Positing, fitting, and selecting regression models for pooled biomarker data

Abstract

Pooling biospecimens prior to performing lab assays can help reduce lab costs, preserve specimens, and reduce information loss when subject to a limit of detection. Since many biomarkers measured in epidemiological studies are positive and right-skewed, proper analysis of pooled specimens requires special methods. In this paper, we develop and compare parametric regression models for skewed outcome data subject to pooling, including a novel parameterization of the gamma distribution that takes full advantage of the gamma summation property. We also develop a Monte Carlo approximation of Akaike’s Information Criterion (AIC) applied to pooled data in order to guide model selection. Simulation studies and analysis of motivating data from the Collaborative Perinatal Project (CPP) suggest that using AIC to select the best parametric model can help ensure valid inference and promote estimate precision.

Minority stress and inflammatory mediators: covering moderates associations between perceived discrimination and salivary interleukin-6 in gay men

“…Descriptive analyses of the dependent variable (salivary IL-6) revealed high positive skew, which is typical of inflammatory biomarkers (Mitchell, Lyles, & Schisterman, 2015; Wu et al, 2012). To best model these data, we followed procedures recommended in past work (Gustavsson, Fagerberg, Sallsten, & Andersson, 2014; Mitchell et al, 2015) and computed generalized linear models (GLM) specifying a gamma distribution and log-link function, also referred to as gamma regression.…”

“…To best model these data, we followed procedures recommended in past work (Gustavsson, Fagerberg, Sallsten, & Andersson, 2014; Mitchell et al, 2015) and computed generalized linear models (GLM) specifying a gamma distribution and log-link function, also referred to as gamma regression. GLM permits flexible modeling of data whose error distribution belongs to the exponential dispersion family (e.g., Poisson, gamma), while the link function allows for a linear relation between specified predictors and the expected value of the response (in this case, logged).…”

Exposure to Persistent Organic Pollutants and Birth Characteristics

“…38 The gamma distribution is similar in shape to lognormal but has been assumed in the pooling literature because of the convenient property where if the individual concentrations follow a gamma distribution, then the pools also follow a gamma distribution which lognormal lacks. 34,[38][39][40][41][42] After employing multiple imputation (100 imputations) to obtain individual level pollutant exposures from pooled samples, we used linear and logistic regression to examine the associations between a 0.1-ng/mL increase in each POP and continuous outcomes and binary birth characteristics, respectively. 34,40 Values of pollutants that were below the limits of quantification were replaced by a near-zero constant, as consistent with EPA guidance.…”

Estimating relative risk of a log‐transformed exposure measured in pools

“…Hence, similar to its linear analogue, the regression calibration step assuming a gamma distribution on X | C ∗ involves adjusting the observed ‘mismeasured’ value with ancillary information based on the relationship between X and C ∗ . To obtain the calibrated value of log X i j for each individual specimen, is estimated for all i , j by optimizing the log‐likelihood of the gamma distribution with constant scale parameter . Calculation of is then straightforward.…”

“…When measured in pools, a log transformation on the pooled measurements can induce computational complexity due to the nonlinearity of the log function. In light of recent developments for regression on a log‐transformed, pooled outcome , we propose an extension of the pooled regression calibration approach that will permit estimation of regression coefficients corresponding to a log‐transformed biomarker, when only pooled measurements are available.…”