Sparse data bias: a problem hiding in plain sight

Effects of treatment or other exposure on outcome events are commonly measured by ratios of risks, rates, or odds. Adjusted versions of these measures are usually estimated by maximum likelihood regression (eg, logistic, Poisson, or Cox modelling). But resulting estimates of effect measures can have serious bias when the data lack adequate case numbers for some combination of exposure and outcome levels. This bias can occur even in quite large datasets and is hence often termed sparse data bias. The bias can arise or be worsened by regression adjustment for potentially confounding variables; in the extreme, the resulting estimates could be impossibly huge or even infinite values that are meaningless artefacts of data sparsity. Such estimate inflation might be obvious in light of background information, but is rarely noted let alone accounted for in research reports. We outline simple methods for detecting and dealing with the problem focusing especially on penalised estimation, which can be easily performed with common software packages.