Limma time course analysis - defining comparisons
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Helen Zhou ▴ 150
@helen-zhou-2654
Last seen 9.3 years ago
United States
Dear Sir/Madam I am trying to analyse a short time series, roughly following section 8.8 in the limma user guide. I am interested in differences between all time points. I am not sure whether I have to make all the pariwise comparisons directly, or whether they can be done indirectly as well. For example, if I want to compare to time points, what is the differences between the two methods listed below. library(bronchialIL13) # Just for the IL13 samples data <- HAHrma[,7:15] # Design targets <- c("h12","h12","h12","h24","h24","h24","h4","h4","h4") lev <- c("h12","h24","h4") f <- factor(targets, levels=lev) design <- model.matrix(~0+f) colnames(design) <- lev fit <- lmFit(data, design) # 2-step contrasts, used to indirectly get 24 to 4 hours as well as the other two comparisons contrasts <- makeContrasts("h24-h12", "h12-h4", levels=design) fit2 <- contrasts.fit(fit, contrasts) fit2 <- eBayes(fit2) # Direct contrast of 24 to 4 hours contrasts2 <- makeContrasts("h24-h4", levels=design) fit3 <- contrasts.fit(fit, contrasts2) fit3 <- eBayes(fit3) # Comparison topTable(fit2, coef=1:2) topTable(fit3, coef=1) More or less the same probe sets are present, but in different order and with different p values. Is the difference because using coef=1:2 will go via an F-test? And if I want the change from 24h-0h as well as 42-12h and 12-4h, is it most correct for me to specify that contrast directly? In my actual experiment I have 4 time points, so will it be enough for me with 3 possible comparisons, or will I have to write all the 6 possible combinations? Thank you in advance for all your help. Yours truly Mrs Helen Zhou P.S. I think this might have been mentioned on the list before, but I could not find the email. In that case, please excuse me for repeating this.
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@james-w-macdonald-5106
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Hi Helen, Helen Zhou wrote: > Dear Sir/Madam > > I am trying to analyse a short time series, roughly > following section 8.8 in the limma user guide. I am > interested in differences between all time points. I > am not sure whether I have to make all the pariwise > comparisons directly, or whether they can be done > indirectly as well. > > For example, if I want to compare to time points, what > is the differences between the two methods listed > below. > > library(bronchialIL13) > # Just for the IL13 samples > data <- HAHrma[,7:15] > # Design > targets <- > c("h12","h12","h12","h24","h24","h24","h4","h4","h4") > lev <- c("h12","h24","h4") > f <- factor(targets, levels=lev) > design <- model.matrix(~0+f) > colnames(design) <- lev > fit <- lmFit(data, design) > # 2-step contrasts, used to indirectly get 24 to 4 > hours as well as the other two comparisons > contrasts <- makeContrasts("h24-h12", "h12-h4", > levels=design) > fit2 <- contrasts.fit(fit, contrasts) > fit2 <- eBayes(fit2) > # Direct contrast of 24 to 4 hours > contrasts2 <- makeContrasts("h24-h4", levels=design) > fit3 <- contrasts.fit(fit, contrasts2) > fit3 <- eBayes(fit3) > # Comparison > topTable(fit2, coef=1:2) > topTable(fit3, coef=1) In the first case you are asking the question 'which reporters are different in either h24 vs h4 _or_ h12 vs h4', whereas in the second case you are asking 'which reporters are different between H24 and h4'. It is entirely possible that you could have a gene that isn't different between h24 and h4, but is different at h12. This would show up in the first comparison but not the second, so if you want to compare time points you are better off making direct contrasts rather than using the F-statistic for multiple contrasts (which will then require the additional step of figuring out which contrast(s) caused the statistic to be significant). Best, Jim > > More or less the same probe sets are present, but in > different order and with different p values. Is the > difference because using coef=1:2 will go via an > F-test? And if I want the change from 24h-0h as well > as 42-12h and 12-4h, is it most correct for me to > specify that contrast directly? In my actual > experiment I have 4 time points, so will it be enough > for me with 3 possible comparisons, or will I have to > write all the 6 possible combinations? > > Thank you in advance for all your help. > > Yours truly > Mrs Helen Zhou > > P.S. I think this might have been mentioned on the > list before, but I could not find the email. In that > case, please excuse me for repeating this. > > _______________________________________________ > Bioconductor mailing list > Bioconductor at stat.math.ethz.ch > https://stat.ethz.ch/mailman/listinfo/bioconductor > Search the archives: http://news.gmane.org/gmane.science.biology.informatics.conductor -- James W. MacDonald, M.S. Biostatistician Affymetrix and cDNA Microarray Core University of Michigan Cancer Center 1500 E. Medical Center Drive 7410 CCGC Ann Arbor MI 48109 734-647-5623
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Dear Jim Thanks you for your answer. As I understand you are recommending me to do direct comparisons between for example 12-4h and 24-12h. However, could there not in theory be a gene that was up a little bit in 12vs4h and 24vs12h, so that the difference for neither of these would be large enough to be significant, but for 24vs4h the combined change might be significant? In that case I guess I would need all 3 comparisons? Thanks you Helen --- "James W. MacDonald" <jmacdon at="" med.umich.edu=""> wrote: > Hi Helen, > > Helen Zhou wrote: > > Dear Sir/Madam > > > > I am trying to analyse a short time series, > roughly > > following section 8.8 in the limma user guide. I > am > > interested in differences between all time points. > I > > am not sure whether I have to make all the > pariwise > > comparisons directly, or whether they can be done > > indirectly as well. > > > > For example, if I want to compare to time points, > what > > is the differences between the two methods listed > > below. > > > > library(bronchialIL13) > > # Just for the IL13 samples > > data <- HAHrma[,7:15] > > # Design > > targets <- > > > c("h12","h12","h12","h24","h24","h24","h4","h4","h4") > > lev <- c("h12","h24","h4") > > f <- factor(targets, levels=lev) > > design <- model.matrix(~0+f) > > colnames(design) <- lev > > fit <- lmFit(data, design) > > # 2-step contrasts, used to indirectly get 24 to 4 > > hours as well as the other two comparisons > > contrasts <- makeContrasts("h24-h12", "h12-h4", > > levels=design) > > fit2 <- contrasts.fit(fit, contrasts) > > fit2 <- eBayes(fit2) > > # Direct contrast of 24 to 4 hours > > contrasts2 <- makeContrasts("h24-h4", > levels=design) > > fit3 <- contrasts.fit(fit, contrasts2) > > fit3 <- eBayes(fit3) > > # Comparison > > topTable(fit2, coef=1:2) > > topTable(fit3, coef=1) > > In the first case you are asking the question 'which > reporters are > different in either h24 vs h4 _or_ h12 vs h4', > whereas in the second > case you are asking 'which reporters are different > between H24 and h4'. > > It is entirely possible that you could have a gene > that isn't different > between h24 and h4, but is different at h12. This > would show up in the > first comparison but not the second, so if you want > to compare time > points you are better off making direct contrasts > rather than using the > F-statistic for multiple contrasts (which will then > require the > additional step of figuring out which contrast(s) > caused the statistic > to be significant). > > Best, > > Jim > > > > > > More or less the same probe sets are present, but > in > > different order and with different p values. Is > the > > difference because using coef=1:2 will go via an > > F-test? And if I want the change from 24h-0h as > well > > as 42-12h and 12-4h, is it most correct for me to > > specify that contrast directly? In my actual > > experiment I have 4 time points, so will it be > enough > > for me with 3 possible comparisons, or will I have > to > > write all the 6 possible combinations? > > > > Thank you in advance for all your help. > > > > Yours truly > > Mrs Helen Zhou > > > > P.S. I think this might have been mentioned on the > > list before, but I could not find the email. In > that > > case, please excuse me for repeating this. > > > > _______________________________________________ > > Bioconductor mailing list > > Bioconductor at stat.math.ethz.ch > > https://stat.ethz.ch/mailman/listinfo/bioconductor > > Search the archives: > http://news.gmane.org/gmane.science.biology.informatics.conductor > > -- > James W. MacDonald, M.S. > Biostatistician > Affymetrix and cDNA Microarray Core > University of Michigan Cancer Center > 1500 E. Medical Center Drive > 7410 CCGC > Ann Arbor MI 48109 > 734-647-5623 >
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Hi Helen, Helen Zhou wrote: > Dear Jim > > Thanks you for your answer. As I understand you are > recommending me to do direct comparisons between for > example 12-4h and 24-12h. However, could there not in > theory be a gene that was up a little bit in 12vs4h > and 24vs12h, so that the difference for neither of > these would be large enough to be significant, but for > 24vs4h the combined change might be significant? In > that case I guess I would need all 3 comparisons? Yes. The 'standard' linear modeling strategy is to fit the model and see if you have a significant F-statistic, then come back and do contrasts to see which particular comparison(s) is/are contributing to that significance. The general idea being that you want to limit the number of comparisons you are making so multiplicity is less of a problem. However, with microarray data this isn't usually what people do. Instead, they usually try to minimize the multiplicity by filtering out uninteresting reporters prior to making comparisons (based on variance, P/M/A calls, IQR, etc) and then computing all contrasts that they are interested in with the reporters that remain. You might consider using decideTests() using the 'nestedF' option - this is intended to correctly detect differential expression when two or more contrasts are significant, so in the case you mention may classify all three contrasts as significant. Best, Jim > > Thanks you > Helen > > --- "James W. MacDonald" <jmacdon at="" med.umich.edu=""> > wrote: > >> Hi Helen, >> >> Helen Zhou wrote: >>> Dear Sir/Madam >>> >>> I am trying to analyse a short time series, >> roughly >>> following section 8.8 in the limma user guide. I >> am >>> interested in differences between all time points. >> I >>> am not sure whether I have to make all the >> pariwise >>> comparisons directly, or whether they can be done >>> indirectly as well. >>> >>> For example, if I want to compare to time points, >> what >>> is the differences between the two methods listed >>> below. >>> >>> library(bronchialIL13) >>> # Just for the IL13 samples >>> data <- HAHrma[,7:15] >>> # Design >>> targets <- >>> > c("h12","h12","h12","h24","h24","h24","h4","h4","h4") >>> lev <- c("h12","h24","h4") >>> f <- factor(targets, levels=lev) >>> design <- model.matrix(~0+f) >>> colnames(design) <- lev >>> fit <- lmFit(data, design) >>> # 2-step contrasts, used to indirectly get 24 to 4 >>> hours as well as the other two comparisons >>> contrasts <- makeContrasts("h24-h12", "h12-h4", >>> levels=design) >>> fit2 <- contrasts.fit(fit, contrasts) >>> fit2 <- eBayes(fit2) >>> # Direct contrast of 24 to 4 hours >>> contrasts2 <- makeContrasts("h24-h4", >> levels=design) >>> fit3 <- contrasts.fit(fit, contrasts2) >>> fit3 <- eBayes(fit3) >>> # Comparison >>> topTable(fit2, coef=1:2) >>> topTable(fit3, coef=1) >> In the first case you are asking the question 'which >> reporters are >> different in either h24 vs h4 _or_ h12 vs h4', >> whereas in the second >> case you are asking 'which reporters are different >> between H24 and h4'. >> >> It is entirely possible that you could have a gene >> that isn't different >> between h24 and h4, but is different at h12. This >> would show up in the >> first comparison but not the second, so if you want >> to compare time >> points you are better off making direct contrasts >> rather than using the >> F-statistic for multiple contrasts (which will then >> require the >> additional step of figuring out which contrast(s) >> caused the statistic >> to be significant). >> >> Best, >> >> Jim >> >> >>> More or less the same probe sets are present, but >> in >>> different order and with different p values. Is >> the >>> difference because using coef=1:2 will go via an >>> F-test? And if I want the change from 24h-0h as >> well >>> as 42-12h and 12-4h, is it most correct for me to >>> specify that contrast directly? In my actual >>> experiment I have 4 time points, so will it be >> enough >>> for me with 3 possible comparisons, or will I have >> to >>> write all the 6 possible combinations? >>> >>> Thank you in advance for all your help. >>> >>> Yours truly >>> Mrs Helen Zhou >>> >>> P.S. I think this might have been mentioned on the >>> list before, but I could not find the email. In >> that >>> case, please excuse me for repeating this. >>> >>> _______________________________________________ >>> Bioconductor mailing list >>> Bioconductor at stat.math.ethz.ch >>> https://stat.ethz.ch/mailman/listinfo/bioconductor >>> Search the archives: > http://news.gmane.org/gmane.science.biology.informatics.conductor >> -- >> James W. MacDonald, M.S. >> Biostatistician >> Affymetrix and cDNA Microarray Core >> University of Michigan Cancer Center >> 1500 E. Medical Center Drive >> 7410 CCGC >> Ann Arbor MI 48109 >> 734-647-5623 >> > > > __________________________________________________ > Do You Yahoo!? > Tired of spam? Yahoo! Mail has the best spam protection around > http://mail.yahoo.com > -- James W. MacDonald, M.S. Biostatistician Affymetrix and cDNA Microarray Core University of Michigan Cancer Center 1500 E. Medical Center Drive 7410 CCGC Ann Arbor MI 48109 734-647-5623
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Dear James and Others I have followed your suggestion from last week, about trying to define all contrasts in a time course analysis, and then using the nestedF option. However, I am afraid that I am still a bit confused. I run the analysis shown below, and try decideTests both with and without method="nestedF". The rsult is also shown below, but too summarize it is: Without nested F: summary(results) # h24-h12 h12-h4 h24-h4 #-1 87 2 237 #0 21714 22280 21266 #1 482 1 780 With nested F summary(resultsF) # h24-h12 h12-h4 h24-h4 #-1 94 41 159 #0 21706 22210 21547 #1 483 32 577 I am not sure why I see such a big (relative) change for 12hour versus 4hour. In both cases I have a direct comparison. Acording to the help page for classifyTestsF that is being called, it says: "classifyTestsF uses a nested F-test approach giving particular attention to correctly classifying genes which have two or more significant t-statistics, i.e., are differential expressed under two or more conditions. For each row of tstat, the overall F-statistics is constructed from the t-statistics as for FStat. At least one constrast will be classified as significant if and only if the overall F-statistic is significant. If the overall F-statistic is significant, then the function makes a best choice as to which t-statistics contributed to this result. The methodology is based on the principle that any t-statistic should be called significant if the F-test is still significant for that row when all the larger t-statistics are set to the same absolute size as the t-statistic in question." I think I understand that. But I am surprised that it makes such a big difference. The difference is even bigger with my real data set with 6 time points, compared to the data from bioconductor that I am using here. Also, which of the two approaches is more trustworthy in the opinion of the bioconductor-list users? With or without nestedF? Thank you Helen # All commands library(bronchialIL13) data(HAHrma) # Just for the IL13 samples data <- HAHrma[,7:15] # Design targets <- c("h12","h12","h12","h24","h24","h24","h4","h4","h4") lev <- c("h12","h24","h4") f <- factor(targets, levels=lev) design <- model.matrix(~0+f) colnames(design) <- lev fit <- lmFit(data, design) # 3-step contrasts, used to directly get all comparisons contrasts <- makeContrasts("h24-h12", "h12-h4", "h24-h4", levels=design) fit2 <- contrasts.fit(fit, contrasts) fit2 <- eBayes(fit2) # results results <- decideTests(fit2, adjust="BH", p.value=0.01) resultsF <- decideTests(fit2, method="nestedF", adjust="BH", p.value=0.01) summary(results) # h24-h12 h12-h4 h24-h4 #-1 87 2 237 #0 21714 22280 21266 #1 482 1 780 summary(resultsF) # h24-h12 h12-h4 h24-h4 #-1 94 41 159 #0 21706 22210 21547 #1 483 32 577 --- "James W. MacDonald" <jmacdon at="" med.umich.edu=""> wrote: > Hi Helen, > > Helen Zhou wrote: > > Dear Jim > > > > Thanks you for your answer. As I understand you > are > > recommending me to do direct comparisons between > for > > example 12-4h and 24-12h. However, could there not > in > > theory be a gene that was up a little bit in > 12vs4h > > and 24vs12h, so that the difference for neither of > > these would be large enough to be significant, but > for > > 24vs4h the combined change might be significant? > In > > that case I guess I would need all 3 comparisons? > > Yes. The 'standard' linear modeling strategy is to > fit the model and see > if you have a significant F-statistic, then come > back and do contrasts > to see which particular comparison(s) is/are > contributing to that > significance. The general idea being that you want > to limit the number > of comparisons you are making so multiplicity is > less of a problem. > > However, with microarray data this isn't usually > what people do. > Instead, they usually try to minimize the > multiplicity by filtering out > uninteresting reporters prior to making comparisons > (based on variance, > P/M/A calls, IQR, etc) and then computing all > contrasts that they are > interested in with the reporters that remain. > > You might consider using decideTests() using the > 'nestedF' option - this > is intended to correctly detect differential > expression when two or more > contrasts are significant, so in the case you > mention may classify all > three contrasts as significant. > > Best, > > Jim > > > > > > Thanks you > > Helen > > > > --- "James W. MacDonald" <jmacdon at="" med.umich.edu=""> > > wrote: > > > >> Hi Helen, > >> > >> Helen Zhou wrote: > >>> Dear Sir/Madam > >>> > >>> I am trying to analyse a short time series, > >> roughly > >>> following section 8.8 in the limma user guide. I > >> am > >>> interested in differences between all time > points. > >> I > >>> am not sure whether I have to make all the > >> pariwise > >>> comparisons directly, or whether they can be > done > >>> indirectly as well. > >>> > >>> For example, if I want to compare to time > points, > >> what > >>> is the differences between the two methods > listed > >>> below. > >>> > >>> library(bronchialIL13) > >>> # Just for the IL13 samples > >>> data <- HAHrma[,7:15] > >>> # Design > >>> targets <- > >>> > > > c("h12","h12","h12","h24","h24","h24","h4","h4","h4") > >>> lev <- c("h12","h24","h4") > >>> f <- factor(targets, levels=lev) > >>> design <- model.matrix(~0+f) > >>> colnames(design) <- lev > >>> fit <- lmFit(data, design) > >>> # 2-step contrasts, used to indirectly get 24 to > 4 > >>> hours as well as the other two comparisons > >>> contrasts <- makeContrasts("h24-h12", "h12-h4", > >>> levels=design) > >>> fit2 <- contrasts.fit(fit, contrasts) > >>> fit2 <- eBayes(fit2) > >>> # Direct contrast of 24 to 4 hours > >>> contrasts2 <- makeContrasts("h24-h4", > >> levels=design) > >>> fit3 <- contrasts.fit(fit, contrasts2) > >>> fit3 <- eBayes(fit3) > >>> # Comparison > >>> topTable(fit2, coef=1:2) > >>> topTable(fit3, coef=1) > >> In the first case you are asking the question > 'which > >> reporters are > >> different in either h24 vs h4 _or_ h12 vs h4', > >> whereas in the second > >> case you are asking 'which reporters are > different > >> between H24 and h4'. > >> > >> It is entirely possible that you could have a > gene > >> that isn't different > >> between h24 and h4, but is different at h12. This > >> would show up in the > >> first comparison but not the second, so if you > want > >> to compare time > >> points you are better off making direct contrasts > >> rather than using the > >> F-statistic for multiple contrasts (which will > then > >> require the > >> additional step of figuring out which contrast(s) > >> caused the statistic > >> to be significant). > >> > >> Best, > >> > >> Jim > >> > >> > >>> More or less the same probe sets are present, > but > >> in > >>> different order and with different p values. Is > >> the > >>> difference because using coef=1:2 will go via an > >>> F-test? And if I want the change from 24h-0h as > >> well > >>> as 42-12h and 12-4h, is it most correct for me > to > >>> specify that contrast directly? In my actual > >>> experiment I have 4 time points, so will it be > >> enough > >>> for me with 3 possible comparisons, or will I > have > >> to > >>> write all the 6 possible combinations? > >>> > >>> Thank you in advance for all your help. > >>> > >>> Yours truly > >>> Mrs Helen Zhou > >>> > >>> P.S. I think this might have been mentioned on > the > >>> list before, but I could not find the email. In > >> that > >>> case, please excuse me for repeating this. > >>> > >>> _______________________________________________ > >>> Bioconductor mailing list > >>> Bioconductor at stat.math.ethz.ch > >>> > https://stat.ethz.ch/mailman/listinfo/bioconductor > >>> Search the archives: > > > http://news.gmane.org/gmane.science.biology.informatics.conductor > >> -- > >> James W. MacDonald, M.S. > >> Biostatistician > >> Affymetrix and cDNA Microarray Core > >> University of Michigan Cancer Center > >> 1500 E. Medical Center Drive > >> 7410 CCGC > >> Ann Arbor MI 48109 > >> 734-647-5623 > >> > > > > > > __________________________________________________ > > Do You Yahoo!? > protection around > > http://mail.yahoo.com > > > > === message truncated ===
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Helen Zhou ▴ 150
@helen-zhou-2654
Last seen 9.3 years ago
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Dear Marta, thank you for your suggestion. I am sorry it has taken me so long to reply. I have had a look at the masigpro package, but it seems to be specificaly for shorter time courses, whereas my real data set has 6 time points. Am I wrong about this? The example shown below is just because it was with public data available in bioconductor. I have also seen someone mention the package "timecourse". Does anyone on this list have any recomendations about that? Thank you Helen --- MARTA AGUDO BARRIUSO <martabar at="" um.es=""> wrote: > > you may try masigpro package, it has been designed > exactly to extract > those "changing a little bit each time point"-genes > > Helen Zhou <zhou.helen at="" yahoo.com=""> escribi??? > > > Dear Jim > > > > Thanks you for your answer. As I understand you > are > > recommending me to do direct comparisons between > for > > example 12-4h and 24-12h. However, could there not > in > > theory be a gene that was up a little bit in > 12vs4h > > and 24vs12h, so that the difference for neither of > > these would be large enough to be significant, but > for > > 24vs4h the combined change might be significant? > In > > that case I guess I would need all 3 comparisons? > > > > Thanks you > > Helen > > > > --- "James W. MacDonald" <jmacdon at="" med.umich.edu=""> > > wrote: > > > >> Hi Helen, > >> > >> Helen Zhou wrote: > >> > Dear Sir/Madam > >> > > >> > I am trying to analyse a short time series, > >> roughly > >> > following section 8.8 in the limma user guide. > I > >> am > >> > interested in differences between all time > points. > >> I > >> > am not sure whether I have to make all the > >> pariwise > >> > comparisons directly, or whether they can be > done > >> > indirectly as well. > >> > > >> > For example, if I want to compare to time > points, > >> what > >> > is the differences between the two methods > listed > >> > below. > >> > > >> > library(bronchialIL13) > >> > # Just for the IL13 samples > >> > data <- HAHrma[,7:15] > >> > # Design > >> > targets <- > >> > > >> > > > c("h12","h12","h12","h24","h24","h24","h4","h4","h4") > >> > lev <- c("h12","h24","h4") > >> > f <- factor(targets, levels=lev) > >> > design <- model.matrix(~0+f) > >> > colnames(design) <- lev > >> > fit <- lmFit(data, design) > >> > # 2-step contrasts, used to indirectly get 24 > to 4 > >> > hours as well as the other two comparisons > >> > contrasts <- makeContrasts("h24-h12", "h12-h4", > >> > levels=design) > >> > fit2 <- contrasts.fit(fit, contrasts) > >> > fit2 <- eBayes(fit2) > >> > # Direct contrast of 24 to 4 hours > >> > contrasts2 <- makeContrasts("h24-h4", > >> levels=design) > >> > fit3 <- contrasts.fit(fit, contrasts2) > >> > fit3 <- eBayes(fit3) > >> > # Comparison > >> > topTable(fit2, coef=1:2) > >> > topTable(fit3, coef=1) > >> > >> In the first case you are asking the question > 'which > >> reporters are > >> different in either h24 vs h4 _or_ h12 vs h4', > >> whereas in the second > >> case you are asking 'which reporters are > different > >> between H24 and h4'. > >> > >> It is entirely possible that you could have a > gene > >> that isn't different > >> between h24 and h4, but is different at h12. This > >> would show up in the > >> first comparison but not the second, so if you > want > >> to compare time > >> points you are better off making direct contrasts > >> rather than using the > >> F-statistic for multiple contrasts (which will > then > >> require the > >> additional step of figuring out which contrast(s) > >> caused the statistic > >> to be significant). > >> > >> Best, > >> > >> Jim > >> > >> > >> > > >> > More or less the same probe sets are present, > but > >> in > >> > different order and with different p values. Is > >> the > >> > difference because using coef=1:2 will go via > an > >> > F-test? And if I want the change from 24h-0h as > >> well > >> > as 42-12h and 12-4h, is it most correct for me > to > >> > specify that contrast directly? In my actual > >> > experiment I have 4 time points, so will it be > >> enough > >> > for me with 3 possible comparisons, or will I > have > >> to > >> > write all the 6 possible combinations? > >> > > >> > Thank you in advance for all your help. > >> > > >> > Yours truly > >> > Mrs Helen Zhou > >> > > >> > P.S. I think this might have been mentioned on > the > >> > list before, but I could not find the email. In > >> that > >> > case, please excuse me for repeating this. > >> > > >> > _______________________________________________ > >> > Bioconductor mailing list > >> > Bioconductor at stat.math.ethz.ch > >> > > https://stat.ethz.ch/mailman/listinfo/bioconductor > >> > Search the archives: > >> > > > http://news.gmane.org/gmane.science.biology.informatics.conductor > >> > >> -- > >> James W. MacDonald, M.S. > >> Biostatistician > >> Affymetrix and cDNA Microarray Core > >> University of Michigan Cancer Center > >> 1500 E. Medical Center Drive > >> 7410 CCGC > >> Ann Arbor MI 48109 > >> 734-647-5623 > >> > > > > _______________________________________________ > > Bioconductor mailing list > > Bioconductor at stat.math.ethz.ch > > https://stat.ethz.ch/mailman/listinfo/bioconductor > > Search the archives: > > > http://news.gmane.org/gmane.science.biology.informatics.conductor > > > > > >
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