Statistical Methods for Reconstructing Infection Curves

The objective of this paper is to consider statistical issues for reconstructing infection curves. We investigate the method of back-calculation using a nonstationary incubation period distribution to account for recent treatment advances. A spline methodology based on a penalized likelihood is used for estimating historical infection rates. Estimates can be obtained through iteratively reweighted least squares. Some theoretical calculations to investigate mean square error are presented. There is tradeoff between bias and variance when choosing the smoothing parameter. An approach for choosing a range of sensible smoothing parameters is suggested. Some of the methods are illustrated with the U.S. AIDS epidemic.

[1]  G. Wahba.  A Comparison of GCV and GML for Choosing the Smoothing Parameter in the Generalized Spline Smoothing Problem , 1985 .

[2]  J B Carlin,et al.  A method of non-parametric back-projection and its application to AIDS data. , 1991, Statistics in medicine.

[3]  R Brookmeyer,et al.  Reconstruction and future trends of the AIDS epidemic in the United States. , 1991, Science.

[4]  S. Lagakos,et al.  The value of AIDS incidence data in assessing the spread of HIV infection. , 1989, Statistics in medicine.

[5]  Mitchell H. Gail,et al.  A Method for Obtaining Short-Term Projections and Lower Bounds on the Size of the AIDS Epidemic , 1988 .

[6]  P. Rosenberg,et al.  Uncertainty in estimates of HIV prevalence derived by backcalculation. , 1990, Annals of Epidemiology.

[7]  B. Yandell,et al.  Automatic Smoothing of Regression Functions in Generalized Linear Models , 1986 .

[8]  P. Bacchetti.  Estimating the Incubation Period of AIDS by Comparing Population Infection and Diagnosis Patterns , 1990 .

[9]  P. Rosenberg,et al.  Mean square error of estimates of HIV prevalence and short-term AIDS projections derived by backcalculation. , 1991, Statistics in medicine.

[10]  J. Goedert,et al.  Therapy may explain recent deficits in AIDS incidence. , 1990, Journal of acquired immune deficiency syndromes.

[11]  B. Silverman,et al.  Some Aspects of the Spline Smoothing Approach to Non‐Parametric Regression Curve Fitting , 1985 .

[12]  R Brookmeyer,et al.  Statistical methods for short-term projections of AIDS incidence. , 1989, Statistics in medicine.

[13]  Ron Brookmeyer,et al.  MINIMUM SIZE OF THE ACQUIRED IMMUNODEFICIENCY SYNDROME (AIDS) EPIDEMIC IN THE UNITED STATES , 1986, The Lancet.

[14]  J M Taylor,et al.  Models for the HIV infection and AIDS epidemic in the United States. , 1989, Statistics in medicine.

[15]  M H Gail,et al.  Backcalculation of flexible linear models of the human immunodeficiency virus infection curve. , 1991, Journal of the Royal Statistical Society. Series C, Applied statistics.

[16]  R. Brookmeyer,et al.  Methods for projecting course of acquired immunodeficiency syndrome epidemic. , 1988, Journal of the National Cancer Institute.

[17]  R Brookmeyer,et al.  Statistical modelling of the AIDS epidemic for forecasting health care needs. , 1990, Biometrics.

[18]  G. Wahba.  Spline models for observational data , 1990 .

[19]  Douglas Nychka,et al.  Bayesian Confidence Intervals for Smoothing Splines , 1988 .