The choice of design for microarray time course experiments will depend on several factors, principally the questions the researcher wishes to address, and the available resources, including mRNA, microarrays, and related reagents. We refer to Yang and Speed (16) for a general discussion of design issues for microarray experiments.

The first and most important microarray time course design question for an investigator will be whether to carry out a longitudinal or cross-sectional study. As explained in Diggle et al. (14), while it is often possible to address the same biological question using either longitudinal or cross-sectional experiments, the major merit of longitudinal time course studies is they provide information about the temporal changes in gene expression levels within units, something that is not possible with cross-sectional studies. In statistical terms, the difference between longitudinal and cross-sectional experiments comes from the fact that gene expression measurements are typically correlated over time within units, and these correlations can be estimated and used to advantage in longitudinal studies. On the other hand, such biological correlations cannot be detected in cross-sectional time course studies, since mRNA is extracted from different sources at different times.

It follows from what has just been said that if temporal changes in gene expression over time are of primary interest to the experimenter, an effort should be made to carry out a longitudinal study wherever possible. We appreciate that in many, and perhaps most, cases this may be infeasible, because of the impossibility of repeatedly sampling the mRNA from the same units. Nevertheless, a good approximation to a longitudinal study can be often realized by creating parallel, identically treated units, and sampling from different ones at different times. The difference between this kind of design and true longitudinal design depends on just how similar are the parallel, identically treated units. In some cases, they can be very similar indeed, and we observe the correlations characteristic of a genuinely longitudinal design, although their origins may be different. In such cases, these designs can be more powerful than cross-sectional studies for detecting changes.

Although we might give the impression that, for design purposes, the distinction between longitudinal and cross-sectional studies is straightforward, this is not really the case. There are many contexts in which hybrid studies pose more challenging design problems. For example, we might run replicate time course experiments on plants grown in a growth chamber, where each replicate consists of a series of successively sampled plants grown together under controlled conditions. This study is cross-sectional from the perspective of plants, but longitudinal from the point of view of growth chambers. The appropriate number of full replicates, and of plants at each time within replicates given fixed resources, will depend on the relative magnitude of the different components of variation.

The number of time points is usually decided by the biological background and the cost of the study. More time points permits a finer analysis of temporal patterns, e.g. a more accurate determination of the time of onset or decay of a gene's expression, but in some experiments accuracy of this kind is not required.

Questions of interest to an investigator might concern the temporal profile of genes for one biological condition, such as a desire to identify cell-cycle-regulated genes. Alternatively, interest might focus on comparison between gene profiles across two or more conditions. We might want to identify those genes which change over time in a wildtype organism, and similarly those genes which change over time in a mutant organism, and identify those genes whose temporal profiles for the wildtype and mutant are different. The latter may include many genes which are unchanging in one or the other of the two biological conditions. The way in which such questions can affect the choice of design is explained in Yang and Speed (16), and we will not revisit that here in detail.

A short time course experiment can be regarded as a single factor experiment with time as a factor (see 17, 18). What makes it different from other single factor experiments is the additional information from the natural ordering of time course samples. This natural ordering of levels will lead to certain comparisons being of greater interest to the researcher, and others of lesser interest. For example, comparisons of each time point mRNA sample with the baseline or differences between consecutive time points are likely to be of greater interest than comparisons between widely separated times. Interest might focus on specific aspects of the temporal patterns of gene responses, such as monotonicity, convexity, and linearity (16).

The design of time course experiments can be considerably more complicated in the two-color comparative experiments (e.g. cDNA arrays) in comparison with single-channel experiments (e.g. Affymetrix chips), although if a common reference design is used, the two cases are fairly similar. For short two-color comparative time courses, it is possible to enumerate all the possibilities to find the optimal design. However, for those with a much larger number of time points, like the yeast cell cycle data in Spellman et al. (5), this is not feasible. There is not much literature on the design of time course experiments, but recently, Glonek and Solomon (19) described a method for designing short cDNA time course experiments. They optimized statistical efficiency and identified so-called admissible designs, and selected efficient designs based on the effects of most interest to the biologists, the number of arrays available, and other resources. Their approach was shown to give designs better than the popular common reference design and those incorporating all possible pair-wise comparisons. Optimal design for microarray time course experiments is a research topic for the future.

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