Recent work has focused attention on statistical inference for the population
distribution of the number of sexual partners based on survey data.
The characteristics of these distributions are of interest as components of
mathematical models for the transmission dynamics of sexually-transmitted
diseases (STDs). Such information can be used both to calibrate theoretical
models, to make predictions for real populations, and as a tool for guiding
public health policy.
Our previous work on this subject has developed likelihood-based statistical
methods for inference that allow for low-dimensional, semi-parametric models.
Inference has been based on several proposed stochastic process models for the
formation of sexual partnership networks. We have also developed model
selection criteria to choose between competing models, and assessed the fit of
different models to three populations: Uganda, Sweden, and the USA. Throughout
this work, we have emphasized the correct assessment of the uncertainty of the
estimates based on the data analyzed. We have also widened the question of
interest to the limitations of inferences from such data, and the utility of
degree-based epidemiological models more generally.
In this paper we address further statistical issues that are important in
this area, and a number of confusions that have arisen in interpreting our
work. In particular, we consider the use of cumulative lifetime partner
distributions, heaping and other issues raised by Liljeros et al. in a recent
working paper.