Monte Carlo simulation of parameter confidence intervals for non-linear regression analysis of biological data using Microsoft Excel

Authors:
Ronald J. W. Lambert;Ioannis Mytilinaios;Luke Maitland;Angus M. Brown
Affiliations:
Applied Microbiology Group, Cranfield Health, Cranfield University, Cranfield MK43 0AL, UK;Applied Microbiology Group, Cranfield Health, Cranfield University, Cranfield MK43 0AL, UK;Applied Microbiology Group, Cranfield Health, Cranfield University, Cranfield MK43 0AL, UK;School of Biomedical Sciences, Queens Medical Centre, University of Nottingham, Nottingham NG7 2UH, UK
Venue:
Computer Methods and Programs in Biomedicine
Year:
2012

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Abstract

This study describes a method to obtain parameter confidence intervals from the fitting of non-linear functions to experimental data, using the SOLVER and Analysis ToolPaK Add-In of the Microsoft Excel spreadsheet. Previously we have shown that Excel can fit complex multiple functions to biological data, obtaining values equivalent to those returned by more specialized statistical or mathematical software. However, a disadvantage of using the Excel method was the inability to return confidence intervals for the computed parameters or the correlations between them. Using a simple Monte-Carlo procedure within the Excel spreadsheet (without recourse to programming), SOLVER can provide parameter estimates (up to 200 at a time) for multiple 'virtual' data sets, from which the required confidence intervals and correlation coefficients can be obtained. The general utility of the method is exemplified by applying it to the analysis of the growth of Listeria monocytogenes, the growth inhibition of Pseudomonas aeruginosa by chlorhexidine and the further analysis of the electrophysiological data from the compound action potential of the rodent optic nerve.