1. Computing tolerance intervals in JMP
Authors : Jean-François Michiels1, Sarah Janssen2, Pierre Lebrun3.
1 Corresponding author, Arlenda SA, Liège, Belgium ( ;
2 Janssen Biologics, Leiden, Netherlands ;3 Arlenda SA, Liège, Belgium
Tolerance intervals
Formulas are depending on the model used to fit the data. Most classical models are:
Normal model
ANOVA 1 random model
linear model with/without random factor
Etc.
Tolerance intervals for Normal model are already available in JMP. ANOVA1 with one random effect is not available in JMP, but can be scripted easily.
However, scientists in the pharma industry are reluctant to scripting and are requesting a user-friendly tool to compute tolerance intervals for their problems. This will also free time for statisticians for most interesting projects.
The add-in can manage the computation separately for different groups and must not crash for dummy errors of the user.
Why an add-in to compute tolerance intervals?
Conclusions
They are two kinds of tolerance intervals. The beta-expectation and beta-content gamma-confidence intervals. Those intervals are widely used in the pharmaceutical industry. For example, in bridging studies a beta-content gamma-confidence tolerance interval is computed on data obtained with a reference process, and a beta-expectation tolerance interval is computed on data obtained with a modified process. If the latter is included is the former, this is a good indication that the outputs are not modified by the process change. Another example is the use of beta-expectation intervals for computing an accuracy profile in the context of assay validation.
Scientists are using tolerance intervals in many studies, for example to establish control limits. Statisticians are required frequently to compute them. Although for complex studies, statisticians certainly must be involved, this add-in provides a tool for scientists to compute tolerance intervals in various configurations (different models, presence of different groups to be computed separately, etc.).
This add-in is provided with a help document as well as various example datasets. This is strongly required that scientists understand the correct interpretation of tolerance intervals, before using the tool.
JMP add-in is one of the tools Arlenda is using to provide scientists direct access to the processing and interpretation of their data.
CLICK FIGURE FOR DETAILS ON TOLERANCE INTERVALS
CLICK HERE FOR SCREEN-SHOTS
CLICK HERE FOR TRICKS IN JSL
JMP Discovery summit, Amsterdam, MARCH 2016

2. Computing tolerance intervals in JMP
b-expectation tolerance interval is a statistical interval within which a specified proportion (beta) of the population is expected to fall.
The way kE is computed depends on the model
b-expectation tolerance intervals
b-content g-confidence tolerance intervals
b-expectation tolerance intervals
b-content g-confidence tolerance interval that is an interval within which a beta proportion of the population fall, with the confidence level gamma.
The way kC is computed depends on the model
b-content g-confidence tolerance intervals
Example
The 95%-proportion tolerance interval computed on new data (blue) fits within the 95%-content 90%-confidence tolerance interval computed on old data (red). This illustrates that either both sets of data originates from the same process or that the known modifications does not affect the results.
CLICK HERE TO RETURN
JMP Discovery summit, Amsterdam, MARCH 2016

3. CLICK HERE TO RETURN
JMP Discovery summit, Amsterdam, MARCH 2016

4. Expressions to fit by group
dt = open("$SAMPLE_DATA/Big Class.jmp");
::By = {"sex","age"};
distr = expr(distr_platform = dt << Distribution( Continuous Distribution( Column( :height ) ) , bygroupanalysis ));
show(distr);
if(length(::By)==0,
byexpression = expr(by()),
if(length(::By)==1,
byexpression = eval expr( by( Column( expr(::By[1]) ) ) ),
byexpression = eval expr( by( Column( expr(::By[1]) ), Column( expr(::By[2]) ) ) ) ) );
distr2 = substitute(Name expr(distr),expr(bygroupanalysis),name expr(byexpression));
eval(distr2);
distr2_reported = distr_platform << report();
distr2_reported["Summary Statistics"][1][1] << make data table(),
distr2_reported[1]["Summary Statistics"][1][1] << make combined data table());
Expressions to fit by group
CLICK HERE TO RETURN
JMP Discovery summit, Amsterdam, MARCH 2016