Consider a situation where observations are to be taken at regularly spaced time points, but in fact several of the observations are missing. It is wished to determine whether the data exhibit a trend. When the data set is complete, then a well known rank test is based on Spearman correlation. For the case of missing observations a new test of trend is proposed which is analogous to the Spearman test in the complete case. Comparisons between this new test and the naïve Spearman test, which simply deletes all missing observations, indicate that the new test is more sensitive in detecting trends.
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Alvo et al. (1994) studied this question.