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We would like your opinion on whether GAMMs are a good option and how best to go about implementing for the following:

During a period of patient care, a nurse will accrue $Y$ colonies of bacteria on their hands. During every hand contact ($n$) (with surface area $A$) with a surface this number may increase a percentage ($\lambda$ %) of what she touches ($V$). However potentially this may also decrease as some percentage ($\beta$ %) of the bacteria are removed. After they finish the care episode, they may wash their hands with efficacy $h$.

The model is hence dependent on $Y=Y(n,A,V,\lambda,\beta,h)$

We think:

$n$=empirical, different for every nurse, $h=lognormal~(1.5,0.1)$, $\lambda=\Gamma(15,3)$, $\beta=$empirical non-negative. $A=lognormal~(7,1.9)$ and $V$=empirical, $h=\Gamma(5.91,0.4)$.

We'd like to know if GAM fitting is an appropriate way of estimating $Y$. Please let us know if you require further clarification.

Regards,

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    $\begingroup$ I'm a little confused -- you you have data on all of your explanatory variables? It seems like not, if you're specifying a distribution for them. Or are you doing something Bayesian, and sampling from a multivariate prior? If so, do your unobserved variables correlate with each other, or with your observed variables? $\endgroup$ Commented Apr 16, 2013 at 18:26
  • $\begingroup$ @ACD The only known input variables are $n$ (the number of surfaces each nurse touches) and $V$ (the contamination level of the surfaces). During each surface contact $\lambda$,$A$, and $\beta$ vary according to the given distributions. $\endgroup$
    – HCAI
    Commented Apr 16, 2013 at 20:29

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I think the model is incomplete. Why not consider her hands as a forest of SIR models? There are some things that "die on the vine" and for that "R" applies.

Here are links on SIR:

It seems that lognormal distributions may apply to some limited set of special cases of disease, but they are not general enough for unilateral applicability.

I have my head in random forests and a forest of SIR models (see IJAM link) is going to account for variation, give you robust answers, and have a basis that is generally applicable to the problem.

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