BACKGROUND
dna methylation  has important regulatory roles in many biological processes and diseases.
it is the only epigenetic mark with a clear mechanism of mitotic inheritance  <cit>  and the only one easily available on a genome scale for epigenome-wide association studies  <cit> .
in vertebrates, the most common form of dnam is 5-methylcytosine.
it is associated with changes in dna-protein interactions and gene expression.
high methylation levels in cytosine-phosphate-guanine -rich promoter regions are strongly associated with transcriptional repression  <cit> .
recent dnam studies provided new etiological insights for human diseases  <cit> .
interestingly, epigenetic changes can be induced by diet, with implications for health  <cit>  and obesity  <cit> .
although significant progress has been made during the last decades, cancer remains a global problem of rising importance  <cit> .
on the other hand, modern omics technologies also enable new approaches for fighting the disease.
‘epigenetic changes can be the earliest initiating factor in a human cancer’  <cit> .
dnam markers for cancer detection have been found and potential dnam driver events have been discussed  <cit> .
the identification of dnam biomarkers indicating the risk of later cancer onset is improving early diagnosis and therapy.
based on the hypothesis that epigenetic variability may reflect differential exposure to genetic and environmental risk factors, it has been proposed that cpg sites with high inter-individual methylation variability might indicate risk of complex diseases  <cit> .
the fact that such sites occur more frequently in the promoters of developmental genes  <cit>  is consistent with this hypothesis, although sites with inter-individual variability are stable within individuals over many years  <cit> .
recently, a classifier based on dnam data to predict the risk of neoplastic development  has been proposed  <cit> .
it considers two features of a cpg’s methylation, the level of methylation and methylation variability.
the latter is the primary feature  selection criterion, the first few hundred most hypervariable cpgs  are considered as ‘risk cpgs’.
the risk score of an individual sample is the fraction of ‘risk cpgs’ with a methylation level higher than a given cut-off.
the optimal number of cpgs considered as well as the optimal cut-off is found by optimizing the area under the curve  through internal cross-validation in the training data.
evora was superior to the two tested popular classification algorithms pamr  <cit>  and spca  <cit>    <cit> .
however, it is known since the first dnam measurements in human cancer that widespread dna hypomethylation is involved  <cit> , but evora, by considering hypermethylated and hypervariable cpgs alone, does not account for such sites.
indeed, promoter hypomethylation has been used as criterion for detecting novel oncogenes in cancer  <cit> .
a refined version of evora was used to predict later neoplastic development  <cit>  in women with normal cytology according to a cervical screening test  <cit> .
this version considered a third feature of cpg methylation, age-correlation.
a cpg was classified as ‘risk cpg’ only if its methylation is both more variable in cases and positively age-correlated  <cit> .
the authors note that the uterine cervix is ‘currently the only human organ allowing relatively easy access to the cell of origin of the associated cancer well in advance of the first morphological signs of neoplastic transformation’.
supervised principal component analysis   <cit>  was developed for the prediction of tumour patients’ survival times based on gene expression data and was later successfully applied to other classification problems.
a samples risk score corresponds to its score on the first principal component  or the corresponding score from a linear combination of several pcs .
standard pca is considered as an unsupervised technique.
in spca the features used for pca are specifically selected for best association with the phenotype of interest .
in the original spca paper, the cox score  was used as the association criterion  <cit>  and only genes with a cox score above a given threshold were considered for pca .
again, the optimal threshold was obtained from internal cross-validation.
here we present model-selection-spca , an enhanced version of spca.
spca determines one model for the prediction of test data from optimisation within the training data.
in contrast, ms-spca determines several models that perform well in the training data and selects specific ones for the prediction of test data, based on parameters of the test data.
this is a natural extension of spca as it answers the question of how to deal with situations where several equally well performing models are found during the training data internal cross-validation.
ms-spca applies all these models to the test data and identifies the most appropriate subset of these models for final prediction.
ms-spca was applied to analyse publicly available genome-wide dnam data of cervical screening samples .
the cases considered correspond to three different stages of cervical cancer development:  women with no cytological signs of neoplasia that have later developed neoplastic transformations  as determined from a subsequent screen after three years,  neoplastic transformations ,  fully developed cancer.
we show that hyper- and hypomethylated, hyper- and hypovariable and positively and negatively age-correlated cpgs exist that are significantly associated with the phenotype.
significant cpgs of one dataset overlap significantly with significant cpgs of other datasets.
genes corresponding to significant cpgs are enriched with developmental genes  and cervical cancer genes  <cit> .
in contrast to evora, ms-spca uses the full non-binary methylation information as well as hyper- and hypomethylated sites.
cpgs most associated with the phenotype in the training data are used for prediction.
the corresponding ranked list of association strength is created by simultaneous consideration of three features of cpg methylation: average methylation difference, methylation variability difference  and age-correlation.
we use a ranks-weighting scheme to account for different weighting of these features.
different weights and numbers of best ranking cpgs are tested by cross-validation in the training data.
therefor we have used the leave-one-out  method .
we present results for all  <dig> possible test data predictions, using either cytology normal case–control data or cin2+ case–control data for training.
cancer data are not used for training because the methylation patterns are very pronounced and would yield many thousands of perfectly predicting models in the training data.
we also divide the cytology normal women dataset into several age-matched subsets , enabling another  <dig> predictions.
altogether, we performed  <dig> predictions in comparison to evora.
ms-spca outperforms evora in nearly all cases.
in most cases the difference is statistically significant.
RESULTS
we analysed six case–control datasets of genome-wide dnam data .
samples from women with normal cytology were used as control groups in all datasets.
table  <dig> shows the corresponding numbers of case and control samples.
the four columns show the geo  <cit>  accession numbers, name of the datasets and the corresponding numbers of contained case and control samples.
significantly associated cpgs
we tested all cpgs in the six datasets for average methylation difference , methylation variation difference  and methylation-age-correlation.
table  <dig> shows the numbers of corresponding significant cpgs.
each test was done for all cpgs , or only hyper-  and hypo-cpgs  .
the higher number of significant hyper-cpgs may reflect the biased cpg choice of the illumina 27k chip  <cit> .
future studies using less biased methods will clarify the relative importance of hyper- and hypomethylation.
table  <dig> shows that methylation patterns are more pronounced in more advanced stages of cancer.
most significant cpgs are found in the data where cases correspond to fully developed cancer, intermediate numbers are found in cin2+ data and almost no significant cpgs are detected in the normal data .
t-test, mann–whitney u test, bartlett’s test, levene’s test and test for methylation-age-correlation.
the three rows per cell correspond to all, hyper- and hypo-cpgs.
numbers of most significant cpgs that are completely separating cases from controls are given in brackets.
there are many significant cpgs in the normal data according to bartlett’s test, but these cpgs are not significant according to a permutation test.
often there is just a single sample largely deviating from the others, so permuting phenotypes does almost not change the p-value .
accordingly, after permuting phenotypes of the normal data one gets about the same number of significant cpgs, according to bartlett’s test.
the other tests do not suffer from the problem, the results are always corresponding to permutation test results.
although there are no statistically significant hyper- or hypomethylated cpgs in the normal data, intersection of the most significant cpgs of these data with the most significant cpgs of the cin2+ and cancer data shows a significant overlap , indicating that many important cpgs are hidden below the threshold for genome-wide significance.
this corresponds to a similar finding in genome-wide association studies  where typically only the minority of a phenotype’s heritability can be explained by the statistically significant single-nucleotide polymorphisms  .
however, taking into account all ~1 m snps allows explanation of most of the heritability  <cit> , ‘most of the genetic variance is simply hidden below the threshold for genome-wide significant associations’  <cit> .
significant cpgs in the normal hpv+ dataset overlap more to the corresponding cin2+ and cancer dataset cpgs than normal hpv- cpgs.
this could indicate that the potential transformation causing methylation patterns are more pronounced in the hpv+ dataset, but the number of hpv+ samples is also higher.
cpgs were ordered according to five different tests  and the number of overlapping cpgs between the first  <dig> of two datasets determined.
the three rows per cell correspond to all, hyper- and hypo-cpgs.
significant overlaps  are shown in bold.
tables  <dig> and  <dig> provide additional evidence that the most significant cpgs correspond to genes involved in cancer onset.
for best ranking cpgs, we identified the corresponding genes and determined their overlap to  <dig> known cervical cancer genes  <cit>  and  <dig>  developmental genes   <cit> .
table  <dig> shows that cervical cancer genes are enriched in nearly all high-ranking genes.
genes from the normal data overlap as significantly as genes from cin2+ and cancer data.
hypo-cpg-genes overlap as well as hyper-cpg-genes.
table  <dig> shows that hyper-cpg-genes are highly enriched with pcgt genes  <cit> , in contrast to hypo-cpg-genes.
genes corresponding to the  <dig> most significant cpgs taken .
the three rows per cell correspond to all, hyper- and hypo-cpgs.
significant overlaps  are shown in bold.
genes corresponding to the  <dig> most significant cpgs taken .
the three rows per cell correspond to all, hyper- and hypo-cpgs.
significant overlaps  are shown in bold.
motivation for supervised pca approach
table  <dig> shows that no single cpg can differentiate between case and control samples in the three normal datasets.
however, the leading principal components  corresponding to the best ranking cpgs do separate cases from controls.
additional file 1: figure s <dig> shows for the normal dataset that the leading pcs do significantly  differentiate, if the cpgs with the highest average methylation difference are used .
prediction of future neoplastic transformation, cin2+ and cancer
selecting the best models from cross-validation in training data
we tested models based on the best ranking cpgs according to cpg ‘combi’ orders  for cross-validation prediction in the five datasets that served as training data: normal, normal hpv+, normal hpv-, cin2+ and cin2+.
in each case the first few hundred best performing models were applied for prediction of all the corresponding independent datasets .
models with the following cross-validation prediction accuracies were used: > <dig>  for the three normal datasets, > <dig>  for cin2+, and > <dig>  for cin2+; resulting in > <dig> models trained on the normal datasets and > <dig> and > <dig> models trained on cin2+ and cin2+, respectively .
the models predicting the training-data best have the following accuracies: ~ <dig>  for the normal datasets,  <dig>  for cin2+ and  <dig> for cin2+ .
the clearer patterns in cin2+, compared to cin2+, might result from the fact that all cin2+ samples were taken from hpv infected women.
rows correspond to training data and columns to test data.
the first number shows the performance of ms-spca, the second the performance of evora .
numbers in brackets show the five evora results as presented in  <cit> .
bold numbers show best predictions.
identifying the likely best predicting models and final prediction
ms-spca selects the final models for prediction on the basis of parameters obtained from analysis of the test data.
figure  <dig> depicts the two parameters eval <dig> and ev1dist for all used models.
figure  <dig> shows the prediction performance of all models ordered according to the difference eval1-ev1dist .
eval <dig> is the normalized largest eigenvalue of the covariance matrix taken from the methylation matrix of the test data.
ev1dist is the euclidean distance between the leading eigenvectors of the model’s covariance matrix in the training data and in the test data.
it can be seen from the colouring in figure  <dig> that the smaller ev1dist and the larger eval <dig> is, the more likely the model makes a good prediction of the test data.
red dots tend to be in the lower right corner, especially for the well predicted advanced transformation stages cin2+ and cancer .
eval <dig> measures how much of the variation in the test data is likely captured by pc <dig>  ev1dist is a measure for how well the model obtained from the training data fits to the test data.
importantly, the two parameters eval <dig> and ev1dist capture information about how likely a model makes a good prediction.
for example, in the first row of figures  <dig>   <dig> and  <dig> models were trained on the normal dataset.
these models predict the cin2+ and cancer data very well , but less so the cin2+ data.
figure  <dig> shows that eval <dig> is generally smaller for cin2+ models and ev1dist is larger.
similarly in the last column: in rows  <dig>   <dig> and  <dig>  where the prediction is very good , eval <dig> is often large and ev1dist is small.
parameters such as eval <dig> and ev1dist open the possibility to automatically select the most appropriate number of principal components to consider for prediction.
the authors of the original spca paper had worked on a similar problem but had not solved it  <cit> .
given that the models trained on cin2+ data have consistently poor eval <dig> and ev1dist, compared to models from other training data, it seems that consideration of more than one pc could improve the prediction performance.
although the two parameters eval <dig> and ev1dist are correlated to each other they also carry important unique information.
each parameter alone is inferior to the sum eval1-ev1dist.
for example, row 3-column  <dig> shows poorly performing models with small ev1dist, row 4-column  <dig> shows poor models with large eval <dig>
figure  <dig> shows that, although there is some variation, the best-ranking models  perform better.
moreover, the cumulative score  enables robust and good prediction by considering only best-ranking models.
the final prediction results that correspond to the auc of the cumulative score at model rank  <dig> are given in table  <dig>  the prediction of a given test dataset by ms-spca is quite consistent, no matter which training dataset is used: normal ~ <dig> , normal hpv+ > <dig> , normal hpv- > <dig> , cin2+ > <dig> , cin2+ > <dig> , cancer ~ <dig>
comparison with evora  <cit>  was performed, using the r-package ‘evora’.
table  <dig> shows the mean prediction values of  <dig> independent runs.
prediction with ms-spca is nearly always superior.
the better performance of ms-spca is statistically significant.
a two-way anova confirms the significantly higher performance of ms-spca, even in comparison to the three previously published prediction results of row  <dig> : we simulated  <dig> evora-auc values for each prediction such that the mean auc and the 95% ci correspond to the numbers given  <cit>  and compared to the aucs of the top  <dig> ranking ms-spca models, p <  <dig> .
it can be seen that the numbers reported by the evora authors  <cit>  are better than those from our own runs.
the original evora method  <cit>  and the ‘evora’ r-package do not consider any information about the age of the women who have provided the samples, although this was considered in a related paper  <cit> .
it is possible that the higher numbers result from taking age into account.
however, ms-spca outperforms these results as well.
moreover, ms-spca was also performing well without the use of age information.
the results are similar to the ones presented in table  <dig>  mostly lower by about  <dig> - <dig> , but higher in the case of normal hpv- → cin2+ by  <dig> .
description of best performing models
a concise description of the models used for predictions is shown in figure  <dig>  models were sorted according to eval1-ev1dist and mean values were calculated from model rank  <dig> up to any other indicated rank.
for instance, rank  <dig> shows the mean numbers of the first  <dig> models.
accordingly, the final rank shows the mean values of all the models used.
interestingly, the figures in a given row are similar, indicating that the model order is also similar for different test data predictions.
best-ranking models typically contain fewer cpgs .
clearly, solid lines are dominating amongst the coloured ones.
that means most of these models include hyper- and hypomethylated cpgs, models with pure hyper- or hypo-cpgs are rare.
the models selected from cross-validation within normal and normal hpv+ data contain cpgs which are mostly ordered by methylation variation difference, the red line ends at >60% .
models in rows 3– <dig> are dominated by methylation difference ordering .
the best performing models  are dominated by age-correlation in the normal training data  and by methylation difference in row  <dig>  hypermethylation and methylation variation difference  are dominating in the best predicting models in row  <dig>
cytologically normal samples contain dnam patterns predisposing for later transformations
samples classified as normal by the standard cytological screening method contain dnam patterns that can clearly differentiate between normal and cin2+ samples and between normal and cancer samples .
interestingly, this conclusion even holds for the normal hpv- samples.
although hpv infection is considered a necessary condition for neoplastic transformation and later cancer, the differentiating dnam patterns exist prior to any hpv infection.
these patterns might contribute to infection itself and/or contribute to transformations after infection.
the latter possibility is supported by our finding that ms-spca trained on normal hpv- data predicts the phenotype of normal hpv+ samples about as well as when trained on cin2+ data.
to further study the problem of phenotype prediction within the normal data, a corresponding stratified 5-fold cross-validation was performed.
both the normal hpv+ and the normal hpv- datasets were subdivided into five equally sized case–control parts, always ensuring that age is matched.
five predictions were performed, taking one set for testing and the remaining four as training data.
additional file 1: figures s2-s <dig> show the plots corresponding to figures  <dig>   <dig> and  <dig> for the five cases using normal hpv+ data for training, and additional file 1: figures s5-s <dig> the same using normal hpv- for training.
clearly, eval1-ev1dist is an important sorting criterion, for instance in cancer prediction from normal hpv- data.
however, additional file 1: figures s <dig> and s <dig> also show that this sorting is selecting the best predicting models in the test data corresponding to the training data  less robustly.
our hypothesis that this is caused by the small size of these test sets  was confirmed by a corresponding calculation .
the larger the test sets are the better eval1-ev1dist selects the best predicting models.
this implies that ms-spca would predict future transformations better in larger test data.
table  <dig> shows the results of the final ms-spca prediction using the cumulative score of the first  <dig> models, in comparison to evora predictions.
ms-spca prediction results are better and more consistent  than evora results.
again, in most cases the advantage of ms-spca is statistically significant.
ms-spca allows the prediction of later neoplastic transformation in hpv infected women with cytologically normal samples .
rows correspond to training datasets and columns to test datasets.
the first number shows the performance of ms-spca, the second the performance of evora .
bold numbers show best predictions.
finally, we also tested if dnam patterns might contribute to infection itself by using the models trained on normal hpv- data to predict independent test data where the “cases” are healthy hpv+ samples  and controls are healthy hpv- samples.
interestingly, this ‘phenotype’ can be predicted even better than the future transformation in the normal hpv+ data: auc >  <dig>  .
this indicates that dnam patterns may contribute to hpv infection.
consistency of models used for predictions, corresponding outstanding cpgs and genes
all phenotype predictions were based on the five models with the largest parameter eval1-ev1dist .
interestingly, the five models chosen for the prediction of different test data were often identical.
for example, three of the five models from the training data normal that were used to predict cin2+, cin2+ and cancer  are identical, i.e.
these three models predict the three different test data very well.
similar model consistency was also found using other data for training: normal hpv+ and hpv- were used to predict four independent test data, cin2+ and cin2+ to predict five test data .
the corresponding intersection of the 4x <dig> or 5x <dig> models is  <dig>   <dig>   <dig> and  <dig>  respectively.
although there is no model amongst the five best that is used for all five test data predictions in the case of training data cin2+, one model is consistently used to predict the four test data normal, normal hpv+, cin2+ and cancer; three of the models used to predict normal hpv- were also used to predict cancer.
not surprisingly, the cpgs used in the five models for final prediction are also largely overlapping.
furthermore, the cpgs of all the five models used to predict one test dataset tend to overlap with the corresponding cpgs used to predict another test dataset.
the numbers of common cpgs used for the prediction of all test datasets based on the five training datasets normal, normal hpv+, normal hpv-, cin2+ and cin2+) are  <dig>   <dig>   <dig>   <dig> and  <dig>  respectively.
for instance,  <dig> same cpgs were used to predict cin2+, cin2+ and cancer from the training dataset normal.
there is one cpg occurring in all these five cpg lists: cg <dig>  located in a cpg island 234 bp upstream of the transcription start site  of the ntm gene.
ntm codes for the protein neurotrimin, which is known to play a role in cell-adhesion  <cit> .
the intersection of the  <dig>   <dig> and  <dig> cpgs is cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig> and cg <dig>  which are all hypermethylated in all six datasets.
although there is no cpg with significant methylation difference between cases and controls in the three normal data , there are cpgs consistently used for the prediction of test data.
the intersection of the  <dig>   <dig> and  <dig> cpgs is cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  cg <dig>  nearly all are hypermethylated in all six datasets.
<dig> cpgs occur in at least two of the five cpg lists with  <dig> of them being located in cpg islands, mostly close to the tss .
nearly all are hypermethylated in the analysed six datasets, but two are clearly hypomethylated: cg <dig> in all six datasets, cg <dig> in five datasets.
they correspond to the genes ccl <dig> and cltcl <dig>  respectively.
both are often overexpressed in cancer cells.
elevated ccl <dig> expression plays a role in ovarian carcinoma  <cit>  and induces metastasis of breast cancer  <cit> .
cltcl <dig> is overexpressed in cervical and other cancers  <cit> .
two genes correspond to more than two of the  <dig> cpgs, both are well-known tumour suppressor genes: dcc  and gata <dig>  the gata <dig> promoter is hypermethylated in cancer  <cit>  and it is involved in ovarian cancer  <cit> .
interestingly, the two most important human dna regions of a recent dnam cervical pre-cancer classifier, epb41l <dig> and dpys  <cit> , are amongst the ~ <dig> regions corresponding to the  <dig> cpgs.
discussion
we have developed ms-spca, an advanced version of the classifier spca  <cit> .
in contrast to spca, ms-spca considers several models that perform well in training data cross-validation and selects the final ones for prediction of test data, based on parameters obtained from the test data.
we tested different parameters and parameter combinations based on the training data but none was performing as well in selecting the best models as our final criterion eval1-ev1dist.
importantly, the values of the parameters eval <dig> and ev1dist are related to the prediction performance.
for instance, figure  <dig> shows that, using cin2+ for training, all corresponding models have relatively poor parameters eval <dig> and ev1dist, compared to the cases using datasets normal or cin2+ for training.
accordingly, the prediction performance using the cin2+ dataset for training is lower .
consideration of > <dig> pc might improve the prediction.
it seems that parameters such as eval <dig> and ev1dist could provide the basis for automatic selection of the most appropriate number of principal components to consider.
we also tested a support vector machine  for prediction using more than one pc, but without any specific criterion for model selection.
the corresponding performance was slightly lower, but a combination of an automatic selection of the number of pcs to consider with advanced learning algorithms such as svm could lead to further improvement.
another point for potential future improvement concerns the number of models to consider.
here we used the few hundred best models according to training data cross-validation performance.
obviously, some diversity of the models is needed such that the final model selection criterion eval1-ev1dist can select the most appropriate ones.
considering only the very few in the training data top performing models might suffer from too low model diversity and over-fitting to the training data, considering many models is time consuming and might result in over-fitting to the test data.
maybe some optimal diversity  can be defined, helping to automatically select the cross-validation performance cut-off and therefore the number of models to consider.
we have shown that the model selection of ms-spca works better the more samples the test set contains.
in the special case that the test set contains only one sample no test data covariance matrix can be calculated.
the corresponding phenotype could be predicted by either a majority vote of all the models  and/or by assigning additional samples to the test set  and applying the criterion eval1-ev1dist.
ms-spca was applied for phenotype prediction from genome-wide dna methylation data.
the procedure involves the following steps: 1) splitting of the training data into k-fold training and test sets , 2) calculation of p-values for all cpgs  for the three features of a cpg’s methylation: average methylation difference, methylation variation difference and methylation-age-correlation, 3) identification of the best models in training data cross-validation: testing models with different weights  and numbers of cpgs in each of the k training datasets 4) predicting the independent test data with the best performing models identified in step  <dig> , 5) the model selection step of ms-spca: ranking these models according to the criterion eval1-ev1dist and using the cumulative risk scores of the first n best ranking models for final prediction .
we have shown that ms-spca performs better than the recent method evora  <cit> .
the first experiments on dna methylation in human cancer showed widespread hypomethylation  <cit> , but after the discovery of tumour suppressor genes one also observed promoter hypermethylation  <cit> .
meanwhile, of all epigenetic modifications, hypermethylation of promoter regions of tumor suppressor genes has been most extensively studied  <cit> .
we have shown that hypermethylation and hypervariability are important factors for neoplastic transformation, but hypomethylation and hypovariability play a role as well.
the 27k cpgs analysed here are biased towards hypermethylated promoter regions  <cit> .
nevertheless, ms-spca performs best if both hyper- and hypomethylated cpgs are considered.
it will be interesting to see if hypomethylated cpgs play an even bigger role in more recent larger and less biased dna methylation assays.
it has been suggested that hypervariable cpgs are most important for the prediction of early cancer development  <cit> , although analysis of other cancer data does not always benefit from considering differential variability  <cit> .
this is in agreement with our results .
ms-spca in combination with the here presented cpg selection method allows for automatic identification of the most appropriate weighting of the cpg’s methylation features.
although hpv infection is considered necessary for cervical cancer development  <cit> , we have shown that specific dna methylation patterns which are likely contributing to later cancer development exist already before any hpv infection.
this is in accordance with previous findings that epigenetic changes may be the earliest initiating factor in a human cancer  <cit> .
on the other hand, it was recently suggested that the earliest changes leading to later transformations might be other epigenetic changes such as chromatin modification rather than dna methylation  <cit> .
if this is true, then the patterns observed in the normal data may be the consequence of other earlier epigenetic changes.
however, even then the analysis of dna methylation can be important for early diagnosis of dangerous transformations as it is detectable before standard cytological screening methods can show evidence of transformations  <cit> .
we have presented evidence that dna methylation patterns exist in cytology normal hpv- samples that  predispose to neoplastic transformations after hpv infection and  predispose to hpv infection itself.
it will be interesting to test if other virus infections are also correlated with specific dna methylation patterns.
given that ms-spca performs well using data from comparatively few samples and only  <dig> % of the gpgs in the human genome  <cit> , it is possible that future dna methylation analysis can provide the accuracy needed for clinical applications.
CONCLUSIONS
ms-spca, an advanced version of the classifier spca, is presented.
it performs well in predicting phenotypes from genome-wide dna methylation data.
ms-spca can be applied to other classification problems.
consideration of more principal components, based on the automatic selection of the corresponding most appropriate number, and additional model selection methods might allow further improvement.

 dna methylation has important regulatory roles in many biological processes and diseases. it is the only epigenetic mark with a clear mechanism of mitotic inheritance and the only one easily available on a genome scale for epigenome-wide association studies. in vertebrates, the most common form of dnam is 5-methylcytosine. it is associated with changes in dna-protein interactions and gene expression. high methylation levels in cytosine-phosphate-guanine -rich promoter regions are strongly associated with transcriptional repression. recent dnam studies provided new etiological insights for human diseases. interestingly, epigenetic changes can be induced by diet, with implications for health and obesity. although significant progress has been made during the last decades, cancer remains a global problem of rising importance. on the other hand, modern omics technologies also enable new approaches for fighting the disease. ‘epigenetic changes can be the earliest initiating factor in a human cancer’. dnam markers for cancer detection have been found and potential dnam driver events have been discussed. the identification of dnam biomarkers indicating the risk of later cancer onset is improving early diagnosis and therapy. based on the hypothesis that epigenetic variability may reflect differential exposure to genetic and environmental risk factors, it has been proposed that cpg sites with high inter-individual methylation variability might indicate risk of complex diseases. the fact that such sites occur more frequently in the promoters of developmental genes is consistent with this hypothesis, although sites with inter-individual variability are stable within individuals over many years. recently, a classifier based on dnam data to predict the risk of neoplastic development has been proposed. it considers two features of a cpg’s methylation, the level of methylation and methylation variability. the latter is the primary feature selection criterion, the first few hundred most hypervariable cpgs are considered as ‘risk cpgs’. the risk score of an individual sample is the fraction of ‘risk cpgs’ with a methylation level higher than a given cut-off. the optimal number of cpgs considered as well as the optimal cut-off is found by optimizing the area under the curve through internal cross-validation in the training data. evora was superior to the two tested popular classification algorithms pamr and spca. however, it is known since the first dnam measurements in human cancer that widespread dna hypomethylation is involved, but evora, by considering hypermethylated and hypervariable cpgs alone, does not account for such sites. indeed, promoter hypomethylation has been used as criterion for detecting novel oncogenes in cancer. a refined version of evora was used to predict later neoplastic development in women with normal cytology according to a cervical screening test. this version considered a third feature of cpg methylation, age-correlation. a cpg was classified as ‘risk cpg’ only if its methylation is both more variable in cases and positively age-correlated. the authors note that the uterine cervix is ‘currently the only human organ allowing relatively easy access to the cell of origin of the associated cancer well in advance of the first morphological signs of neoplastic transformation’. supervised principal component analysis was developed for the prediction of tumour patients’ survival times based on gene expression data and was later successfully applied to other classification problems. a samples risk score corresponds to its score on the first principal component or the corresponding score from a linear combination of several pcs. standard pca is considered as an unsupervised technique. in spca the features used for pca are specifically selected for best association with the phenotype of interest. in the original spca paper, the cox score was used as the association criterion and only genes with a cox score above a given threshold were considered for pca. again, the optimal threshold was obtained from internal cross-validation. here we present model-selection-spca, an enhanced version of spca. spca determines one model for the prediction of test data from optimisation within the training data. in contrast, ms-spca determines several models that perform well in the training data and selects specific ones for the prediction of test data, based on parameters of the test data. this is a natural extension of spca as it answers the question of how to deal with situations where several equally well performing models are found during the training data internal cross-validation. ms-spca applies all these models to the test data and identifies the most appropriate subset of these models for final prediction. ms-spca was applied to analyse publicly available genome-wide dnam data of cervical screening samples. the cases considered correspond to three different stages of cervical cancer development: women with no cytological signs of neoplasia that have later developed neoplastic transformations as determined from a subsequent screen after three years, neoplastic transformations, fully developed cancer. we show that hyper- and hypomethylated, hyper- and hypovariable and positively and negatively age-correlated cpgs exist that are significantly associated with the phenotype. significant cpgs of one dataset overlap significantly with significant cpgs of other datasets. genes corresponding to significant cpgs are enriched with developmental genes and cervical cancer genes. in contrast to evora, ms-spca uses the full non-binary methylation information as well as hyper- and hypomethylated sites. cpgs most associated with the phenotype in the training data are used for prediction. the corresponding ranked list of association strength is created by simultaneous consideration of three features of cpg methylation: average methylation difference, methylation variability difference and age-correlation. we use a ranks-weighting scheme to account for different weighting of these features. different weights and numbers of best ranking cpgs are tested by cross-validation in the training data. therefor we have used the leave-one-out method. we present results for all possible test data predictions, using either cytology normal case–control data or cin2+ case–control data for training. cancer data are not used for training because the methylation patterns are very pronounced and would yield many thousands of perfectly predicting models in the training data. we also divide the cytology normal women dataset into several age-matched subsets, enabling another predictions. altogether, we performed predictions in comparison to evora. ms-spca outperforms evora in nearly all cases. in most cases the difference is statistically significant.  we analysed six case–control datasets of genome-wide dnam data. samples from women with normal cytology were used as control groups in all datasets. table  shows the corresponding numbers of case and control samples. the four columns show the geo accession numbers, name of the datasets and the corresponding numbers of contained case and control samples. significantly associated cpgs we tested all cpgs in the six datasets for average methylation difference, methylation variation difference and methylation-age-correlation. table  shows the numbers of corresponding significant cpgs. each test was done for all cpgs, or only hyper- and hypo-cpgs. the higher number of significant hyper-cpgs may reflect the biased cpg choice of the illumina 27k chip. future studies using less biased methods will clarify the relative importance of hyper- and hypomethylation. table  shows that methylation patterns are more pronounced in more advanced stages of cancer. most significant cpgs are found in the data where cases correspond to fully developed cancer, intermediate numbers are found in cin2+ data and almost no significant cpgs are detected in the normal data. t-test, mann–whitney u test, bartlett’s test, levene’s test and test for methylation-age-correlation. the three rows per cell correspond to all, hyper- and hypo-cpgs. numbers of most significant cpgs that are completely separating cases from controls are given in brackets. there are many significant cpgs in the normal data according to bartlett’s test, but these cpgs are not significant according to a permutation test. often there is just a single sample largely deviating from the others, so permuting phenotypes does almost not change the p-value. accordingly, after permuting phenotypes of the normal data one gets about the same number of significant cpgs, according to bartlett’s test. the other tests do not suffer from the problem, the results are always corresponding to permutation test results. although there are no statistically significant hyper- or hypomethylated cpgs in the normal data, intersection of the most significant cpgs of these data with the most significant cpgs of the cin2+ and cancer data shows a significant overlap, indicating that many important cpgs are hidden below the threshold for genome-wide significance. this corresponds to a similar finding in genome-wide association studies where typically only the minority of a phenotype’s heritability can be explained by the statistically significant single-nucleotide polymorphisms. however, taking into account all ~1 m snps allows explanation of most of the heritability, ‘most of the genetic variance is simply hidden below the threshold for genome-wide significant associations’. significant cpgs in the normal hpv+ dataset overlap more to the corresponding cin2+ and cancer dataset cpgs than normal hpv- cpgs. this could indicate that the potential transformation causing methylation patterns are more pronounced in the hpv+ dataset, but the number of hpv+ samples is also higher. cpgs were ordered according to five different tests and the number of overlapping cpgs between the first of two datasets determined. the three rows per cell correspond to all, hyper- and hypo-cpgs. significant overlaps are shown in bold. tables  and provide additional evidence that the most significant cpgs correspond to genes involved in cancer onset. for best ranking cpgs, we identified the corresponding genes and determined their overlap to known cervical cancer genes and developmental genes. table  shows that cervical cancer genes are enriched in nearly all high-ranking genes. genes from the normal data overlap as significantly as genes from cin2+ and cancer data. hypo-cpg-genes overlap as well as hyper-cpg-genes. table  shows that hyper-cpg-genes are highly enriched with pcgt genes, in contrast to hypo-cpg-genes. genes corresponding to the most significant cpgs taken. the three rows per cell correspond to all, hyper- and hypo-cpgs. significant overlaps are shown in bold. genes corresponding to the most significant cpgs taken. the three rows per cell correspond to all, hyper- and hypo-cpgs. significant overlaps are shown in bold. motivation for supervised pca approach table  shows that no single cpg can differentiate between case and control samples in the three normal datasets. however, the leading principal components corresponding to the best ranking cpgs do separate cases from controls. additional file 1: figure s shows for the normal dataset that the leading pcs do significantly differentiate, if the cpgs with the highest average methylation difference are used. prediction of future neoplastic transformation, cin2+ and cancer selecting the best models from cross-validation in training data we tested models based on the best ranking cpgs according to cpg ‘combi’ orders for cross-validation prediction in the five datasets that served as training data: normal, normal hpv+, normal hpv-, cin2+ and cin2+. in each case the first few hundred best performing models were applied for prediction of all the corresponding independent datasets. models with the following cross-validation prediction accuracies were used: > for the three normal datasets, > for cin2+, and > for cin2+; resulting in > models trained on the normal datasets and > and > models trained on cin2+ and cin2+, respectively. the models predicting the training-data best have the following accuracies: ~ for the normal datasets, for cin2+ and for cin2+. the clearer patterns in cin2+, compared to cin2+, might result from the fact that all cin2+ samples were taken from hpv infected women. rows correspond to training data and columns to test data. the first number shows the performance of ms-spca, the second the performance of evora. numbers in brackets show the five evora results as presented in. bold numbers show best predictions. identifying the likely best predicting models and final prediction ms-spca selects the final models for prediction on the basis of parameters obtained from analysis of the test data. figure  depicts the two parameters eval and ev1dist for all used models. figure  shows the prediction performance of all models ordered according to the difference eval1-ev1dist. eval is the normalized largest eigenvalue of the covariance matrix taken from the methylation matrix of the test data. ev1dist is the euclidean distance between the leading eigenvectors of the model’s covariance matrix in the training data and in the test data. it can be seen from the colouring in figure  that the smaller ev1dist and the larger eval is, the more likely the model makes a good prediction of the test data. red dots tend to be in the lower right corner, especially for the well predicted advanced transformation stages cin2+ and cancer. eval measures how much of the variation in the test data is likely captured by pc ev1dist is a measure for how well the model obtained from the training data fits to the test data. importantly, the two parameters eval and ev1dist capture information about how likely a model makes a good prediction. for example, in the first row of figures  and models were trained on the normal dataset. these models predict the cin2+ and cancer data very well, but less so the cin2+ data. figure  shows that eval is generally smaller for cin2+ models and ev1dist is larger. similarly in the last column: in rows and where the prediction is very good, eval is often large and ev1dist is small. parameters such as eval and ev1dist open the possibility to automatically select the most appropriate number of principal components to consider for prediction. the authors of the original spca paper had worked on a similar problem but had not solved it. given that the models trained on cin2+ data have consistently poor eval and ev1dist, compared to models from other training data, it seems that consideration of more than one pc could improve the prediction performance. although the two parameters eval and ev1dist are correlated to each other they also carry important unique information. each parameter alone is inferior to the sum eval1-ev1dist. for example, row 3-column shows poorly performing models with small ev1dist, row 4-column shows poor models with large eval figure  shows that, although there is some variation, the best-ranking models perform better. moreover, the cumulative score enables robust and good prediction by considering only best-ranking models. the final prediction results that correspond to the auc of the cumulative score at model rank are given in table  the prediction of a given test dataset by ms-spca is quite consistent, no matter which training dataset is used: normal ~, normal hpv+ >, normal hpv- >, cin2+ >, cin2+ >, cancer ~ comparison with evora was performed, using the r-package ‘evora’. table  shows the mean prediction values of independent runs. prediction with ms-spca is nearly always superior. the better performance of ms-spca is statistically significant. a two-way anova confirms the significantly higher performance of ms-spca, even in comparison to the three previously published prediction results of row: we simulated evora-auc values for each prediction such that the mean auc and the 95% ci correspond to the numbers given and compared to the aucs of the top ranking ms-spca models, p < . it can be seen that the numbers reported by the evora authors are better than those from our own runs. the original evora method and the ‘evora’ r-package do not consider any information about the age of the women who have provided the samples, although this was considered in a related paper. it is possible that the higher numbers result from taking age into account. however, ms-spca outperforms these results as well. moreover, ms-spca was also performing well without the use of age information. the results are similar to the ones presented in table  mostly lower by about -, but higher in the case of normal hpv- → cin2+ by. description of best performing models a concise description of the models used for predictions is shown in figure  models were sorted according to eval1-ev1dist and mean values were calculated from model rank up to any other indicated rank. for instance, rank shows the mean numbers of the first models. accordingly, the final rank shows the mean values of all the models used. interestingly, the figures in a given row are similar, indicating that the model order is also similar for different test data predictions. best-ranking models typically contain fewer cpgs. clearly, solid lines are dominating amongst the coloured ones. that means most of these models include hyper- and hypomethylated cpgs, models with pure hyper- or hypo-cpgs are rare. the models selected from cross-validation within normal and normal hpv+ data contain cpgs which are mostly ordered by methylation variation difference, the red line ends at >60%. models in rows 3– are dominated by methylation difference ordering. the best performing models are dominated by age-correlation in the normal training data and by methylation difference in row hypermethylation and methylation variation difference are dominating in the best predicting models in row cytologically normal samples contain dnam patterns predisposing for later transformations samples classified as normal by the standard cytological screening method contain dnam patterns that can clearly differentiate between normal and cin2+ samples and between normal and cancer samples. interestingly, this conclusion even holds for the normal hpv- samples. although hpv infection is considered a necessary condition for neoplastic transformation and later cancer, the differentiating dnam patterns exist prior to any hpv infection. these patterns might contribute to infection itself and/or contribute to transformations after infection. the latter possibility is supported by our finding that ms-spca trained on normal hpv- data predicts the phenotype of normal hpv+ samples about as well as when trained on cin2+ data. to further study the problem of phenotype prediction within the normal data, a corresponding stratified 5-fold cross-validation was performed. both the normal hpv+ and the normal hpv- datasets were subdivided into five equally sized case–control parts, always ensuring that age is matched. five predictions were performed, taking one set for testing and the remaining four as training data. additional file 1: figures s2-s show the plots corresponding to figures  and for the five cases using normal hpv+ data for training, and additional file 1: figures s5-s the same using normal hpv- for training. clearly, eval1-ev1dist is an important sorting criterion, for instance in cancer prediction from normal hpv- data. however, additional file 1: figures s and s also show that this sorting is selecting the best predicting models in the test data corresponding to the training data less robustly. our hypothesis that this is caused by the small size of these test sets was confirmed by a corresponding calculation. the larger the test sets are the better eval1-ev1dist selects the best predicting models. this implies that ms-spca would predict future transformations better in larger test data. table  shows the results of the final ms-spca prediction using the cumulative score of the first models, in comparison to evora predictions. ms-spca prediction results are better and more consistent than evora results. again, in most cases the advantage of ms-spca is statistically significant. ms-spca allows the prediction of later neoplastic transformation in hpv infected women with cytologically normal samples. rows correspond to training datasets and columns to test datasets. the first number shows the performance of ms-spca, the second the performance of evora. bold numbers show best predictions. finally, we also tested if dnam patterns might contribute to infection itself by using the models trained on normal hpv- data to predict independent test data where the “cases” are healthy hpv+ samples and controls are healthy hpv- samples. interestingly, this ‘phenotype’ can be predicted even better than the future transformation in the normal hpv+ data: auc > . this indicates that dnam patterns may contribute to hpv infection. consistency of models used for predictions, corresponding outstanding cpgs and genes all phenotype predictions were based on the five models with the largest parameter eval1-ev1dist. interestingly, the five models chosen for the prediction of different test data were often identical. for example, three of the five models from the training data normal that were used to predict cin2+, cin2+ and cancer are identical, i.e. these three models predict the three different test data very well. similar model consistency was also found using other data for training: normal hpv+ and hpv- were used to predict four independent test data, cin2+ and cin2+ to predict five test data. the corresponding intersection of the 4x or 5x models is and respectively. although there is no model amongst the five best that is used for all five test data predictions in the case of training data cin2+, one model is consistently used to predict the four test data normal, normal hpv+, cin2+ and cancer; three of the models used to predict normal hpv- were also used to predict cancer. not surprisingly, the cpgs used in the five models for final prediction are also largely overlapping. furthermore, the cpgs of all the five models used to predict one test dataset tend to overlap with the corresponding cpgs used to predict another test dataset. the numbers of common cpgs used for the prediction of all test datasets based on the five training datasets normal, normal hpv+, normal hpv-, cin2+ and cin2+) are and respectively. for instance, same cpgs were used to predict cin2+, cin2+ and cancer from the training dataset normal. there is one cpg occurring in all these five cpg lists: cg located in a cpg island 234 bp upstream of the transcription start site of the ntm gene. ntm codes for the protein neurotrimin, which is known to play a role in cell-adhesion. the intersection of the and cpgs is cg cg cg cg cg cg cg and cg which are all hypermethylated in all six datasets. although there is no cpg with significant methylation difference between cases and controls in the three normal data, there are cpgs consistently used for the prediction of test data. the intersection of the and cpgs is cg cg cg cg cg cg cg cg cg cg cg cg cg nearly all are hypermethylated in all six datasets. cpgs occur in at least two of the five cpg lists with of them being located in cpg islands, mostly close to the tss. nearly all are hypermethylated in the analysed six datasets, but two are clearly hypomethylated: cg in all six datasets, cg in five datasets. they correspond to the genes ccl and cltcl respectively. both are often overexpressed in cancer cells. elevated ccl expression plays a role in ovarian carcinoma and induces metastasis of breast cancer. cltcl is overexpressed in cervical and other cancers. two genes correspond to more than two of the cpgs, both are well-known tumour suppressor genes: dcc and gata the gata promoter is hypermethylated in cancer and it is involved in ovarian cancer. interestingly, the two most important human dna regions of a recent dnam cervical pre-cancer classifier, epb41l and dpys, are amongst the ~ regions corresponding to the cpgs. discussion we have developed ms-spca, an advanced version of the classifier spca. in contrast to spca, ms-spca considers several models that perform well in training data cross-validation and selects the final ones for prediction of test data, based on parameters obtained from the test data. we tested different parameters and parameter combinations based on the training data but none was performing as well in selecting the best models as our final criterion eval1-ev1dist. importantly, the values of the parameters eval and ev1dist are related to the prediction performance. for instance, figure  shows that, using cin2+ for training, all corresponding models have relatively poor parameters eval and ev1dist, compared to the cases using datasets normal or cin2+ for training. accordingly, the prediction performance using the cin2+ dataset for training is lower. consideration of > pc might improve the prediction. it seems that parameters such as eval and ev1dist could provide the basis for automatic selection of the most appropriate number of principal components to consider. we also tested a support vector machine for prediction using more than one pc, but without any specific criterion for model selection. the corresponding performance was slightly lower, but a combination of an automatic selection of the number of pcs to consider with advanced learning algorithms such as svm could lead to further improvement. another point for potential future improvement concerns the number of models to consider. here we used the few hundred best models according to training data cross-validation performance. obviously, some diversity of the models is needed such that the final model selection criterion eval1-ev1dist can select the most appropriate ones. considering only the very few in the training data top performing models might suffer from too low model diversity and over-fitting to the training data, considering many models is time consuming and might result in over-fitting to the test data. maybe some optimal diversity can be defined, helping to automatically select the cross-validation performance cut-off and therefore the number of models to consider. we have shown that the model selection of ms-spca works better the more samples the test set contains. in the special case that the test set contains only one sample no test data covariance matrix can be calculated. the corresponding phenotype could be predicted by either a majority vote of all the models and/or by assigning additional samples to the test set and applying the criterion eval1-ev1dist. ms-spca was applied for phenotype prediction from genome-wide dna methylation data. the procedure involves the following steps: 1) splitting of the training data into k-fold training and test sets, 2) calculation of p-values for all cpgs for the three features of a cpg’s methylation: average methylation difference, methylation variation difference and methylation-age-correlation, 3) identification of the best models in training data cross-validation: testing models with different weights and numbers of cpgs in each of the k training datasets 4) predicting the independent test data with the best performing models identified in step, 5) the model selection step of ms-spca: ranking these models according to the criterion eval1-ev1dist and using the cumulative risk scores of the first n best ranking models for final prediction. we have shown that ms-spca performs better than the recent method evora. the first experiments on dna methylation in human cancer showed widespread hypomethylation, but after the discovery of tumour suppressor genes one also observed promoter hypermethylation. meanwhile, of all epigenetic modifications, hypermethylation of promoter regions of tumor suppressor genes has been most extensively studied. we have shown that hypermethylation and hypervariability are important factors for neoplastic transformation, but hypomethylation and hypovariability play a role as well. the 27k cpgs analysed here are biased towards hypermethylated promoter regions. nevertheless, ms-spca performs best if both hyper- and hypomethylated cpgs are considered. it will be interesting to see if hypomethylated cpgs play an even bigger role in more recent larger and less biased dna methylation assays. it has been suggested that hypervariable cpgs are most important for the prediction of early cancer development, although analysis of other cancer data does not always benefit from considering differential variability. this is in agreement with our results. ms-spca in combination with the here presented cpg selection method allows for automatic identification of the most appropriate weighting of the cpg’s methylation features. although hpv infection is considered necessary for cervical cancer development, we have shown that specific dna methylation patterns which are likely contributing to later cancer development exist already before any hpv infection. this is in accordance with previous findings that epigenetic changes may be the earliest initiating factor in a human cancer. on the other hand, it was recently suggested that the earliest changes leading to later transformations might be other epigenetic changes such as chromatin modification rather than dna methylation. if this is true, then the patterns observed in the normal data may be the consequence of other earlier epigenetic changes. however, even then the analysis of dna methylation can be important for early diagnosis of dangerous transformations as it is detectable before standard cytological screening methods can show evidence of transformations. we have presented evidence that dna methylation patterns exist in cytology normal hpv- samples that predispose to neoplastic transformations after hpv infection and predispose to hpv infection itself. it will be interesting to test if other virus infections are also correlated with specific dna methylation patterns. given that ms-spca performs well using data from comparatively few samples and only % of the gpgs in the human genome, it is possible that future dna methylation analysis can provide the accuracy needed for clinical applications.  ms-spca, an advanced version of the classifier spca, is presented. it performs well in predicting phenotypes from genome-wide dna methylation data. ms-spca can be applied to other classification problems. consideration of more principal components, based on the automatic selection of the corresponding most appropriate number, and additional model selection methods might allow further improvement. 
we analysed four independent case–control datasets that correspond to different stages of cervical cancer: cases currently cytologically normal, but will later develop neoplastic transformations, cases showing neoplastic transformations and cases with confirmed cancer. the first dataset was split into several smaller case–control datasets positive or negative). ms-spca applies several models that perform well in the training data to the test data and selects the very best models for final prediction based on parameters of the test data. however, in a recent application to phenotype prediction from dnam data spca was inferior to the specific method evora. we have applied ms-spca for phenotype prediction from genome-wide dnam data. dna methylation has important regulatory roles in many biological processes and diseases. we demonstrate that cytology normal hpv+ and hpv- samples contain dnam patterns which are associated with later neoplastic transformations. we present evidence that dnam patterns exist in cytology normal hpv- samples that predispose to neoplastic transformations after hpv infection and predispose to hpv infection itself. we expect that ms-spca will be useful for analysing recent larger dnam data to predict future neoplastic transformations. it is the only epigenetic mark with a clear mechanism of mitotic inheritance and the only one easily available on a genome scale. cpg hypermethylation of promoter regions is often associated with silencing of tumour suppressor genes and hypomethylation with activation of oncogenes. ms-spca can be applied to many classification problems. supervised principal component analysis is a popular machine learning method. additional improvements could include usage of more than one principal component, with automatic selection of the optimal number of pcs. we present model-selection-spca, an enhanced version of spca. ms-spca performs significantly better than evora.
 dna methylation has important regulatory roles in many biological processes and diseases. it is the only epigenetic mark with a clear mechanism of mitotic inheritance and the only one easily available on a genome scale. aberrant cytosine-phosphate-guanine methylation has been discussed in the context of disease aetiology, especially cancer. cpg hypermethylation of promoter regions is often associated with silencing of tumour suppressor genes and hypomethylation with activation of oncogenes. supervised principal component analysis is a popular machine learning method. however, in a recent application to phenotype prediction from dnam data spca was inferior to the specific method evora.  we present model-selection-spca, an enhanced version of spca. ms-spca applies several models that perform well in the training data to the test data and selects the very best models for final prediction based on parameters of the test data. we have applied ms-spca for phenotype prediction from genome-wide dnam data. cpgs used for prediction are selected based on the quantification of three features of their methylation. we analysed four independent case–control datasets that correspond to different stages of cervical cancer: cases currently cytologically normal, but will later develop neoplastic transformations, cases showing neoplastic transformations and cases with confirmed cancer. the first dataset was split into several smaller case–control datasets positive or negative). we demonstrate that cytology normal hpv+ and hpv- samples contain dnam patterns which are associated with later neoplastic transformations. we present evidence that dnam patterns exist in cytology normal hpv- samples that predispose to neoplastic transformations after hpv infection and predispose to hpv infection itself. ms-spca performs significantly better than evora.  ms-spca can be applied to many classification problems. additional improvements could include usage of more than one principal component, with automatic selection of the optimal number of pcs. we expect that ms-spca will be useful for analysing recent larger dnam data to predict future neoplastic transformations. epigeneticsdna methylationcancerfeature selectionmachine learningclassifier 