed, in the example, the chocolate cake etc are specific sources that can be called 'vehicles'.
This is how I interpret the information in the reference of David Heymann. Please let me know what you think about that.
Prattingerova Jana replied on 1/25/2012 10:13:04 PM:
Dear Arnold,
I understand however I think it is a little bit complicated for those who are not experienced in epidemiology. It is a pity that there is not an international definition. I have read in The Lancet " ....such travel is an important source of infection". According to Czech definition it is a nonsence and e.g. student wouldn't pass his/her exam if he told this to the teacher.
U
Arnold Bosman replied on 1/25/2012 10:24:42 PM:
Dear Jana
Thank you again. Perhaps this is a good reason that we could try to find an easier and more simple way of defining those concepts in the chapter online. For this purpose we have developed this FEMWIKI, to allow a larger group of experts provide input and exchange views.
If you would like, we would welcome some new texts that you could provide, in the chapter above, with the aim to reduce confusion.
This can be done by clicking on the 'edit' button on top of the chapter. Feel free to ask for some clarification if needed.
Best regards
Arnold
Prattingerova Jana replied on 1/27/2012 9:32:46 PM:
I will try to find the clearest one.Jana
Vladimir Prikazsky replied on 6/4/2015 11:21:01 AM:
Dears
I just had a little trigger for this discussion. If the agents can survive and multiply in water e.g. vibrio and other mentioned here above then water is a source. Otherwise it's a vehiculum. This has implications for investigation of the source.
Vladimir
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