title: Efficient interval estimation of a ratio of marginal probabilities in matched-pair data: non-iterative method.
abstract: Matched-pair designs have been commonly employed in diagnostic, epidemiologic and laboratory studies. For estimation of a ratio of two marginal probabilities in matched-pair data, a Wald-type logarithmic method is computationally simple, but an actual coverage rate is known to be smaller than a nominal one and a length of the confidence interval is shorter than it should be. The Fieller-type method based on constrained maximum likelihood (CML) estimators possesses asymptotically optimum statistical properties and a coverage rate is close to a nominal one. However, hitherto the limits have been obtained by numerical iterations. In this paper, we derive the efficient confidence limits based on CML as analytical solutions of a quartic equation and present the confidence limits in a closed form.
authors.affiliation: Biostatistics Branch, DCEG, National Cancer Institute, EPS/Room 8028, 6120 Executive Blvd, Rockville, MD 20852-7244, USA. namj@mail.nih.gov
authors.forename: Jun-Mo
authors.initials: JM
authors.lastname: Nam
mesh_terms: D056808:Biostatistics / Q000379:methods*; D016001:Confidence Intervals; D003627:Data Interpretation, Statistical; D005260:Female; D006801:Humans; D016013:Likelihood Functions; D015233:Models, Statistical; D021141:Nucleic Acid Amplification Techniques; D011336:Probability; D014247:Trichomonas Vaginitis / Q000175:diagnosis / Q000652:urine
references.citation: Control Clin Trials. 2001 Aug;22(4):373-89
references.pmid: 11514039
references.citation: Stat Med. 2006 Sep 15;25(17):3039-47
references.pmid: 16345058
references.citation: Stat Med. 1998 Apr 30;17(8):873-90
references.pmid: 9595617
references.citation: Stat Med. 1998 Apr 30;17(8):857-72
references.pmid: 9595616
references.citation: Stat Med. 2008 Jul 20;27(16):3209-10
references.pmid: 18561289
references.citation: Pediatrics. 1998 Oct;102(4 Pt 1):939-44
references.pmid: 9755269
references.citation: Biometrics. 1988 Jun;44(2):323-38
references.pmid: 3291957
references.citation: Stat Med. 1998 Oct 15;17(19):2207-17
references.pmid: 9802179
references.citation: Stat Med. 2007 Nov 10;26(25):4684-5
references.pmid: 17721871
references.citation: Biometrics. 1987 Mar;43(1):201-5
references.pmid: 3646071
references.citation: Stat Med. 2002 Mar 15;21(5):689-99
references.pmid: 11870810