There is nothing wrong with having no replicates and there is still plenty of thing you can do with your single snapshot of data.

However, there is a whole pile of things you cannot do and cannot claim. You have to be careful selecting the words and never mixing these things up. Even if you are careful and correct there will be still plenty of misunderstanding just because most reviewers have certain set of expectations for microarray experiments hardwired.

You can only conduct a pilot study, some call it "data scouting". You can only use you data to generate hypotheses and maybe some of these hypotheses could be tested separately - by RT-PCR, Western, more microarrays in the future, etc. You are not going to "prove" anything without replication, thus don't even try. On the other hand, one shot or a few replicates makes little difference any way. Three replicates would be three times as expensive and still not a good evidence on its own.

Export tab-delimited table from Affy. Use J5 metric to scoop deferentially expressed genes

http://www.ncbi.nlm.nih.gov/pubmed/16323966

(Ask Dr. James Lyons-Weiler from Univ. of Pittsburg about details and updates)

Put the genes on the map using something like DAVID http://david.abcc.ncifcrf.gov/

Plot the charts of pathways with these genes using KEGG http://www.genome.jp/kegg/

Maybe you will get your story together. Compelling the skeptics to believe it will be a different chapter. You can only do so much with a single shot. But it's nothing by far.

Good luck.

Normally of any there are 5 tests that can be used for sorts of Group (Control and/or Experiment), variables (Independent and Response) and treatment levels that one may be working upon> They are

1.Standard t-test

2. paired t-test

3. one way ANOVA (Analysis of Variance)

4. two way ANOVA

5. Linear Regression

MS office - Excel should be able to do all these above test. There are statistical packages like Minitab, SPSS etc that can handle these type of analysis.

You also refer to this link it will get a step-by-step approach to choose a right test.

You also can consider rank sum test. For software, you can try R.

Try the free excel add-in BRB-ArrayTools http://linus.nci.nih.gov/BRB-ArrayTools.html. It might help you.

Everything is explained in the user manual.

Best wishes

gitools is another interactive program you can take a look at. If you want to look at bioinformatics for gene expression (assuming thats what you wanted to do as you were asking about microArray) then you do need n=3 as you need the p value to do the analysis. The most common way is to plot them as a "heat map" - I am in the middle of learning about gitools which I found in a publication recently, will update you of the progress if you are interested.

you can't compare 1 v 1 in a statistically meaningful way because you cannot generate a p-value. the p-value tells you the odds that you observe the difference by chance. In short, you need to assay more samples to find differentially expressed genes

Limma can actually (if you use the eBayes test) analyze the data even if you have no replicates. But doing the test w/o replicates is statistically similar to using just the fold-change. so I would suggest that if have to do a "dirty" analysis like this - we have all been there one time or another :-) some people think that replication is a waste of money - to just sort the values by fold-change and take, say, top 50-100 genes that meet a fold change threshold, like say 1.5-2x (+/-1 on the log2 scale). If you want to derive a p-value (a highly suspect proposition given that you have no replicates...) then you could calculate an array-wide standard deviation of the fold-change values. This is actually similar to what the limma-eBayes does, it performs variance shrinkage by calculating variance as a blend of array-wide variance and gen-level variance (using replicates). Hope this helps! And demand them to perform more replicates next time! You will have an easier time with (statistically-literate) reviewers.

Hi,

the problem with having only one control and one treated sample is that you do not have any estimation about the variance of the gene expression (for the 2 conditions). For "Gene A" you have only one expression value coming from the treated sample and one from the control. Without knowing the variance you are not able to apply any statistical test to the data. The only think you can do with them is to subtract the expression values mesured in the control from the treated sample and rank them according to the result.

hope this help

r

Statistics needs replicates, otherwise how could you estimate a tendency caused by a factor? Microarrays do not differ from basic scientific works, therefore to say something for a candidate gene you need several independent observations (at least 3).

To René: you can always calculate an array-level pooled variance using the fold-change values, and then p-values by assuming that the data is normally distributed (same as calculating Z-scores on the array level). But it is, of course, a well known fact that there are significant gene-level differences in variance that cannot naturally be estimated without replicates. But it is the best one can do. Using the fold change to rank the genes is akin to assuming the the gene-level variance is same for all genes (and hence does not effect the ranking).

I would STRONGLY encourage using more than one array per sample and control. Recommended minimum is 3, I think. By using 4 replicates you allow one experiment to be failure (and to be excluded from experiment). These should be different samples (biological replicates)

Reasons:

1. With three or more replicates you should start to see the variation in the biological groups. This is as important as the average signal within the groups.

2. If there is ever any interest to publish the results the reviewers will attack your work with 1 - 2 replicates. Work might not get through in any reasonable journal.

3. I bet you'll find more discussions/recommendation from web. Check " number of replicates microarrays" or "guidelines on microarray data analysis".

Sorry for the cold shower. I do not follow research gate and normally just delete the emails. However, this time the question title sounded like something that I wanted to give my opinion. You should discuss with your boss on issues 2 and 3 as the data is also a money issue.

You have several probes per gene, so you could use these as technical replicates, and use e.g. a t-test to compare. We did this in R using Bioconductor, for a different purpose.

This would give you an answer as to whether a gene is significantly differentially expressed between two samples, as assessed by multiple probes.

The problem then is how to interpret the result. Because you only have one biological sample of each condition, you have no information on the variation between biological replicates, so you cannot say whether your significant result would be true for two different biological samples under the same biological conditions. This is the reason why standard tools do not work this way - biologists usually need to measure an effect in several replicate biological samples, because measurements tend to differ stochastically between organisms.

Hello Petri, I completely agree (and it is good that you are making the point). But there is no use crying over spillt milk, as they say. I have sometimes thought that is is bad, that limma kind of allows you to calculate p-values even for experiments that never should have been performed :-). But if the situation is what it is then doing what I suggested is the best way.

Maybe I dont get the problem, but I don't see any help in the answers given.

There is a very simple problem (as I understood): there is a single, unique measured value under condition A (say, from the "treatment group") and another single unique measured value under condition B ("control group"). For a statistical analysis it is not really interesting if such mesurements are done for one particular gene or for a whole genome.(*)

Hence, we have just an unreplicated measurement/experiment. We have only 2 values, one from group A and one from group B. We do NOT have any information about the variance of these values. We do not know what to expect from other (yet unmeasured) individuals. The only thing we can do, though, is to assert that in this particular case (for these particular individuals mesured in this particular experiment) the observed difference in signal intensities (the apparent differential expression). As long has we do not have any information about the inter-individual variability of the measurements of this genes expression we can not give any expectation about what difference to find in other individuals other than just saying that the observed difference is the best guess so far.

However, there might still be information available about the inter-individual variances - not in this experiment, but there are probably other experiments available in databases dealing with the same biological source and the same technology (biochemistry, signal generation, measurement, instrument, data processing). One could used this information, calculate the expected variance (or standrad deviation, sd) of the gene expression, use the error propagation to get the variance or sd of the difference and so be able to compare the observed difference to the expected sd (what is called a relative effect size). For the n=1 case, the sem used for the construction of confidence intervals or tests equals the sd. The degrees of freedom are given by the number of measurements used to determine the variances (as usual, so to say).

(*) unless the variation between the expression of different genes within the same individual would provide some information about the variability of the gene expression between individuals, what typically is not the case. Moderated statistics (as used for instance in limma) borrow variance information from different genes, but this variance information means variace of the same gene withing replicates - and there are no replicates in this experiment!

Maybe the simplest would be to normalise your two arrays with MAS5.0. This will gives the present and absent genes, which can be a first step filtering. Next you can filter out genes based on the ratio (fold-change). I would never try to published such results, nevertheless, if you can confirm with qPCR, it become a strong study.

As already stated, biological replicates really should be included (at least 3, but 4 or 5 would be far better). The simple reason is that to determine robust statistical significance, you need to capture and quantify the population variance, and without replicates, you really cannot do that.

Having said that, if these are conventional Affymetrix cartridge arrays and thus have both mis-match and perfect-match probes in the probe sets, then you can use a BioConductor package called SScore to compare a single pair of arrays as you have (SScore can not be used with Affy high throughput perfect-match only arrays, aka Gene Titan arrays).

SScore does not use probe summarized (ie. normalized) data - it uses raw probe intensities and treats the individual probes in each probe set as independent measures. SScore was thus specifically designed to work in those situations where only a single pair of arrays was available for comparison (although it has been expanded to handle replicates as well, if available).

see:

Richard E. Kennedy, Robnet T. Kerns, Xiangrong Kong, Kellie J. Archer and Michael F. Miles. 2006. SScore: an R package for detecting differential gene expression without gene expression summaries. Bioinformatics 22(10):1272-1274

The BioConductor package is based on the SScore algporithm of Zhang et al:

Zhang,L. et. al. 2002. A new algorithm for analysis of oligonucleotide arrays: Application to expression profiling in mouse brain regions. J. Mol. Biol., 317:225–235.

You can find out about R and BioConductor at their web sites:

http://cran.r-project.org/

http://www.bioconductor.org/

Strange, what SSscore tries to do, since the different probes in a probe set are explicitly not independent. Seems to me a bit like generating information out of nothing...

Hi Masato,

What Affymetrix platform are you using? If you're using HGU133 arrays then you might consider using the PINC algorithm - see this paper by Reid and Fodor 2008: http://www.biomedcentral.com/1471-2105/9/489.

Best of luck!

Well this is similar to what we did in Tamplin et al 2008 BMC Genomics

Statistical testing for differential expression between mutant and wild-type was performed on single probe level taking the duplicate chips into account employing the Wilcoxon paired rank test. The p-value threshold was adjusted by either family-wise error rate (FWER, Bonferroni procedure) or the false discovery rate (FDR, Bejamini-Hochberg technique)

So you calculate the fold change between paired probes for each gene probe set, this give you a distribution of fold changes per gene, then you test for the distributions mean being significantly greater or less than 0 and adjust the pvalue to account for all of the tests being done on the entire array. Realisticly you should run more arrays.

As to numbers of replicates, this depends on the question being asked and the varibalility of your system both biologically (i.e.,between individuals) and technically (i.e., your ability to isolate mRNA and grow cells), do not blindly use 3 sample as it is the minimum needed for a students t test, that will lead to statistical results with little biological meaning.

There is nothing wrong with running a pilot array to see if the system is working. Just calculate the fold change on your arrays and rank ithem by fold change and see if you are getting any anticipated results. Then add on more arrays to build out your statistics. Pilot analysis using qRT-PCR is a great way to guage the variability in your experiment to determine the numenbr of arrays needed.

I have atttached two PDFs they are oldies but goodies for a basic primer on microarrays. You should consult newer articles though as times have moved on, but this is a great place to start.

here is the second artilce as apparently I can only attach one at a time. I regret joining this poorly designed forum.

There is nothing wrong with having no replicates and there is still plenty of thing you can do with your single snapshot of data.

However, there is a whole pile of things you cannot do and cannot claim. You have to be careful selecting the words and never mixing these things up. Even if you are careful and correct there will be still plenty of misunderstanding just because most reviewers have certain set of expectations for microarray experiments hardwired.

You can only conduct a pilot study, some call it "data scouting". You can only use you data to generate hypotheses and maybe some of these hypotheses could be tested separately - by RT-PCR, Western, more microarrays in the future, etc. You are not going to "prove" anything without replication, thus don't even try. On the other hand, one shot or a few replicates makes little difference any way. Three replicates would be three times as expensive and still not a good evidence on its own.

Export tab-delimited table from Affy. Use J5 metric to scoop deferentially expressed genes

http://www.ncbi.nlm.nih.gov/pubmed/16323966

(Ask Dr. James Lyons-Weiler from Univ. of Pittsburg about details and updates)

Put the genes on the map using something like DAVID http://david.abcc.ncifcrf.gov/

Plot the charts of pathways with these genes using KEGG http://www.genome.jp/kegg/

Maybe you will get your story together. Compelling the skeptics to believe it will be a different chapter. You can only do so much with a single shot. But it's nothing by far.

Good luck.

Hi I would also recommend to use GCRMA normalization method and limma package R for differential gene expression. I am also doing some sort of Microarrays data analysis.

The question was about "the easiest way". It is described in Loguinov et al.,2004: candidate genes are outliers in "M vs. A"scatter plot, where M = log2(AVG intensity in experiment/AVG intensity in control), A = log2(AVG intensity in experiment*AVG intensity in control)/2. It is exploratory differential gene expression analysis (limited or no replication). For confirmatory analysis one needs: 1) apply more biological replicates as mentioned in replies on the question, or/and 2) apply independent experiments e.g. RT-qPCR. As to normalization, there are two types of it: 1) within chip pair(e.g. global normalization using loess), 2) between chip pairs (i.e. between biological replicates). For the details and R software - please see the paper in Genome Biology.

Thank you all for your kind and very helpful comments!

Now I understand why my data is useless for sort of meta-analysis in terms of biological variance...

Personally all I want is just a bunch of candidate miRNAs that are differentially expressed in different biological states, so I'll use my data just as a pilot study.

My boss wanted me to do much more analysis using this data, but since all this have turned out now I'll explain the current situation to him.

Sorry that I cannot reply to every comment, but all of these comments really helped me. So thank you again. I'll do my best.

with one sample per group you can not do any statistics, in this case you can only talk about THIS particular sample and you can not do any inferecen about population behavior. NO matter the method you use. If you use the within chip replicates to "infere" differenciall expression, this is not right since they are not trully biological replicates , thay are just technical ones or ar least different proportions of one gene. The only thing you can do is analyze fold changes, however the fold change you will see can not be extrapolated as a population behaviour.

Hi Michael,

so "These probe pair level error estimates are then used in the calculation of a measure of relative change in gene expression, called the significance score or S-score".

I still do not see what qualifies a relative difference over an absolute difference for inference/generalization. After normalizing to the average probe set signal, these relative deviations may be modeled by the normal distribution. So far I can follow. However, this does not provide any information about the variance of expected S scores between individuals. If you would take another individual, you will get another S score. Again you can model its expected value using a normal distribution, but this does not help you to assess the variance in the expected S scores between different individuals. What this proposed method does is to give you "significance score" for having measured a difference in a single particular unique case (the measurement significance). It is just completely wrong to assume that this will tell you something about the significance of an effect (significance in the common statistical notation).

Still, although surrounded by beautiful scientific pharses like "error model", "distribution" and "significance", I don't see the point solving the problem of inference. This is a constructive point - I will probably learn something new... (or get disappointed by an insufficient reviewing process)

You've received very solid answers from everyone, just a couple of comments that might be helpful.

1) What kind of Affy chip are you using? It needs to be an older design if you're going to employ the 'probe pairs in a probe set' fold change analysis. Newer Affy chips don't use the 'perfect-match and mismatch' probe pairs in probe set design.

2) As mentioned by others, p-value results from a single control chip vs. a single treatment chip yield results associated with technical, not biological, variance. Studies with replicated observations give you technical + biological variance. Usually researchers tolerate/ minimize the technical variance, and try to preserve the biological variance, because that's where most of us are looking for answers, in the biology.

3) You might consider looking at other data sets, like those in the Gene Expression Omnibus. Are any of them a close match to your study? If so, see what they genes they found. Now look at your results for those genes- do they show a good match for direction and magnitude of change? Now you can start to infer some biological reliability

4) Microarrays are being unfairly blamed. It'snot really the chip's fault, that you have this problem- it would be the same for a Western Blot or maze performance or a political poll. it's the samples (or in your case lack of them) that is the problem. If subjects in your population are normally distributed, then the likelihood that you have picked a representative control subject for your first chip is ~32% (within 1 standard deviation of a normal distribution). The same is true for your treatment subject. The chances that you have been lucky enough to get BOTH a 'representative' control subject AND a 'representative' treatment subject is the product of those, 32% * 32% = ~10% - not so good.

So the odds are good that you can use single chip analysis protocols to get 'significant' results, but the goods are odd. Those genes identified in this way represent magnitudes of change that the chips are capable of discriminating, not gene changes important to the biological question under study. Try not to misinterpret technically observable changes as biologically important ones, but keep in mind that a biologically important change must be technically observable, or you will never see it!

You already have a whole array of very good suggestions but I just want to also add this site as suggestions for anaylsis tools for Affy GeneChips which you may go through and may be of help.

http://ipmb.sinica.edu.tw/affy/document/tool_kits.pdf

Also you should join the Affy web to use their tools.

Using a single experiment, you will be able to analyse if the samples were run under similar conditions and get the statistical differences within the probesets used according to the design of array chips you are using, but definitely to make a statement about biological relevance one has to perform duplicate or triplicate experiments or perform meta-analyses with other similar experiments, using relevant tools and normalisations. One must use different tool, train yourself and see how user friendly ach is in noramlising, visuaiising, clustering, classifying, getting the statistical evaluation of the expression pattern to understand the biological change between the control and test sample. Then the genes with greater fold differences may be tested by other means as suggested above to confirm. overall you will get the picture, but you will need to do followup experiments to report you results as valid or significant.

This is way out of my field, so I am clueless about software. A general approach not yet mentioned is bootstrapping -- creating estimated confidence intervals etc. by using an array as a population and repeatedly taking slightly smaller samples from it.

No Douglas, this also does not allow inference to the "population". Bootstrapping can not generate information "de novo" or "out of nothing". It is just a way to analyse available information (lika all other statistics methods). With bootstrapping you get finally to the same results as mentioned above: you get a hint of a resonable confidence you can assign to the statement "this difference of gene X between these two individuals is reliably measured", but NOT for any statement like "in any two such individuals a (more or less similar) difference can be expected". Still, if you take another individual the results might be completely different! You just don't have this information in this data. The only way to get this information is from actually measured other individuals (either in your own experiment or taken from other peoples research [considering possible biases]).

Jochen, I think there is a difference between "a" population (my reference) and "the" population (your reference). I completely agree with the substance of your comment, as far as it goes.

I think there seems to be some confusion about what Masato can actually do with just a single pair of arrays for analysis. Obviously, there is nothing that can be said about population differences, as there has been no population sampling (as stated by several, that would require biological replication).

However, it is certainly possible to test and determine statistical significance of differences observed between those two arrays. If these were individual patients in a clinical study, the test would be simply phrased as "what genes are expressed at significantly different levels between the two test subjects". Even with only a single pair of arrays, that question can be answered, and with statistical significance. In my own experience, it is easiest and quickest if the arrays are conventional Affymetrix cartridge arrays, as there are several statistical approaches that have been developed (and peer reviewed) to do that for those specific array types, along with the tools to do so (most freely available in R/BioConductor).

Dear Masato, you have got a plenty of good suggestions. I have never worked with a single replicate; however, if there is no way around it, I would do the following. Affymetrix chip usually contains several probes targeting the same gene. If after normalization of your experiment and control you'll get differential expression in 2-3 independent probes corresponding to the same gene, this is a hint for regulation. To find these genes, I would 1) use only those genes, which are represented by 2 or more probes of different sequence 2) Use the relative values: set the maximal expression for each probe in 2 experiments to 100%. 2) make a T-test between the values for different probes; take those with p

I have 2 technical replicates in which they have individually 3 time point data .I want to do t-test and calculate p value .I don't understand how to design model matrix so that i can use limma .My sample data is already treated against control. In my sample data i have a fold change values.