I use my lab data to construct a predictive model for the interactions between phage and bacteria. the model gave me a log curve. I develop experiments (triplicates) and got the real curves. Now I want to check by using statistics if my model represents the reality. Which is the right test for it? Is it right, to use an a-posteriori correction factor to increase the agreement between my model and reality?
Thanks in advance
I would advise to modify the predictive model by incorporating an added term, a multiplicated term and a term in the power coefficient, then optimise these terms by curve fitting to a series of experimemtal data. If you get anything larger than 0 for the added term, it may account for a potential portion of the culture that is immune to infection, anything different from 1 for the multiplicated term indicates differences in the infection process (speed, efficiency, etc) and a power term different from 1 may e.g. indicate different burst sizes or else.
However, you will need more data than just the two experiments you have apparently by now. The 10°7 cell experiment is useless anyway because you reach the maximum already with the first measured timepoint. I would recommend further experiments with lower cell numbers and more measured time points. In particular, behavior at much lower cell numbers, where the maximum is reached much later or not at all any more is essential for evaluating the model!
Your graphs show a measure of agreement between the forecasts and the observations. A statistical way of measuring the goodness-of fit of the model is by Pearson's chi-square test given by
chisquare = sigma[(observed-forecast)2/forecast] which under the null hypothesis of perfect agreement follows a chisquare distribution with k-1 degrees of freedom. Here k is the number of cells used.
Thanks to Johann and Ette for your answers. I'll follow your suggestions. Johann, I already was done more experiments combinning different numbers of cells and phages, the figure is only one example of what I am asking. Thank you very much for giving me these tips to adjust the model, I was wondering if it was a valid action.
Ette, thank you very much, is clear for me that the chi-square test is useful to evaluate differences between the predicted and experimental set of values. The question about it is how to do it with triplicated experiments. Do I have to do three comparisons for triplicates? I mean, compare the three experimental values with the same predictor value?
These links may help you
http://www.itl.nist.gov/div898/handbook/pmd/section4/pmd44.htm
https://stats.stackexchange.com/questions/30763/assessing-the-accuracy-of-a-deterministic-mathematical-model
https://www.mathworks.com/solutions/mathematical-modeling/evaluating-optimizing-models.html
http://scienceblogs.com/goodmath/2006/06/25/validity-of-mathematical-model/
http://onlinelibrary.wiley.com/doi/10.1002/9781119019770.ch9/summary
Conference Paper Verification and validation of simulation models
Article ON THE VALIDITY OF MATHEMATICAL-MODELING OF THE SPINE
Chapter Model Verification and Validation Techniques
- Badges
- Science topic
- Similar topics
- Biological Science
- Microbiology
- Microorganisms
- Bacteria