SURVIVORSHIP MODELS FOR SEXUALLY TRANSMISSIBLE DISEASES
SMITH, MELVYN LEE
Doctor of Philosophy
Motivated by the type of data naturally generated at Venereal Disease clinics, the author develops a general theory of survivorship analysis of sexually transmissible diseases (STD), with specific reference to estimating the survival distribution of incubation times and comparing groups with respect to incubation period distributions. Data pertaining to STD are often right-censored (known only to be greater than a certain value) or left-censored (known only to be less than a certain value), and samples are often truncated (potential sample points less than or greater than certain values excluded from the sample, with no knowledge of how many values are excluded); hence a theory of censorship (observation censoring and sample truncation) is presented, permitting a logical classification of censorship statistical literature and greater insight into the relationship between event and censoring times. A generalized Wilcoxon test for k samples with double-censoring (mixed right- and left-censoring) and unequal censoring distributions is derived. This test may be used to compare survival experiences (distrbutions of incubation periods) in groups with double-censoring where censoring patterns may not be equal. Application is made of survival techniques to incubation periods of gonorrheal and Chlamydial urethral and eye infections. The parametic form of the survival curve is shown to relate to the effectiveness of the immunologic process in altering the course of the disease: (1) mucosal infections with no effective immunity (gonorrheal urethritis and newborn conjunctivitis; Chlamydial newborn conjunctivitis and pneumonitis) are lognormal; (2) mucosal infections with some effective immunity (Chalmydial urethritis and Chlamydial adult eye disease) tend to be Weibull; (3) non-mucosal infections (neonatal goncoccal arthritis) are not necessarily lognormal. A mathematical derivation of the lognormal distribution incorporating the notion of no effective immunologic response is given. The symptomatic incubation period of male gonorrheal urethritis is shown to be lognormal. Further, it is shown that the mean, median, and geometric dispersion of this distribution have progressively increased since the introduction of sulfa in the 1930's and penicillin in the 1940's. It is proposed that this increase in the gonorrhea incubation period is the prime reason for failure to control the epidemic. Comprehensive reviews of statistical censorship literature and of ghonorrhea-Chlamydia literature are included.