IDEAS home Printed from https://ideas.repec.org/p/boc/usug12/03.html
   My bibliography  Save this paper

Numerical integration with an application in sample size reestimation

Author

Listed:
  • Adrian Mander

    (MRC Biostatistics Unit Hub for Trials Methodology, Cambridge)

  • Jack Bowden

    (MRC Biostatistics Unit Hub for Trials Methodology, Cambridge)

Abstract

We introduce a new integrate() function for Mata that evaluates single-dimensional integrals. This function uses three different Gaussian quadrature algorithms: Gauss–Hermite and Gauss–Laguerre for indefinite integrals; and Gauss–Legendre for definite integrals. The algorithms were implemented using the methods of Golub and Welsch (Mathematics of Computation, 1968). The user can specify any integrand by defining a new function in the Mata language. The integrand function is allowed to have two arguments: the first is the variable of integration, and the second is a real scalar. Thus the integrate() function can be used in combination with optimise() to solve for the value of x in an integral f(u,x) du = 0.05. Such calculations are used in the sample size re-estimation methodology introduced by Li, Shih, and Xie (Biostatistics, 2002). We apply these methods to a clinical trial where a single interim analysis is carried out, and the analysis is used to reevaluate the sample size.

Suggested Citation

  • Adrian Mander & Jack Bowden, 2012. "Numerical integration with an application in sample size reestimation," United Kingdom Stata Users' Group Meetings 2012 03, Stata Users Group.
    • Handle: RePEc:boc:usug12:03
    as

    Download full text from publisher

    File URL: http://repec.org/usug2012/UK12_mander.pdf
    Download Restriction: no
    ---><---

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boc:usug12:03. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Christopher F Baum (email available below). General contact details of provider: https://edirc.repec.org/data/stataea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.