R MATRIX ALGORITHMICALLY SINGULAR

Greetings! I have run several models and the covariance steps have been unsuccessful due to the following error: R MATRIX ALGORITHMICALLY SINGULAR COVARIANCE MATRIX UNOBTAINABLE R MATRIX IS OUTPUT T MATRIX - EQUAL TO RS*R, WHERE S* IS THE INVERSE OF S - IS OUTPUT Does anyone have an idea as to what this indicates and how to 'fix" it? Thanks in advance for any help/input you can offer! Susan Susan Hudachek, M.S., Ph.D. Animal Cancer Center Veterinary Teaching Hospital Colorado State University 300 West Drake Road Fort Collins, CO 80523-1620 PHONE: (970) 219-7599 FAX: (970) 297-1254 EMAIL: Susan.Hudachek

Hi Susan, The most common reason is that you got too many parameters. But if there is someone who could summarize all other possible reasons for this kind of error, it would be really appreciated. If your model is not over-parameterized, there's one way to avoid it. You could try adding "Matrix=S" into $COV block. This would give you a similar estimate of covariance matrix if your sample size is large enough. Hope it helps, Tianli **************************************************** Tianli Wang PhD Candidate Department of Pharmaceutics University of Minnesota

Greetings! I have run several models and the covariance steps have been unsuccessful due to the following error: R MATRIX ALGORITHMICALLY SINGULAR COVARIANCE MATRIX UNOBTAINABLE R MATRIX IS OUTPUT T MATRIX - EQUAL TO RS*R, WHERE S* IS THE INVERSE OF S - IS OUTPUT Does anyone have an idea as to what this indicates and how to 'fix" it? Thanks in advance for any help/input you can offer! Susan Susan Hudachek, M.S., Ph.D. Animal Cancer Center Veterinary Teaching Hospital Colorado State University 300 West Drake Road Fort Collins, CO 80523-1620 PHONE: (970) 219-7599 FAX: (970) 297-1254 EMAIL: [email protected]

Dear Susan, Tianli, These kind of problems may be caused by numerical instability of the covariance step which seems to be unscaled in contrast to the estimation step. Inspection of the T (or R) matrix helps identifying the associated parameters: locate the largest number on the diagonal and look up that parameter. You are likely to find out that that particular parameter is much smaller than others. Such a parameter can be rescaled in the $PK block, e.g. by dividing it with a constant (or by exponentiation). Obviously, a very large parameter would result in the opposite behaviour. Other sources of numerical instability, apart from the aforementioned over-parameterization, are numerous but include: suboptimal choice of integration procedure (ADVAN and TOL), estimation mode (FOCE INTER is less stable than FOCE etc.), suboptimal design and outlying observations or individuals. Best regards, Jeroen Jeroen Elassaiss-Schaap, PhD Modeling & Simulation Expert Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) Early Clinical Research and Experimental Medicine Schering-Plough Research Institute T: +31 41266 9320

Hi Susan, The most common reason is that you got too many parameters. But if there is someone who could summarize all other possible reasons for this kind of error, it would be really appreciated. If your model is not over-parameterized, there's one way to avoid it. You could try adding "Matrix=S" into $COV block. This would give you a similar estimate of covariance matrix if your sample size is large enough. Hope it helps, Tianli **************************************************** Tianli Wang PhD Candidate Department of Pharmaceutics University of Minnesota

Hi Susan and Tianli, I am not the mathematician to argue with the behaviour of matrices, but I have my way of "dealing" with this message. First, it does not bother me too much. It comes (always?) with "Minimization successful" and that's better than having "rounding errors". It means that your minimum is fairly well described. Second, not having the covariance step does not hinder me to develop my models further. You get the tables you ask for and with those you can create the scatter plots which tell you a lot about the problems of your model. Third, I am a happy user of PsN which gives me the option to add "-retries=6 -picky" thus running the model six times with slightly altered starting values. Sometimes I find among the six results one where the covariance step was executed (it may not be the one with the lowest OFV). This way I can compare models and identify the parameter that might be either redundant or not supported by enough data. Other NMusers will answer more competently, Joachim -------------------------------------------------------------------------- AstraZeneca UK Limited is a company incorporated in England and Wales with registered number: 03674842 and a registered office at 15 Stanhope Gate, London W1K 1LN. Confidentiality Notice: This message is private and may contain confidential, proprietary and legally privileged information. If you have received this message in error, please notify us and remove it from your system and note that you must not copy, distribute or take any action in reliance on it. Any unauthorised use or disclosure of the contents of this message is not permitted and may be unlawful. Disclaimer: Email messages may be subject to delays, interception, non-delivery and unauthorised alterations. Therefore, information expressed in this message is not given or endorsed by AstraZeneca UK Limited unless otherwise notified by an authorised representative independent of this message. No contractual relationship is created by this message by any person unless specifically indicated by agreement in writing other than email. Monitoring: AstraZeneca UK Limited may monitor email traffic data and content for the purposes of the prevention and detection of crime, ensuring the security of our computer systems and checking Compliance with our Code of Conduct and Policies.

Dear Susan, Tianli, These kind of problems may be caused by numerical instability of the covariance step which seems to be unscaled in contrast to the estimation step. Inspection of the T (or R) matrix helps identifying the associated parameters: locate the largest number on the diagonal and look up that parameter. You are likely to find out that that particular parameter is much smaller than others. Such a parameter can be rescaled in the $PK block, e.g. by dividing it with a constant (or by exponentiation). Obviously, a very large parameter would result in the opposite behaviour. Other sources of numerical instability, apart from the aforementioned over-parameterization, are numerous but include: suboptimal choice of integration procedure (ADVAN and TOL), estimation mode (FOCE INTER is less stable than FOCE etc.), suboptimal design and outlying observations or individuals. Best regards, Jeroen Jeroen Elassaiss-Schaap, PhD Modeling & Simulation Expert Pharmacokinetics, Pharmacodynamics & Pharmacometrics (P3) Early Clinical Research and Experimental Medicine Schering-Plough Research Institute T: +31 41266 9320