# Prevalence models in health science

I chose to divide generic prediction models applied in health science and administration into two main groups: Models based on general activity measures such as number of hospitalizations, LOS, number of visits, cost, diagnose groups, age, geography and other background information. A second and neglected group of models is based on prevalence of specific activity measures common for a substantial part of the population in question. Prediction models in health take advantage of RFM-I methodology from market analysis, which have previously been mentioned in posts on SAS macros on this blog, below I discuss the simplicity of prevalence models.

Prevalence models have my special attention as pivot for machine learning and deep learning models. Prevalence models include indicators on activity common among 1%, 5% or 10% of a population, e.g. diagnoses, operations and procedures common to 1% of the patients from a ward with a retroperspective ranging from months to years. Background information on age, gender, geography, total cost etc may be added, furthermore and more importantly a clinical specialist may request addition or exclusion of operations, procedures and have other demands for quantitative measures mirroring the clinical developmental program of a specialization. Prevalence models offer very flexible modelling frameworks for quality analysis and decision support tools in the clinic.

In the result below I define a population of patients visiting a ward within a particular month. Then I add information on their activity patterns from the LPR (Danish National Health Register) in 2 years retroperspective and information on whether they are hospitalized (acute) within the next month. Indicators are defined using a short dummy-variable coding function and aggregated with ML techniques. The R-function use a key-variable V_CPR, and needs to be adapted before it is applicable in other settings…

```
dummyl <- function(data, varname, vallevels,datevar,evaldate){
data<-data[trimws(data[[which(names(data)==varname)]]) %in% vallevels,]
df<-as.data.frame(matrix(0,nrow(data),2*length(vallevels))
for(i in 1:length(vallevels)){
df[,c(i,i+length(vallevels))]<-c(1.0*(trimws(data[[which(names(data)==varname)]])==trimws(vallevels[i])),log(as.integer(as.Date(evaldate)as.Date(data[[which(names(data)==datevar)]]))))
df[1.0*(trimws(data[[which(names(data)==varname)]])==trimws(vallevels[i]))<1,i+length(vallevels)]<-rep(NA,sum(1.0*(trimws(data[[which(names(data)==varname)]])==trimws(vallevels[i]))<1))
names(df)[c(i,i+length(vallevels))]<-c(vallevels[i],paste0(c(vallevels[i],"_dto"),sep="",collapse=""))
}
dt<-setorderv(cbind.data.frame(data,df),c("V_CPR",varname,datevar),c(1,1,-1))
return(dt)
}
```

A 200 line code script generates a fairy good raw prevalence model for prediction of acute hospitalization with a AUC above 0.92, the probability of aligning a pair of patients correct based on estimated risk for acute hospitalization is very high. Least squares and subsequently logistic regression makes a solid foundation for a stable and adjustable prediction model.

```
#Example of usage, generating indicators for 5% prevalence model used for accumalating measures in regression analysis
temp<-unique(Dat[,c("V_CPR","val")])
tbl<-table(temp$val)
lvs_5pct5*length(cprnr)/100])
lvs_5pct
dt<-dummyl(Dat,"val",lvs_5pct,"date","2017-12-01")
```

The data extraction and manipulation uses SQL and ML R-packages RODBC, tidyr, stringr and dplyr. Estimation requires basic R algorithms and GLM modeling.