Limitations and Mathematical Models - Case Study Example

Mathematical models should be given room for error when it comes to their limitations. Making mathematical models depend on the current findings of the scientific community. For example, if the necessary data is inadequate to produce a numerical estimate of exposure to a certain disease, qualitative assessments are allowed to describe the probability of acquiring the disease based on the defined factors. With this in mind, assumptions are allowed, as long as the defining variables of the model are based on parameters whose contribution to the development of the disease has been found by several valid studies. Furthermore, the variability and uncertainty of these models should be described extensively (World Health Organization, 2005).

            Therefore, as technology continuously improves, mathematical models similarly change constantly to adapt to the new findings discovered. What the State should do is keep itself updated regarding the newest models that represent risks for certain diseases.

 Exposure Assessments

            Of course, despite the recognition that mathematical models may not identify all the interplaying risks involved and put enough weight on them, everyone should be vigilant in meticulously looking at how the mathematical models were obtained to determine whether they put enough weight on all identified risk factors or not. In my opinion, all mathematical models on exposure assessments should be validated by the researchers themselves, especially if they are to be used in passing laws by the state.

            Laws should not be based on unfound mathematical models because they direct the focus of concerned government agencies toward what was identified by the mathematical model as the defining risk factors for the development of the disease. When many studies have proven obesity as one of the more important risk factors in the development of cardiovascular diseases that have caused mortality in a lot of Americans, even first lady Michelle Obama herself promoted a healthy diet and exercise. Thalidomide, a drug widely available for use in women, was banned from the market as it was found through several studies that it causes physical malformation in these women’s newborns.   

             In addition, lawmakers should also choose the exposure assessment and corresponding mathematical model that cater to their purposes (World Health Organization, 2008). For example, if they are planning to mitigate the spread of infectious disease, an overestimation of the infective agent’s potential is better than underestimating them. However, a more stringent exposure assessment and mathematical model should be used in allowing drugs into the market, which may either be therapeutic or toxic depending on their concentration.       

Model Validity

            As discussed above, the reliability of models in sufficiently representing real-life situations is crucial, especially in the government. Model validity must thus be conducted regularly. However, one must note that even if a model is valid for one purpose, it does not mean the same is true for other objectives as well. Remember that models are made based on specific objectives (World Health Organization, 2005).

            First and foremost, validity largely depends on the state of data and documentation. When data is poorly gathered and/or insufficiently documented, the model is not valid, no matter how logical the model seems to be. Documentation must be clear, honest, fully referenced, provided with background, and ended with conclusions. As for the model, World Health Organization (2008) suggests that it must answer four questions, namely: “Is the model plausible? Is the model appropriate for the set objectives, Is the model implemented correctly, and does the model output makes sense?” As an example, model validity can be done by randomly selecting individuals from the population in question, and determining whether these individuals adhere to the model or not, such as that conducted by Xue et al. (2005) in determining the validity of their model describing ozone exposure assessment.

            Of course, recognition adds to the credibility of the model. It is thus recommended that models, together with all the used data during the development and the testing of the validity of the model, should be published in an appropriate peer review scientific journal. Not only does it face the scrutiny of the reviewers that determine whether the model is worth publishing or not, but it will also face the critique of journal readers once the model is presented to the public (World Health Organization, 2008).