{'fraction_non_alphanumeric': 0.008100810081008101, 'fraction_numerical': 0.0, 'mean_word_length': 5.780487804878049, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
A shrinkage estimator for subgroup analysis without the exchangeability assumption

ABSTRACT Shrinkage estimators for exploratory subgroup analyses are intuitively appealing and can greatly improve estimation over standard analysis approaches; however, adoption of these estimators has been limited by reliance on the exchangeability assumption. This paper describes a new shrinkage estimator that does not rely on this assumption. Rather than assuming that treatment effect sizes within subgroups are randomly distributed around an overall mean, this new estimator assumes that the difference between the effect sizes in any given pair of subgroups is randomly distributed around zero. The estimator is illustrated using data from a clinical trial in which the treatment effect size in one region was substantially different from the sizes in other regions. Simulation results show that the estimator has properties that are comparable to or superior to a standard shrinkage estimator when exchangeability is assumed, while allowing the flexibility to handle situations where exchangeability cannot be assumed.