Bayesian Regression Model

Sep-13-2024

Bayesian Regression Model

Bayesian Regression model were used for generating numerical synthetic data for BW, LB and OM domain. MCMCregress function from MCMCpack R package MCMCpack: Markov Chain Monte Carlo in R were used to build the model.

Example for LB Domain

Variable full name
- LBCAT (Category for Lab Test)
- LBTEST (Lab Test or Examination Name)
- LBTESTCD (Lab Test or Examination Short Name)
- LBSTRESN (Standardized Result in Numeric Format)

A group of Control, male rats were chosen whrere
value of LBCAT variable was CLINICAL CHEMISTRY.
Mean of all LBTESTCD (PHOS, CA, CHOL, BIL, ALP etc) calculated for that group.

let’s say following table represent Mean of LBTESTCD.

LBTESTCD	MEAN
ALT	58
PROT	60
ALB	36
CL	105
GLUC	7

To build a model for ALT, algorithmically we chose two nearest value.
In this case, we chose PROT and ALB
Model Formula:

MCMCpack::MCMCregress("ALT ~ PROT + ALB", b0=0,B0=0.1, data= line)

Here line is the table that contain LBSTRESN (Standardized Result in Numeric Format)
for LBTESTCD (Lab Test or Examination Short Name)

ALT	PROT	ALB	CL	GLUC
58	59	36	105	6
59	60	37	104	9
57	61	35	106	6

Here is the model output:

INTERCEPT	COF_PROT	COF_ALB
0.05027991	2.3874235	-1.956665
-4.40402458	1.9721626	-1.627903
0.31785474	2.9303049	-3.017695

NOTE: Error column removed from the table because we did not use in any calculation.

We used a randomly chosen sample/row from the model output and
calculated synthetic ALT value for a specific animal.

ALT = INTERCEPT + COF_PROT * PROT + COF_ALB * ALB

• some noise added

noise <- stats::rnorm(1,mean=0,sd=(standard_deviation_of_that_group_for_ALT)

final_value = ALT + noise

• NOTE
  when predicted value returned negative, algorithmically a different sample was chosen and value re-calculated. We try this approach maximum ten times if a value returns negative. If value returns negative after ten try, absolute value of the negative value is taken as final value.