Ordinary least square (OLS) estimation of a linear regression model is well-known to be highly sensitive to outliers. It is common practice to (1) identify and remove outliers by looking at the data and (2) to fit OLS and form confidence intervals and p-values on the remaining data as if this were the original data collected. This standard “detect-and-forget” approach has been shown to be problematic, and in this paper we highlight the fact that it can lead to invalid inference and show how recently developed tools in selective inference can be used to properly account for outlier detection and removal. Our inferential procedures apply to a general class of outlier removal procedures that includes several of the most commonly used approaches. We conduct simulations to corroborate the theoretical results, and we apply our method to three real data sets to illustrate how our inferential results can differ from the traditional detect-and-forget strategy. A companion R package, outference, implements these new procedures with an interface that matches the functions commonly used for inference with lm in R.

R code used for each data set to perform negative binomial regression, calculate overdispersion statistic, generate summary statistics, remove outliers

**Correlation is significant at the 0.01 level (2-tailed).*Correlation is significant at the 0.05 level (2-tailed).'Correlation is significant at the 0.1 level (2-tailed).For each model, the two categories of sibling pairs are derived from Table 2. In each case, a possible fit (in bold) is indicated by the second correlation being less than the first.

MLR models of age at onset of T1D after removing outliers (N = 354).