Difference between revisions of "Dose response assessment"
(Creating stub for dose response with links to other MRA components) 
(→Available Dose Response Models) 

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−  +  [http://wiki.camra.msu.edu/index.php?title=Dose_Response_%28Home_Page%29 Back to Dose Response Home]  
+  
+  ==Dose Response==  
+  In the QMRA framework, the dose response assessment phase is the quantitative yardstick for the risk estimate, as this phase estimates a risk of response (infection, illness or death) with respect to a known dose of a pathogen. The basis of the dose response phase is the dose response models, which are mathematical functions derived to describe the dose response relationship for specific pathogens. Therefore, for a particular endpoint (response), a specific pathogen and exposure route there is a unique dose response relationship and consequently a dose response model. Dose response models are necessary as it is not possible to perform a direct study (even with animals) to assess dose corresponding to an acceptably low risk.  
+  
+  
+  ===Dose Response Models===  
+  
+  To be plausible a model should consider the discrete (particulate) nature of organisms, which has a high variability at  
+  low dose. It should also be based on the concept of infection from one or more “survivors” of initial dose.  
+  Therefore dose response models for QMRA need to be physiologically plausible and be derived from what is known of the general infection process. There are two models which are derived based on these needs for the QMRA dose response relationship, the exponential and beta Poisson models.  
+  
+  ==== Types of Models ====  
+  
+  '''Exponential Dose Response Model'''  
+  
+  Assumptions:  
+  *Poisson distribution of organisms among replicated doses (mean number in dose=d).  
+  *One organism is capable of producing an infection if it arrives at an appropriate site.  
+  *Organisms have independent and identical probability (k) of surviving to reach and infect at an appropriate site. Some sources use the letter 'r' instead of 'k' (equation 1). Here we define r=1/k, so the alternative form for equation 1 can be given as P(response) = 1 exp(dose/r)  
+  
+  <br>  
+  '''BetaPoisson Model''' <br>  
+  
+  Assumptions same as the exponential model except:  
+  *Nonconstant survival and infection probabilities  
+  *Survival probabilities (k) are given by the beta distribution  
+  
+  The slope of the betaPoisson dose response curve is more shallow than the exponential. The exponential model is the same as the betaPoisson model when alpha approaches infinity. The parameters are alpha and N50. N50 is the dose at which 50% of the population is expected to be affected. The betaPoisson model is sometimes expressed with a beta parameter instead of an N50 parameter; N50=beta*[2^(1/alpha)1]. Both the alpha and the beta parameters derive from the use of the beta distribution to model nonconstant pathogen survival probabilities.  
+  
+  The exact form of the betaPoisson model uses the confluent hypergeometric function, which can be difficult to optimize. However since both the exact and approximate form of the beta Poisson dose response models demonstrate linearity in the low dose range, and there is not a substantial difference between the forms in fitting dose response data, there is not reason to not use the more intuitive form of the beta Poisson. Equation 2 shows the approximate form of the beta Poisson using the N<sub>50</sub> parameter, which can be directly optimized using dose response data or estimated using the conversion in equation 4.  
+  
+  [[File:Revised_exponential.pngthumbleft400px]] [[File:Beta_poisson_with_beta_conversion.pngthumbcenter400px]]<br />  
+  
+  
+  
+  
+  
+  
+  
+  
+  
+  == Utility of Using Dose Response Models ==  
+  
+  An optimized dose response model allows for greater flexibility and a wider range of understanding in the estimated risk. Rather than having a median infectious or lethal dose for a pathogen a model that can describe the full range of probability of response beyond just the median and one that is still accurate at low doses.  
+  
+  
+  == Available Dose Response Models ==  
+  You can access completed dose response analysis for each microbe by clicking the name of the pathogen in the following table.  
+  {  
+   STYLE="verticalalign: top; textalign: center"  
+  { border = "1"  
+    
+   rowspan = "1"  '''Bacteria'''{{#ask:[[Recommended DR Model::<q>[[Category:Bacterium]]</q>]]format = templateintrotemplate =DRallmodelsTableStartoutrotemplate =DRallpreferredModelsTableEndmainlabel =showheaders =hidetemplate=DRallmodelsROW?RDR Best Fit=Best Fit Model?RDR Parameter=Parameter?RDR N50=N50?RDR Host=Host ?RDR Strain=Agent Strain ?RDR Route=Route?RDR Dose=Dose?RDR Unit=Dose Unit?RDR Response=Response?RDR Reference=Referencelimit=500}}  
+    
+   rowspan = "1"  '''Prion'''{{#ask:[[Recommended DR Model::<q>[[Category:Prion]]</q>]]format = templateintrotemplate =DRallmodelsTableStartoutrotemplate =DRallpreferredModelsTableEndmainlabel =showheaders =hidetemplate=DRallmodelsROW?RDR Best Fit=Best Fit Model?RDR Parameter=Parameter?RDR N50=N50?RDR Host=Host ?RDR Strain=Agent Strain ?RDR Route=Route?RDR Dose=Dose?RDR Unit=Dose Unit?RDR Response=Response?RDR Reference=Referencelimit=500}}  
+    
+   rowspan = "1"  '''Protozoa'''{{#ask:[[Recommended DR Model::<q>[[Category:Protozoan]]</q>]]format = templateintrotemplate =DRallmodelsTableStartoutrotemplate =DRallpreferredModelsTableEndmainlabel =showheaders =hidetemplate=DRallmodelsROW?RDR Best Fit=Best Fit Model?RDR Parameter=Parameter?RDR N50=N50?RDR Host=Host ?RDR Strain=Agent Strain ?RDR Route=Route?RDR Dose=Dose?RDR Unit=Dose Unit?RDR Response=Response?RDR Reference=Referencelimit=500}}  
+    
+   rowspan = "1"  '''Virus'''{{#ask:[[Recommended DR Model::<q>[[Category:Virus]]</q>]]format = templateintrotemplate =DRallmodelsTableStartoutrotemplate =DRallpreferredModelsTableEndmainlabel =showheaders =hidetemplate=DRallmodelsROW?RDR Best Fit=Best Fit Model?RDR Parameter=Parameter?RDR N50=N50?RDR Host=Host ?RDR Strain=Agent Strain ?RDR Route=Route?RDR Dose=Dose?RDR Unit=Dose Unit?RDR Response=Response?RDR Reference=Referencelimit=500}}  
+    
+  }  
+  }  
+  
+  ==Criteria for choosing dose response models==  
+  
+  We prefer dose response models with the following criteria, in rough order of importance:  
+  
+  #Statistically acceptable fit (fail to reject goodness of fit, p > 0.05)  
+  #Human subjects, or animal models that mimic human pathophysiology well  
+  #Infection as the response, rather than disease, symptoms, or death  
+  #Exposure route similar/identical to the exposure route of natural infection  
+  #Pathogen strain is similar to strains causing natural infection  
+  #Pooled model using data from 2 or more experiments, provided the data sets are statistically similar (fail to reject that datasets are from the same distribution, p > 0.05)  
+  #Low ID<sub>50</sub>/LD<sub>50</sub> (to obtain a conservative risk estimate)  
+  
+  We generally recommend a single dose response model, and we justify the decision in terms of the above criteria. This decision is somewhat subjective, since dose response datasets seldom meet all of these criteria. If all available models are unsatisfactory, we choose a single model to ‘recommend with reservations’. Our recommended model will seldom (if ever) be the best model for all applications. The user should carefully choose the model that is most appropriate for their particular problem.  
+  
+  
+  ==[[Dose Response Mathematical & Statistical Approaches SummaryMathematical & Statistical Approaches]]==  
+  
+  Various regression techniques are used to characterize doseresponse relationships via a mathematical function. Doseresponse relationships are probabilistic and will therefore take a value between 0 and 1. A doseresponse analysis begins with a '''bestfit''' test of doseresponse data. These data are usually provided in the literature as a comparison of the median dose concentration and number of organisms that experienced a given effect (infection, illness, death; known as the '''endpoint''') at that dose. The statistical technique '''maximum likelihood estimation (MLE)''' is used to fit the data to theoretical distributions, typically either '''BetaPoisson''' or '''Exponential''' due to their biologic plausibility. This process calculates the probability of obtaining the observed data given a theoretical distribution by minimizing '''deviance (Y)''' of each of these model fits:  
+  
+  <center>Y=2(lnM<sub>1</sub>  lnM<sub>2</sub>)</center>  
+  
+  Where L<sub>1</sub>, L<sub>2</sub> are maximized likelihood estimates for the full (L<sub>2</sub>) and restricted (L<sub>1</sub>) models. Optimized deviance follows a Χ<sup>2</sup> distribution with ''k – m'' degrees of freedom, where ''k'' is the number of doses and ''m'' is the number of doseresponse parameters of a given model. This allows the analyst to reject the model if Y > Χ<sup>2</sup><sub>''km,α''</sub>. If both models are significant, the model with the lowest deviance when compared to the full (for example the empirical model with a separate parameter for each dose group) model is chosen. '''Bootstrapping''' is performed to characterize the uncertainty of parameter estimates (r, α, N<sub>50</sub>, etc.) of the distribution, most commonly by generating confidence intervals. The estimates from this approach approximate the uncertainty associated with the “true” distribution by repeatedly sampling the data and recomputing a statistic.  
+  
+  In some cases, it is necessary to '''pool''' data from different studies to compare strains or increase confidence in a doseresponse model. The ability to pool data is assessed via a '''hypothesis test''' (null: no difference in doseresponse parameter(s)), where the deviance of the pooled dataset (Y<sub>T</sub>) is added to each individual optimized deviance (Y<sub>1</sub>, Y<sub>2</sub>..) and Δ is compared to a Χ<sup>2</sup> distribution with df= (number of parameters in each dataset) ‒ (total number of parameters):  
+  
+  <center>Δ=Y<sub>T</sub>  (Y<sub>1</sub> + Y<sub>2</sub> +...)</center>  
+  
+  If these approaches are not sufficient to describe the model fit, more complex approaches must be applied.  
+  
+  ==[[Dosing ExperimentsDosing Experiments]]==  
+  
+  '''Bacteria''': [[Bacillus Anthracis: Feeding Experiments''Bacillus anthracis'']], [[Feeding Experiment for Burkholderia''Berkholderia mallei and pseudomallei'']], [[Feeding Experiment for Campylobacter jejuni''Campylobacter jejuni'']], [[Feeding Experiment for Coxiella burnetii''Coxiella burnetii'']], [[Feeding Experiment for Escherichia coli''Escherichia coli'']], [[Feeding Experiment for enterohemorrhagic Escherichia coli (EHEC)enterohemorrhagic ''Escherichia coli'' (EHEC)]], [[Feeding Experiment for Francisella tularensis''Francisella tularensis'']], [[Feeding Experiment for Legionella pneumophila''Legionella pneumophila'']], [[Feeding Experiment for Rickettsia rickettsi''Rickettsia rickettsi'']], [[Feeding Experiment for Salmonella nontyphoid''Salmonella'' nontyphoid]], [[Feeding Experiment for Salmonella typhoid''Salmonella'' typhoid]], [[Feeding Experiment for Salmonella anatum''Salmonella anatum'']], [[Feeding Experiment for Salmonella newport''Salmonella newport'']], [[Feeding Experiment for Salmonella meleagridis''Salmonella meleagridis'']], [[Feeding Experiment for Shigella species''Shigella sp.'']], [[Feeding Experiment for Vibrio cholera''Vibrio cholera'']], [[Feeding Experiment for Yersinia pestis''Yersinia pestis'']] <br />  
+  '''Prion''': [[Feeding Experiment for PrionPrion]] <br />  
+  '''Protozoa''': [[Feeding Experiment for Cryptosporidium parvum and Cryptosporidium hominis''Cryptosporidium parvum'' and ''Cryptosporidium hominis'']], [[Feeding Experiment for Endamoeba coli''Endamoeba coli'']], [[Feeding Experiment for Giardia duodenalis''Giardia duodenalis'']], [[Feeding Experiment for Naegleria''Naegleria fowleri'']] <br />  
+  '''Virus''': [[Feeding Experiment for Adenovirus4Adenovirus4]], [[Feeding Experiment for Echovirus12Echovirus12]], [[Feeding Experiment for EnterovirusEnterovirus]], [[Feeding Experiment for InfluenzaInfluenza]], [[Feeding Experiment for Lassa virusLassa virus]], [[Feeding Experiment for RhinovirusRhinovirus]], [[Feeding Experiment for RotavirusRotavirus]], [[Feeding Experiment for SARSSARS]] <br />  
+  
    
Besides dose response assessment, the other major components of microbial risk assessment are [[hazard identification]], [[exposure assessment]], and [[risk characterization]].  Besides dose response assessment, the other major components of microbial risk assessment are [[hazard identification]], [[exposure assessment]], and [[risk characterization]]. 
Latest revision as of 11:25, 5 July 2017
Contents
Dose Response
In the QMRA framework, the dose response assessment phase is the quantitative yardstick for the risk estimate, as this phase estimates a risk of response (infection, illness or death) with respect to a known dose of a pathogen. The basis of the dose response phase is the dose response models, which are mathematical functions derived to describe the dose response relationship for specific pathogens. Therefore, for a particular endpoint (response), a specific pathogen and exposure route there is a unique dose response relationship and consequently a dose response model. Dose response models are necessary as it is not possible to perform a direct study (even with animals) to assess dose corresponding to an acceptably low risk.
Dose Response Models
To be plausible a model should consider the discrete (particulate) nature of organisms, which has a high variability at low dose. It should also be based on the concept of infection from one or more “survivors” of initial dose. Therefore dose response models for QMRA need to be physiologically plausible and be derived from what is known of the general infection process. There are two models which are derived based on these needs for the QMRA dose response relationship, the exponential and beta Poisson models.
Types of Models
Exponential Dose Response Model
Assumptions:
 Poisson distribution of organisms among replicated doses (mean number in dose=d).
 One organism is capable of producing an infection if it arrives at an appropriate site.
 Organisms have independent and identical probability (k) of surviving to reach and infect at an appropriate site. Some sources use the letter 'r' instead of 'k' (equation 1). Here we define r=1/k, so the alternative form for equation 1 can be given as P(response) = 1 exp(dose/r)
BetaPoisson Model
Assumptions same as the exponential model except:
 Nonconstant survival and infection probabilities
 Survival probabilities (k) are given by the beta distribution
The slope of the betaPoisson dose response curve is more shallow than the exponential. The exponential model is the same as the betaPoisson model when alpha approaches infinity. The parameters are alpha and N50. N50 is the dose at which 50% of the population is expected to be affected. The betaPoisson model is sometimes expressed with a beta parameter instead of an N50 parameter; N50=beta*[2^(1/alpha)1]. Both the alpha and the beta parameters derive from the use of the beta distribution to model nonconstant pathogen survival probabilities.
The exact form of the betaPoisson model uses the confluent hypergeometric function, which can be difficult to optimize. However since both the exact and approximate form of the beta Poisson dose response models demonstrate linearity in the low dose range, and there is not a substantial difference between the forms in fitting dose response data, there is not reason to not use the more intuitive form of the beta Poisson. Equation 2 shows the approximate form of the beta Poisson using the N_{50} parameter, which can be directly optimized using dose response data or estimated using the conversion in equation 4.
Utility of Using Dose Response Models
An optimized dose response model allows for greater flexibility and a wider range of understanding in the estimated risk. Rather than having a median infectious or lethal dose for a pathogen a model that can describe the full range of probability of response beyond just the median and one that is still accurate at low doses.
Available Dose Response Models
You can access completed dose response analysis for each microbe by clicking the name of the pathogen in the following table.

Criteria for choosing dose response models
We prefer dose response models with the following criteria, in rough order of importance:
 Statistically acceptable fit (fail to reject goodness of fit, p > 0.05)
 Human subjects, or animal models that mimic human pathophysiology well
 Infection as the response, rather than disease, symptoms, or death
 Exposure route similar/identical to the exposure route of natural infection
 Pathogen strain is similar to strains causing natural infection
 Pooled model using data from 2 or more experiments, provided the data sets are statistically similar (fail to reject that datasets are from the same distribution, p > 0.05)
 Low ID_{50}/LD_{50} (to obtain a conservative risk estimate)
We generally recommend a single dose response model, and we justify the decision in terms of the above criteria. This decision is somewhat subjective, since dose response datasets seldom meet all of these criteria. If all available models are unsatisfactory, we choose a single model to ‘recommend with reservations’. Our recommended model will seldom (if ever) be the best model for all applications. The user should carefully choose the model that is most appropriate for their particular problem.
Mathematical & Statistical Approaches
Various regression techniques are used to characterize doseresponse relationships via a mathematical function. Doseresponse relationships are probabilistic and will therefore take a value between 0 and 1. A doseresponse analysis begins with a bestfit test of doseresponse data. These data are usually provided in the literature as a comparison of the median dose concentration and number of organisms that experienced a given effect (infection, illness, death; known as the endpoint) at that dose. The statistical technique maximum likelihood estimation (MLE) is used to fit the data to theoretical distributions, typically either BetaPoisson or Exponential due to their biologic plausibility. This process calculates the probability of obtaining the observed data given a theoretical distribution by minimizing deviance (Y) of each of these model fits:
Where L_{1}, L_{2} are maximized likelihood estimates for the full (L_{2}) and restricted (L_{1}) models. Optimized deviance follows a Χ^{2} distribution with k – m degrees of freedom, where k is the number of doses and m is the number of doseresponse parameters of a given model. This allows the analyst to reject the model if Y > Χ^{2}_{km,α}. If both models are significant, the model with the lowest deviance when compared to the full (for example the empirical model with a separate parameter for each dose group) model is chosen. Bootstrapping is performed to characterize the uncertainty of parameter estimates (r, α, N_{50}, etc.) of the distribution, most commonly by generating confidence intervals. The estimates from this approach approximate the uncertainty associated with the “true” distribution by repeatedly sampling the data and recomputing a statistic.
In some cases, it is necessary to pool data from different studies to compare strains or increase confidence in a doseresponse model. The ability to pool data is assessed via a hypothesis test (null: no difference in doseresponse parameter(s)), where the deviance of the pooled dataset (Y_{T}) is added to each individual optimized deviance (Y_{1}, Y_{2}..) and Δ is compared to a Χ^{2} distribution with df= (number of parameters in each dataset) ‒ (total number of parameters):
If these approaches are not sufficient to describe the model fit, more complex approaches must be applied.
Dosing Experiments
Bacteria: Bacillus anthracis, Berkholderia mallei and pseudomallei, Campylobacter jejuni, Coxiella burnetii, Escherichia coli, enterohemorrhagic Escherichia coli (EHEC), Francisella tularensis, Legionella pneumophila, Rickettsia rickettsi, Salmonella nontyphoid, Salmonella typhoid, Salmonella anatum, Salmonella newport, Salmonella meleagridis, Shigella sp., Vibrio cholera, Yersinia pestis
Prion: Prion
Protozoa: Cryptosporidium parvum and Cryptosporidium hominis, Endamoeba coli, Giardia duodenalis, Naegleria fowleri
Virus: Adenovirus4, Echovirus12, Enterovirus, Influenza, Lassa virus, Rhinovirus, Rotavirus, SARS
Besides dose response assessment, the other major components of microbial risk assessment are hazard identification, exposure assessment, and risk characterization.