Model predicted values around mean using training data - r

Question

I tried to ask these questions through imputations, but I want to see if this can be done with predictive modelling instead. I am trying to use information from 2003-2004 NHANES to predict future NHANES cycles. For some context, in 2003-2004 NHANES measured blood contaminants in individual people's blood. In this cycle, they also measured things such as triglycerides, cholesterol etc. that influence the concentration of these blood contaminants.
The first step in my workflow is the impute missing blood contaminant concentrations in 2003-2004 using the measured values of triglycerides, cholesterol etc. This is an easy step and very straightforward. This will be my training dataset.
For future NHANES years (for example 2005-2006), they took individual blood samples combined them (or pooled in other words) and then measured blood contaminants. I need to figure out what the individual concentrations were in these cycles. I have individual measurements for triglycerides, cholesterol etc. and the pooled value is considered the mean. Could I use the mean, 2003-2004 data to unpool or predict the values? For example, if a pool contains 8 individuals, we know the mean, the distribution (2003-2004) and the other parameters (triglycerides) which we can use in the regression to estimate the blood contaminants in those 8 individuals. This would be my test dataset where I have the same contaminants as in the training dataset, with a column for the number of individuals in each pool and the mean value. Alternatively, I can create rows of empty values for contaminants, add mean values separately.
I can easily run MICE, but I need to make sure that the distribution of the imputed data matches 2003-2004 and that the average of the imputed 8 individuals from the pools is equal to the measured pool. So the 8 values for each pool, need to average to the measured pool value while the distribution has to be the same as 2003-2004.
Does that make sense? Happy to provide context if need be. There is an outline code below.
library(mice)
library(tidyverse)
library(VIM)
#Papers detailing these functions can be found in MICE Cran package
df <- read.csv('2003_2004_template.csv', stringsAsFactors = TRUE, na.strings = c("", NA))
#Checking out the NA's that we are working with
non_detect_summary <- as.data.frame(df %>% summarize_all(funs(sum(is.na(.)))))
#helpful representation of ND
aggr_plot <- aggr(df[, 7:42], col=c('navyblue', 'red'),
numbers=TRUE,
sortVars=TRUE,
labels=names(df[, 7:42]),
cex.axis=.7,
gap=3,
ylab=c("Histogram of Missing Data", "Pattern"))
#Mice time, m is the number of imputed datasets (you can think of this as # of cycles)
#You can check out what regression methods below in console
methods(mice)
#Pick Method based on what you think is the best method. Read up.
#Now apply the right method
imputed_data <- mice(df, m = 30)
summary(imputed_data)
#if you want to see imputed values
imputed_data$imp
#finish the dataset
finished_imputed_data <- complete(imputed_data)
#Check for any missing values
sapply(finished_imputed_data, function(x) sum(is.na(x))) #All features should have a value of zero
#Helpful plot is the density plot. The density of the imputed data for each imputed dataset is showed
#in magenta while the density of the observed data is showed in blue.
#Again, under our previous assumptions we expect the distributions to be similar.
densityplot(x = imputed_data, data = ~ LBX028LA+LBX153LA+LBX189LA)
#Print off finished dataset
write_csv(finished_imputed_data, "finished_imputed_data.csv")
#This is where I need to use the finished_imputed_data to impute the values in the future years.