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In the analyses of incomplete longitudinal clinical trial data, there has been a shift, away from simple ad hoc methods that are valid only if the data are missing completely at random (MCAR), to more principled (likelihood-based or Bayesian) ignorable analyses, which are valid under the less restrictive missing at random (MAR) assumption. The availability of the necessary standard statistical software allows for such analyses in practice. Although the possibility of data missing not at random (MNAR) cannot be ruled out, it is argued that analyses valid under MNAR are not well suited for the primary analysis in clinical trials. Therefore, rather than either forgetting about or blindly shifting to an MNAR framework, the optimal place for MNAR analyses is within a sensitivity analysis context. Such analyses can be used, for example, to assess how sensitive results from an ignorable analysis are to possible departures from MAR and how much results are affected by influential observations. In this article, we apply the local influence sensitivity tool (Verbeke et al., 2001) to a longitudinal depression trial, thereby applying it to continuous outcomes from clinical trials.

The present study examines duration-sensitive neurons in the inferior colliculus (IC) of the least horseshoe bat, Rhinolophus pusillus, from China. In contrast to other bat species tested for duration selectivity so far, echolocation pulses emitted by horseshoe bats are generally longer and composed of a long constant-frequency (CF) component followed by a short downward frequency-modulated (FM) sweep (CF-FM pulse). We used combined CF-FM pulses to analyze the differential effects that these two pulse components had on the duration tuning in neurons of the horseshoe bat's IC. Consistent with results from other mammals, duration-sensitive neurons found in the least horseshoe bat fall into three main classes: short-pass, band-pass, and long-pass. Using a CF stimulus alone, 54% (51/95) of all IC neurons showed at least one form of duration selectivity at one or more stimulus intensities. In 65 of the 95 IC neurons tested with CF pulses, we were also able to test their duration selectivity for a combined CF-FM pulse, which increased the ratio of duration-sensitive neurons to 66% (43/65). Seven to 15 neurons that failed to show duration tuning for CF bursts became duration sensitive for CF-FM pulses, with most of them exhibiting short-pass (depending on stimulus intensity, between 4 and 8 neurons) or band-pass tuning (1–3 neurons). Increasing stimulus intensities did not affect the duration tuning in 53% (23/43) of duration-sensitive neurons for CF bursts and in about 26% (7/27) for CF-FM stimuli. In the remaining neurons, increasing sound levels generally reduced the ratio of duration-sensitive neurons to 33% for CF and 37% for CF-FM stimulation. In those that remained duration sensitive, louder CF bursts shortened best durations in band-pass neurons and cutoff durations in short- and long-pass neurons, whereas louder CF-FM stimuli reduced the cutoff durations only in short-pass neurons. Bandwidths of band-pass neurons were not significantly affected by any stimulus configuration, with only a slight trend for increasing bandwidths for louder CF bursts (but not CF-FM stimuli). Best durations and cutoff durations reached higher values than those in the other bat species examined so far and roughly match the longer durations of echolocation pulses emitted by horseshoe bats. Therefore presentation of a CF-FM stimulus improved the duration sensitivity in IC neurons by increasing the ratio of duration-tuned neurons and making them less susceptible to changes in signal intensity.