Log transformation, normalization and skewness I'm French Resident in Haematology working on myeloma disease.
I've got a 360 patient-cases continuous variable (MRD) which range from 0 to 7%.
The fact, MRD is a residual variable disease calculated with a sensibility-technique of 10^-5, Thus any value below 10^-5 is returned to 0,00000.
I want to analyse in a regression model this continuous variable and need then to have normal fitting.
In the series, there is a plenty of values equal to 0 du to the limit sensibility of the assay (10^-5), Then how would you transform the variable considering 0 values to have a normal fitted distribution ?
the log-transform would be a good idea but i'm not sure how to replace 0 values not to be irrelevent

Thank you very much for helping !!
Edit - 02/02/2023 -
The aim is to :
estimate MRD distribution in each subgroups(n=2 or 3) of my population (thoses subgroups have well known different prognostics)
And i want to be able to compare the distribution of MRD of each subgroup to "estimate a disease clearence kinetics" for each.
Then this MRD would be more a predictor than an outcome considering a Cox model and hazard ratio, i wish to provide information like =
"In this subgroup... this hazard ratio represent the decrease in risk of a event that is associated with each log fold reduction in disease MRD.
NB : Outcome are survival outcome : overal survival, progression free survival and relapse risk

I am most likely echoing what @EdM mentioned above. For -ve values I would suggest adding a small jitter such that the lowest of the -ve values changes to 0.001. Which means you choose an offset value such that the smallest -ve value is now 0.001 and the corresponding values are shifted up the constant offset value accordingly.
There is no rule that the continuous outcome should be normally distributed, only the residual after the model fit should be normally distributed. You could also try truncated normal distribution to ignore values below the threshold.
