Nonparametric Estimation of a Delay Distribution Based on Left‐Censored and Right‐Truncated Data

• Published in: Biometrics Vol. 55; no. 2; pp. 345 - 349
• Main Author: Cui, Jisheng
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishing Ltd 01.06.1999; International Biometric Society
• Subjects: acquired immunodeficiency syndrome; Acquired Immunodeficiency Syndrome - epidemiology; AIDS; Analysis of Variance; Analytical estimating; Australia - epidemiology; Biometrics; Biometry; Censored data; Censoring; Censorship; Data Interpretation, Statistical; Delay distribution; disease outbreaks; Epidemics; Epidemiologic Methods; Estimation methods; Estimators; Humans; Nonparametric estimation; probability distribution; Standard error; Truncation; Australia
• ISSN: 0006-341X; 1541-0420
• DOI: 10.1111/j.0006-341X.1999.00345.x

This paper proposes a nonparametric method for estimating a delay distribution based on left‐censored and right‐truncated data. A variance‐covariance estimator is provided. The method is applied to the Australian AIDS data in which some data are left censored and some data are not left censored. This situation arises with AIDS case‐reporting data in Australia because reporting delays were recorded only from November 1990 rather than from the beginning of the epidemic there. It is shown that inclusion of the left‐censored data, as opposed to analyzing only the uncensored data, improves the precision of the estimate.