# Thread: Is ARIMA model appropriate for this dental research?

1. ## Is ARIMA model appropriate for this dental research?

Hi members.
Please, I have a doubt in my study for doctoral thesis…

Title: “Development of a thermal cycling protocol for dental materials”.
Objective: to create a protocol for thermal aging, from measurements that were found in people mouth.
Doubt: What analyses could I use for this variation temperature data?
Experimental unit: six volunteers
Variable: temperature

Context:
In one day there is 16000 data. In 3 days, there is 48000 data for each volunteers.
Then, I have 6 x 48000 = 288.000 temperature values !!!!

A student of PhD in dentistry did a work to describe an average pattern of temperature (°C) variation in the oral cavity of six volunteers.

She collected oral temperature data (°C) for 3 days, in 6 patients at each 4 of 4 seconds.

The aim is to establish an average pattern of temperature variation, according to the time, temperature variation and the number of changes per day.

The patients have different routines of each others and per day, so, is there any statistical analyses that I can establish a standard protocol with her data?

Basically, she would like to find an answer like as: A person, on average, per day, has three temperature increases of 40°C , which was maintained for 40 seconds, and 3 temperature decreases from 16°C maintained for 40 seconds.

Is ARIMA test appropriate for this study?

TIA
Ivan

2. ## Re: Is ARIMA model appropriate for this dental research?

This really is not an ARIMA question, it is a design of experiment question. The answer if you can use ARIMA for this is, well sure. As long as the time series is linear you can almost always use ARIMA. But ARIMA is commonly a method you need a lot of experience doing to do well and you have to understand the context of the data neither of which is likely it seems to me given what you said.

ARIMA does not address generalizability at all, whether the cases you have is adequate to address a larger population is doubtful at best. Further you won't be able to project months in advance this way unless you assume that the further future is like the near future. Nor can time series address confounds -whether environmental factors influence the results you found. There is a more complex form of ARIMA, some call this ARIMAX, some multivariate ARIMA, others transfer functions, that does deal with that to some extent.

3. ## The Following User Says Thank You to noetsi For This Useful Post:

victorxstc (04-04-2014)

4. ## Re: Is ARIMA model appropriate for this dental research?

Could you suggest another way, more simple, to analyse this data?

5. ## Re: Is ARIMA model appropriate for this dental research?

The person you really need to talk to is victor a dentist who writes statistical papers. I will show him this thread. Autoregressive distributed lag models (a form of regression where lags of the dependent variable are predictors as well as other variables and with autoregression addressed) might work depending on the stationarity of different variables. I am relatively new to time series and know nothing of the substantive issues you are addressing (that is the ones related to dentist work).

6. ## Re: Is ARIMA model appropriate for this dental research?

Originally Posted by iivanchuk
Basically, she would like to find an answer like as: A person, on average, per day, has three temperature increases of 40°C , which was maintained for 40 seconds, and 3 temperature decreases from 16°C maintained for 40 seconds.
I am no expert in stats, so I would throw my two cents. I think the above quoted objective needs simple average and confidence interval calculation! (seriously) And if you have a better and more sophisticated approach to model it (like ARIMA), it would be even better. But I don't understand why you need to do ARIMA? Do you want to forecast something or reject a hypothesis? Can't you calculate the confidence intervals for the averages of temperature increases, and then make a protocol that increases the temperature to a "random" temperature within the confidence interval?

A person, on average, per day, has three temperature increases (2 to 4) of 40°C [32 to 48°C], which was maintained for 40 seconds [30 to 50 sec], and 3 temperature decreases from 16°C [6 to 26°C] maintained for 40 seconds [30 to 50 sec].

Then create a machine that does the same, but instead of increasing the temperature to 40 degrees, it would increase it to a temperature within your found 95%CI (32 to 48)... (and it will pick that temperature randomly) The same can apply to the time (a randomly picked duration from the span of 30 to 50 sec).

The above was my suggestion to deal with the changes in the pattern of the model, which might be better modeled with ARIMA etc (that I don't know).

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Moreover, as noetsi stated the current protocol is flawed by the small sample size. You would need much more volunteers from different ages, backgrounds, genders, etc.

7. ## Re: Is ARIMA model appropriate for this dental research?

As victor notes all ARIMA is going to do is project forward in time your results. I don't understand why you would want to project forward in time this analysis.

It is always a good idea, and for a disertation required generally, to do a literature review that shows how this type of analysis has been done in the past. That is a very good idea to do.

8. ## Re: Is ARIMA model appropriate for this dental research?

Thanks noetsi and victor...

We told about ARIMA, because we wanted to predict from these data what occur on other days and to predict how much temperature variations occur in one year, for example... Do you think that it can be done?

You have all reason about the number of patients, however, it's very difficult to find people who don't mind about stay with a sensor in mouth all the time, and eating with it, for some days...

So, thank you all for the answers, and we'll start to study and to try the tips that you all gave us!

Originally Posted by noetsi
As victor notes all ARIMA is going to do is project forward in time your results. I don't understand why you would want to project forward in time this analysis.

It is always a good idea, and for a disertation required generally, to do a literature review that shows how this type of analysis has been done in the past. That is a very good idea to do.

9. ## Re: Is ARIMA model appropriate for this dental research?

We told about ARIMA, because we wanted to predict from these data what occur on other days and to predict how much temperature variations occur in one year, for example... Do you think that it can be done?
I think it can be done, the question is what assumptions are being made. If you assume that the results are changing over time (and that this change will continue into the future and is stochastic in nature) than time series such as ARIMA will work (but is quite complex if you have no experience in it - so you should see if someone who works in time series in your university will help out). If you assume that future results can be predicted exactly from your data than some form of regression that deals with autoregressive error may work (this is really a determanistic not stochastic process and I do not work with it so take this with a grain of salt).

6 people, although I understand your problem, is simply two few I suspect to reliably generalize from. Make sure you committee accepts it before you do it.

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