Formulations and multivariate analysis

Last year, I was involved in setting up the infrastructure for our pre-formulation efforts and I came across this tour de force of a paper from Amgen.  The authors used a combination of differential scanning fluorimetry (DSF) and viscosity measurements in a 96-well plate format.  In the experiment, the factors that were varied were pH (5.0,5.5,6.0), cation (none, Ca2+, Mg2+), and excipient (none, sucrose, proline) to create a full-factorial experiment.  The authors then go a step further and include all their data for analysis.  Nice.

To code this into JMP, I used the following:
Concentration (coded): 1, 2, 3 = 89, 119, and 114 mg/mL
Ion = L1, L2, L3 = none, Ca2+, and Mg2+
Excipient = L1, L2, L3 = none, sucrose, and proline

Note: the ion and excipient are treated as categorical in the evaluation.

The ANOVA from the fit to the DSF data comes back with a very good fit to the data using all the factors:

Source	DF	Sum of Squares	Mean Square	F Ratio
Model	19	611.26126	32.1716	49.5988
Error	60	38.91824	0.6486	Prob > F
C. Total	79	650.17950		<.0001*

The statistically significant factors (p<0.05) are really just the main effects, the ions at L1 and L2 and the excipients at L1 and L2.  There is also a pair-wise interaction between the pH and ion L2 as well as between ion L1 and Excipient L1.

Term		Estimate	Std Error	t Ratio	Prob>|t|
Intercept		45.502467	0.322875	140.93	<.0001*
Concentration		-0.520754	0.111047	-4.69	<.0001*
pH		2.7281615	0.111047	24.57	<.0001*
Ion[L1]		1.785547	0.127117	14.05	<.0001*
Ion[L2]		-1.500541	0.127117	-11.80	<.0001*
Excipient[L1]		-0.969638	0.127117	-7.63	<.0001*
Excipient[L2]		0.7882553	0.127117	6.20	<.0001*
(Concentration-2.0125)*(pH-1.9875)		-0.119482	0.13696	-0.87	0.3865
(Concentration-2.0125)*Ion[L1]		-0.227752	0.156054	-1.46	0.1497
(Concentration-2.0125)*Ion[L2]		0.066692	0.156054	0.43	0.6706
(pH-1.9875)*Ion[L1]		0.1370117	0.156054	0.88	0.3835
(pH-1.9875)*Ion[L2]		-0.385211	0.156054	-2.47	0.0164*
(Concentration-2.0125)*Excipient[L1]		0.0222476	0.156054	0.14	0.8871
(Concentration-2.0125)*Excipient[L2]		0.0222476	0.156054	0.14	0.8871
(pH-1.9875)*Excipient[L1]		-0.235211	0.156054	-1.51	0.1370
(pH-1.9875)*Excipient[L2]		0.170345	0.156054	1.09	0.2794
Ion[L1]*Excipient[L1]		0.4098935	0.179382	2.29	0.0259*
Ion[L1]*Excipient[L2]		0.0247083	0.179382	0.14	0.8909
Ion[L2]*Excipient[L1]		-0.082699	0.179382	-0.46	0.6464
Ion[L2]*Excipient[L2]		-0.234551	0.179382	-1.31	0.1960

The next step is to fit with only the statistically significant factors and that's for the next installment!