Building a Stronger Instrument in an Observational Study of Perinatal Care for Premature Infants
Statistics and Probability
An instrument is a random nudge toward acceptance of a treatment that affects outcomes only to the extent that it affects acceptance of the treatment. Nonetheless, in settings in which treatment assignment is mostly deliberate and not random, there may exist some essentially random nudges to accept treatment, so that use of an instrument might extract bits of random treatment assignment from a setting that is otherwise quite biased in its treatment assignments. An instrument is weak if the random nudges barely influence treatment assignment or strong if the nudges are often decisive in influencing treatment assignment. Although ideally an ostensibly random instrument is perfectly random and not biased, it is not possible to be certain of this; thus a typical concern is that even the instrument might be biased to some degree. It is known from theoretical arguments that weak instruments are invariably sensitive to extremely small biases; for this reason, strong instruments are preferred. The strength of an instrument is often taken as a given. It is not. In an evaluation of effects of perinatal care on the mortality of premature infants, we show that it is possible to build a stronger instrument, we show how to do it, and we show that success in this task is critically important. We also develop methods of permutation inference for effect ratios, a key component in an instrumental variable analysis.