Nonlinear modeling of serial immunologic data: A case study

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

This article concerns the analysis of serial immunologic data from a clinical trial of immunosuppressive chemotherapy in the treatment of multiple sclerosis. The goal of the analysis is to relate levels of drug dose to levels of an immunologic outcome variable. I propose a new, nonlinear model for the analysis of such data. The model assumes that the mean function is the solution of an ordinary differential equation in time, parameters of which are related to the dose via a regression function. The defining differential equation is that which gives rise to the generalized logistic function, a flexible form that includes a number of popular growth models. We fit the model, which accounts for random effects and time series autocorrelation, by maximum likelihood. Results suggest strong treatment effects in two active-drug groups and a small but significant effect in a placebo group. These findings agree well with previously reported analyses of clinical outcomes from the trial. An empirical comparison suggests that nonlinear models of this kind can fit better than linear models of comparable complexity.

Original languageEnglish (US)
Pages (from-to)891-898
Number of pages8
JournalJournal of the American Statistical Association
Volume86
Issue number416
DOIs
StatePublished - Jan 1 1991

Fingerprint

Nonlinear Modeling
Nonlinear Model
Dose
Drugs
Multiple Sclerosis
Chemotherapy
Treatment Effects
Regression Function
Growth Model
Random Effects
Autocorrelation
Clinical Trials
Logistics
Maximum Likelihood
Linear Model
Ordinary differential equation
Time series
Differential equation
Model
Nonlinear modeling

Keywords

  • Autoregressive model
  • Azathioprine
  • Generalized logistic model
  • Multiple sclerosis
  • Placebo effect
  • Random effects model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Nonlinear modeling of serial immunologic data : A case study. / Heitjan, Daniel F.

In: Journal of the American Statistical Association, Vol. 86, No. 416, 01.01.1991, p. 891-898.

Research output: Contribution to journalArticle

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