The best replacement for sleep study is pneumogram.

The best alternatives to sleep study are rated as following:
★★★★★  pneumogram
★★★  polysomnogram
★★★  lab sleep study
★★  polysomnography

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Speaking about sleep study, one probably shouldn't forget about cpap.

Other search terms related to sleep study and their ratings are:
★★★★★ cpap
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Google Trends

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sleep study
pneumogram
polysomnogram