Abstract
Missing data are a fact of life in medical research. Subjects refuse to answer sensitive questions (e.g., questions about income or drug use), are unable to complete an MRI exam because of metallic implants, or drop out of studies and do not contribute further data. In each of these cases, data are “missing” or not complete. How should this be accommodated in a data analysis? Statistical computing packages will typically drop from the analysis all observations that are missing any of the variables (outcomes or predictors). So, for example, a linear regression predicting a patient’s number of emergency room visits from their age, gender, race, income, and current drug use will drop any observation missing even one of those variables. Analysis of data using this strategy is called complete case analysis because it requires that the data be complete for all variables before that observation can be used in the analysis.
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Notes
- 1.
Recall that the likelihood is the probability of observing the data. The probability of a specific count for a Poisson model, conditional on being 1 or greater is given by \(P(x) = \frac{{\lambda }^{x}{e}^{-\lambda }} {x!(1-{e}^{-\lambda })}\). The product over the entire sample is given by \(L = \frac{{\lambda }^{\Sigma {x}_{i}}{e}^{-n\lambda }} {\Pi {x}_{i}!{(1-{e}^{-\lambda })}^{n}}\), where n is the sample size, and x i is the count for individual i. It is equivalent and easier to maximize the logarithm of L. We can also ignore the factorial term which does not depend on λ, giving logL = Σx i log \(\lambda - n\lambda - n\log (1 - {e}^{\lambda })\).
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Vittinghoff, E., Glidden, D.V., Shiboski, S.C., McCulloch, C.E. (2012). Missing Data. In: Regression Methods in Biostatistics. Statistics for Biology and Health. Springer, Boston, MA. https://doi.org/10.1007/978-1-4614-1353-0_11
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DOI: https://doi.org/10.1007/978-1-4614-1353-0_11
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