Statistical Methods for Unusual Count Data: Examples From Studies of Microchimerism

Abstract

Natural acquisition of small amounts of foreign cells or DNA, referred to as microchimerism, occurs primarily through maternal-fetal exchange during pregnancy. Microchimerism can persist long-term and has been associated with both beneficial and adverse human health outcomes. Quantitative microchimerism data present challenges for statistical analysis, including a skewed distribution, excess zero values, and occasional large values. Methods for comparing microchimerism levels across groups while controlling for covariates are not well established. We compared statistical models for quantitative microchimerism values, applied to simulated data sets and 2 observed data sets, to make recommendations for analytic practice. Modeling the level of quantitative microchimerism as a rate via Poisson or negative binomial model with the rate of detection defined as a count of microchimerism genome equivalents per total cell equivalents tested utilizes all available data and facilitates a comparison of rates between groups. We found that both the marginalized zero-inflated Poisson model and the negative binomial model can provide unbiased and consistent estimates of the overall association of exposure or study group with microchimerism detection rates. The negative binomial model remains the more accessible of these 2 approaches; thus, we conclude that the negative binomial model may be most appropriate for analyzing quantitative microchimerism data.

Figure 1.

Fetal microchimerism concentrations in peripheral blood mononuclear cells of healthy women (controls) and women with systemic sclerosis (cases), Seattle, Washington, 1991–2009. Values are presented as log₁₀ (genome equivalents of fetal microchimerism per 100,000 total genome equivalents tested).

Figure 2.

Male microchimerism concentrations in peripheral blood (buffy coat) of healthy women (controls), women with colon cancer, and women with breast cancer, Denmark, 1993–2006. Values are presented as log₁₀ (genome equivalents of male microchimerism per 100,000 total genome equivalents tested).