• <tr id="yyy80"></tr>
  • <sup id="yyy80"></sup>
  • <tfoot id="yyy80"><noscript id="yyy80"></noscript></tfoot>
  • 99热精品在线国产_美女午夜性视频免费_国产精品国产高清国产av_av欧美777_自拍偷自拍亚洲精品老妇_亚洲熟女精品中文字幕_www日本黄色视频网_国产精品野战在线观看 ?

    Comparison of Cox Model Methods in A Low-dimensional Setting with Few Events

    2016-11-17 08:41:21FranciscoOjedaChristianMuller2DanielaBornigen2DavidAlexandreTregoueArneSchillertMatthiasHeinigTanjaZeller2RenateSchnabel2
    Genomics,Proteomics & Bioinformatics 2016年4期

    Francisco M.Ojeda*,Christian Mu¨ller2,b,Daniela Bo¨rnigen2,c,David-Alexandre Tre′goue¨t,Arne Schillert,Matthias Heinig,Tanja Zeller2,g,Renate B.Schnabel2,h

    1Department of General and Interventional Cardiology,University Heart Center Hamburg-Eppendorf,20246 Hamburg,Germany

    2German Center for Cardiovascular Research(DZHK),Hamburg/Kiel/Luebeck,Germany

    3Sorbonne Universite′s,Universite′Pierre et Marie Curie Paris 06,Institut National pour la Sante′et la Recherche Me′dicale(INSERM),Unite′Mixte de Recherche en Sante′(UMR_S)1166,F(xiàn)-75013 Paris,F(xiàn)rance

    4Institute for Cardiometabolism and Nutrition(ICAN),F(xiàn)-75013 Paris,F(xiàn)rance

    5Institut fu¨r Medizinische Biometrie und Statistik,Universita¨t zu Lu¨beck,Universita¨tsklinikum Schleswig-Holstein,Campus Lu¨beck,23562 Lu¨beck,Germany

    6Institute of Computational Biology,German Research Center for Environmental Health,Helmholtz Zentrum Mu¨nchen,85764 Neuherberg,Germany

    ORIGINAL RESEARCH

    Comparison of Cox Model Methods in A Low-dimensional Setting with Few Events

    Francisco M.Ojeda1,*,a,Christian Mu¨ller1,2,b,Daniela Bo¨rnigen1,2,c,David-Alexandre Tre′goue¨t3,4,d,Arne Schillert5,2,e,Matthias Heinig6,f,Tanja Zeller1,2,g,Renate B.Schnabel1,2,h

    1Department of General and Interventional Cardiology,University Heart Center Hamburg-Eppendorf,20246 Hamburg,Germany

    2German Center for Cardiovascular Research(DZHK),Hamburg/Kiel/Luebeck,Germany

    3Sorbonne Universite′s,Universite′Pierre et Marie Curie Paris 06,Institut National pour la Sante′et la Recherche Me′dicale(INSERM),Unite′Mixte de Recherche en Sante′(UMR_S)1166,F(xiàn)-75013 Paris,F(xiàn)rance

    4Institute for Cardiometabolism and Nutrition(ICAN),F(xiàn)-75013 Paris,F(xiàn)rance

    5Institut fu¨r Medizinische Biometrie und Statistik,Universita¨t zu Lu¨beck,Universita¨tsklinikum Schleswig-Holstein,Campus Lu¨beck,23562 Lu¨beck,Germany

    6Institute of Computational Biology,German Research Center for Environmental Health,Helmholtz Zentrum Mu¨nchen,85764 Neuherberg,Germany

    Received 19 November 2015;revised 1 March 2016;accepted 22 March 2016 Available online 17 May 2016

    Handled by Andreas Keller

    Proportional hazards regression;

    Penalized regression;

    Events per variable;

    Coronary artery disease

    Prognostic models based on survival data frequently make use of the Cox proportional hazards model.Developing reliable Cox models with few events relative to the number of predictors can be challenging,even in low-dimensional datasets,with a much larger number of observations than variables.In such a setting we examined the performance of methods used to estimate a Cox model,including(i)full model using all available predictors and estimated by standard techniques,(ii)backward elimination(BE),(iii)ridge regression,(iv)least absolute shrinkage and selection operator(lasso),and(v)elastic net.Based on a prospective cohort of patients with manifestcoronary artery disease(CAD),we performed a simulation study to compare the predictive accuracy,calibration,and discrimination of these approaches.Candidate predictors for incident cardiovascular events we used included clinical variables,biomarkers,and a selection of genetic variants associated with CAD.The penalized methods,i.e.,ridge,lasso,and elastic net,showed a comparable performance,in terms ofpredictive accuracy,calibration,and discrimination,and outperformed BE and the fullmodel.Excessive shrinkage was observed in some cases for the penalized methods,mostly on the simulation scenarios having the lowest ratio of a number of events to the number of variables.We conclude that in similar settings,these three penalized methods can be used interchangeably.The full model and backward elimination are notrecommended in rare eventscenarios.

    Introduction

    The applications of prognostic models,thatis,models that predict the risk of a future event,include among others[1]:(i)informing individuals about a disease course or the risk of developing a disease,(ii)guiding further treatment decisions,and(iii)selecting patients for therapeutic research.Prognostic models derived using time-to-event(or survival)data often make use of the Cox proportional hazards model.Thernau and Grambsch[2]describe this model as the‘workhorse of regression analysis for censored data”.When the number of events is small relative to the number of variables,the development of a reliable Cox model can be difficult.This can be challenging even in a low-dimensional setting where the number of predictors is much smaller than the number of observations. Existing rules of thumb are based on the number of events per variable(EPV),which is recommended to be between 10 and 20[3,4].When performing variable selection,these EPV rules are applied to the number of candidate variables considered,not just those in the final model[3,4].Penalized regression methods that shrink the regression coefficients towards 0 are an option in a rare event setting,which may effectively increase the EPV[5],thus producing better results.Examples of these methods include ridge regression[6],the least absolute shrinkage and selection operator(lasso)[7],and the elastic net[8],which is a combination of the former two.Backward elimination(BE)is another widely used method[9]that seemingly reduces the number of predictors by applying P values and a significance level α to discard predictors(α=0.05 is often used).

    Our aim in this work was to compare,in a low EPV and low-dimensional setting,the performance of different approaches to computing the Cox proportional hazards model.We consider the following methods:(i)full model,computed using all predictors considered via maximization of the partiallog-likelihood(termed‘full”model),(ii)BE with significance levels α=0.05 and α=0.5(BE 0.05 and BE 0.5),(iii)ridge,(iv)lasso,and(v)elastic net(for simplicity termed‘elastic”thereafter).

    Results

    Simulation results

    Simulations were used to compare different methods based on a prospective cohort study of patients with manifest coronary artery disease(CAD)[10].Two main scenarios were considered:(1)clinical variables relevant to CAD such as age,gender,body mass index(BMI),high density lipoprotein(HDL)over low density lipoprotein(LDL)cholesterol ratio,current smoking,diabetes,and hypertension,as well as blood-based biomarkers such as C-reactive protein(CRP)and creatinine as predictors;and(2)information on 55 genetic variants in addition to the variables used in scenario 1.These variants represented either loci that have been previously shown to be associated,at the genome-wide significance level,with CAD,or recently-identified CAD loci[11].Baseline characteristics are shown in Table S1.There are 1731 participants involved,with a median age of 63 years and 77.6%male.Table S2 provides information of the genetic variants used.The median follow-up was 5.7 years.In each scenario,a Weibull ridge model was fitted in the cohort.Each fitted model was considered the true model and was used to simulate the survival time. Censored Weibull quantile-quantile(Q-Q)plots of the models’exponentiated residuals are shown in Figure S1.Deviations from the Weibull distribution are observed in both scenarios.

    Cox proportional hazards models were calculated on the simulated datasets using the different methods considered(full model,BE,ridge,lasso,and elastic net)for EPV equal to 2.5,5,and 10,respectively.BE 0.05 selected no variable in 64%(scenario 1)and 62%(scenario 2)of the simulations performed with EPV=2.5.For the same EPV,BE 0.5 selected no variable in 18%and 10%of the simulations for scenarios 1 and 2,respectively.This resulted in a model that predicted the same survival probability for all individuals in the dataset(this model is basically a Kaplan-Meier estimator).The same occurred for BE with other EPV values and also for the lasso(32%and 25%)and the elastic net(8%and 2%)with EPV=2.5.The ridge method also produced constant predictions(10%and 4%of the simulations,EPV=2.5)as a consequence of shrinking the coefficients too strongly(in all cases where the elastic net gave constant predicted survival probabilities it was equal to or very close to the ridge model in the sense that elastic net mixing parameter was zero or almost zero).Consequently,the computation of the calibration slope and the concordance becomes impossible.

    The calibration slope could not be calculated either,when a model assigned a predicted survival probability of 1 to at least one individual.This occurred for the full model in 72(EPV=2.5)and 3(EPV=5)simulations in scenario 1,and in 12 simulations in scenario 2(EPV=2.5).BE and the penalized models(ridge,lasso,and elastic net)had 62 and 8 simulations,respectively,that predicted a survival probability of 1(all of them in scenario 1).The root mean square error(RMSE)could be computed in all these cases.However for consistency,the results shown below only reported the RMSE for the simulations where the concordance and calibration slope could be computed.Table 1 gives the number of simulations used to compute RMSE,calibration slope,and concordance on each scenario.

    Table1 Number of simulations used when presenting results for different models out of a maximum of 1000 simulations

    For both scenarios we found a decrease of the RMSE as the EPV increases(Figure 1).The penalized methods(ridge,lasso,and elastic net)have lower RMSE than the full model and the two BE variants considered.BE with a lower significance level(BE 0.05)showed a better RMSE than a higher significance level(BE 0.5)in our simulations.In both scenarios 1(Figure 1A)and 2(Figure 1B),the elastic net had the best RMSE,that is,the RMSE that was closer to zero.

    Looking at the average of the calibration slope across the simulations(Figure 2),the lasso method showed the best performance,being of all the methods the one with an average calibration slope closest to the ideal value of 1.Here,we observed that the average calibration slope for the ridge and the elastic net for scenario 1 and EPV=2.5 was above 10(above 5 for EPV=5,F(xiàn)igure 2A).A similar but less extreme average calibration slope was observed in scenario 2(Figure 2B).These extreme average calibration slopes for the ridge and elastic net were caused by excessive shrinkage of the regression coefficients.The extreme calibration slopes corresponded almost exclusively to models where the elastic net equal led or was comparable to the ridge model.

    Using a trimmed mean,5%on each tail of the distribution,as a robust estimator of the mean,reduced the extreme calibration slopes in scenario 1 and EPV=2.5 from approximately 15 to 9 for the ridge and from 12 to 6 for the elastic net.In scenario 2,the trimmed mean reduced the average calibration slope from approximately 4 to 2.26 for the ridge and from 2.4 to 1.12 for the elastic net(data not shown).Examining the median calibration slope(Figure S2),we observed that the ridge has the best calibration slope in both scenarios with EPV=2.5 and the elastic net with EPV=5.The distribution of the calibration slope across simulations is shown as boxplots in Figures S3(scenario 1)and S4(scenario 2).On the boxplots we see how the interquartile range(IQR)of the calibration slopes becomes narrower with increasing EPV,and that in both scenarios the ridge has the greatest calibration slope IQR for EPV=2.5.For both the ridge and the elastic net,the increase in IQR with the decreasing EPV is proportionally larger on the 75th percentile-median difference,than in the median-25th percentile difference.A particular simulation in scenario 2 with EPV=2.5 that produced extreme calibration slopes was examined.The calibration slopes for this simulation were 22 for the elastic net and 52.5 for the ridge. A scatter plot of the points(log odds)used to compute the calibration slope is shown in Figure S5.Here we observed that the range of the estimated log odds of event is much shorter than that of the true log odds,indicating that too much shrinkage was applied.

    In both scenarios and all EPV values tested,the concordance was higher for the 3 penalized methods considered,except scenario 1 with EPV=2.5,for which BE 0.05 had the highest concordance(Figure 3).In those cases for which the penalized methods showed better discrimination,either lasso or ridge had the highest concordance.

    BE and ridge

    To further explore the methods considered,a hybrid method was considered,where BE was followed by an application of ridge regression,that is,the coefficients of the variables selected by BE were shrunk using ridge.Both BE 0.05 and BE 0.5 were examined.The results showed that RMSE of both BE 0.05 and BE 0.5 was improved by the application of ridge(Figure S6),but it was still higher than that when using ridge,lasso,or elastic net alone.With the application of ridge,both the average and the median calibration slope of BE came closer to the ideal value of 1(Figures S7 and S8),whereas the concordance of BE(Figure S9)improved only slightly.

    Additional simulations

    The three penalized methods considered have a tuning parameter,which gives the amount of shrinkage that is applied to the regression coefficients.The elastic net has an additional tuning parameter which determines how close the elastic net fit is to the lasso or ridge fit.These tuning parameters were selected in our simulations by 10-fold cross-validation.We next explored the sensitivity of the simulation results(RMSE,calibration slope,and concordance)for the penalized methods to the number of folds used in the cross-validation during the selection of tuning parameters.In particular,we wanted to examine whether the extreme calibration slopes observed in some of the simulations were attributed to the method used to select the tuning parameters.To do this,the simulations were repeated using 5-fold cross-validation(instead of 10-fold cross-validation as was done in the analyses shown above).RMSE,calibration slope,and concordance were overall similar to the previous results using 10-fold cross-validation(data not shown),including the distribution of the calibration slopes,in particular,the extreme values observed in some simulations.

    Figure1 Average RMSEs across simulations for both scenarios using different models

    Further additional simulations were run for the penalized methods using the predictor variables to balance the 10-folds used in the cross-validation.The observations were clustered in 10 groups via K-means and then each of the 10-folds used was chosen randomly so that it would contain approximately one tenth of the individuals on each cluster.Here again,the results for the RMSE,calibration slope,and concordance were similar to those for the initial simulations using 10-fold cross-validation,including the extreme values for the calibration slopes observed in some simulations(results not shown).

    Application to clinical data

    The different methods considered,to compute a Cox model,were applied to the clinical data that were used as the basis of our simulations.We used the same scenarios as in the simulations(which are defined in terms ofthe candidate predictors used).The regression coefficients for both scenarios considered are shown in Tables S3 and S4.In scenario 1(EPV=23.2),creatinine was selected by all models performing selection(BE 0.05,BE 0.5,lasso,and elastic net),representing the only predictor selected by BE 0.05.BE 0.5 additionally selected ageand C-reactive protein.The lasso and elastic net selected,on top of these two,LDL/HDL ratio,hypertension,and gender. In scenario 2(EPV=3.3),creatinine was the only predictor selected by BE 0.05,while BE 0.5 selected age additionally. None of the 55 variants considered was selected by these two methods.Lasso and the elastic net selected the same number of variables(24),of which 23 variables were selected by both methods.To quantify the discrimination of the different models we used the C-index[12],which estimates the probability that for a pair of individuals the one with the longest survival has also the longest predicted survival probability.The C-index is an extension of the area under the Receiver Operating Characteristics(ROC)curve(AUC)and has a similar interpretation[13].In scenario 1,the full model had a C-index of 0.599(Table 2).The highest C-index(0.601)was attained using ridge,followed by the elastic net and lasso(0.600).For scenario 2,the highest C-index was attained by the ridge(0.607),followed by the lasso(0.603)and the full model(0.601),while the elastic net had a C-index of 0.600. Both BE regressions considered had C-indices≤0.577.The BE C-indices improved slightly after applying ridge regression.

    Figure2 Average calibration slopes across simulations using different models

    The full model had the calibration slope further away from the ideal value of 1 in both scenarios considered(0.868 and 0.5,respectively).The best calibration slope was achieved in scenario 1 by the lasso(1.012),followed by the combinations of BE 0.05 and BE 0.5 with the ridge(0.974 and 0.960,respectively),the elastic net(1.05),and the ridge method(1.065). The fact that these calibration slopes for the penalized methods were higher than 1 indicates that slightly too much shrinkage was applied by these three methods.In scenario 2,the best calibration slope was produced by the elastic net,followed by the lasso and ridge.Both BE methods had a calibration slopeless than 0.65,indicating overfitting.The BE calibration slope was improved after applying ridge regression.

    Figure3 Average concordance across simulations using different models

    Table2 C-indices and calibration slopes for clinical data example in both scenarios considered using different models

    Discussion

    In this work we aimed to compare methods to compute a proportional hazards model in a rare event low-dimensional setting.Applying simulations based on a dataset of patients with manifest CAD,we compared the full model that used all predictors,BE withα=0.05 orα=0.5,ridge regression,lasso,and elastic net.The penalized methods,i.e.,ridge,lasso,and elastic net,outperformed the full model and BE,Nonetheless,there is no single penalized method that performs best for all metrics and both scenarios considered.BE performance was improved by shrinking the selected variable coefficients with ridge regression;however,this hybrid method was not better than ridge regression,lasso,or elastic net alone.

    Ambler et al.[14]observed that the lasso and the ridge for Cox proportional hazards models have not been compared often in a low-dimensional setting.Porzelius et al.[15]investigated several methods that are usually applied in highdimensional settings and produced sparse model fits,including the lasso and elastic net,in a low-dimensional setting,via simulations.They found the overall performance was similar in terms of sparseness,bias,and prediction performance,and no method outperforms the others in all scenarios considered. Benner et al.[16]found on their simulations that the lasso,ridge,and elastic net had an overall similar performance in low-dimensional settings.Ambler et al.[14],whose approach we follow in this paper,compared the models considered here on two datasets.They also studied the non-negative garrotte and shrank the coefficients of the full model by a single factor(estimated by bootstrap[17]),but they did not examine the elastic net.In their simulations,the ridge method performed better,except that lasso outperformed ridge for the calibration slope.The full model and BE performed the worst on low EPV settings.They recommend the ridge method,except when one is interested in variable selection where lasso would be better. They also observed that in some cases the ridge shrunk the coefficients slightly too much.Lin et al.[18]compared Cox models estimated by maximization of the partial likelihood,F(xiàn)irth’s penalized likelihood[19]and using the Bayesian approaches.They focused on the estimation of the regression coefficients and the coverage of their confidence intervals. They recommend using Firth’s penalized likelihood method when the predictor of interest is categorical and EPV<6. Firth’s method was originally proposed as a solution to the problem of‘monotone likelihood’that may occur in datasets with low EPVs and that causes the standard partial likelihood estimates of the Cox model to break down.

    In our simulations,there was no clear-cut winner,but certainly the penalized methods(ridge,lasso,and elastic net)performed better than the full model and BE.The elastic net showed the best predictive accuracy and all three penalized methods considered had comparable discrimination.In some of our simulations,the penalized methods shrunk the coefficients too much(in some cases extremely setting them to zero,including the ridge),even though the‘‘true”model was being fitted.This behavior was observed both when using 10-fold and 5-fold cross-validation to select the tuning parameters of the penalized approaches and even after attempting to balance the folds based on the predictors.This suggests,as it was also pointed out previously[14],that more work should be done in developing methods to select the tuning parameters of the penalized approaches.Van Houwelingen et al.[20]describe a strategy involving penalized Cox regression,via the ridge,that can be used to obtain survival prognostic models for microarray data.In the first step of this approach,the global test of association[21]is applied and ridge regression is used only if the test is significant. Even though this approach is suggested in a highdimensional setting,applying this global test on a low dimensional setting before applying a penalized approach may help identify situations,where a penalized method may apply excessive shrinkage.

    In our clinical dataset application on the scenario that included clinical variables,biomarkers,and genetic variants,the three penalized methods also had a comparable performance in terms of calibration and discrimination and showed better calibration than the full model and BE,in line with our simulation results.

    Some limitations apply to our study.First,the Cox models received as input all variables used in the true underlying models to simulate the data,that is,there were no noise predictors. This may have given an unfair advantage to ridge regression which does penalization but not variable selection like the lasso or elastic net.Second,all simulations are based on a single clinical cohort,which may be representative of other cohorts,but we cannot compare,the similarity or dissimilarity of the observed simulation results in other datasets.Third,we examined only on the Cox proportional hazards model and did not consider alternative approaches to prognostic models for survival data like full parametric approaches or nonparametric ones(e.g.,survival random forest[22]).Future work will address some of these limitations on other datasets and using non-parametric models.

    Conclusion

    All three methods using penalization,i.e.,ridge,lasso,and elastic net,provided comparable results in the setting considered and may be used interchangeably in a low EPV low-dimensional scenario if the goal is to obtain a reliable prognostic model and variable reduction is not required.If variable selection is desired,then the lasso or the elastic net can be used.Since too much shrinkage may be applied by a penalized method,it is important to inspect the fitted model to look for signs of excessive shrinkage.In a low EPV setting,the use of the full model and BE is discouraged,even when the coefficients of variables selected by BE are shrunk with ridge regression.This study adds new information to the few existing comparisons of penalized methods for Cox proportional hazards regression in low-dimensional datasets with a low EPV.

    Materials and methods

    Data

    Athero Gene[10]is a prospective cohort study of consecutive patients with manifest CAD and at least one stenosis of 30% or more present in a major coronary artery.For the present study we focus on the combined outcome of non-fatalmyocardial infarction and cardiovascular mortality.Time to event information was obtained by regular follow-up questionnaires and telephone interviews,and verified by death certificates and hospital or general practitioner charts.

    Genotyping was performed in individuals of European descent only using the Genome-Wide Human SNP 6.0 Array(Affymetrix,Santa Clara,USA).The Markov chain haplotyping algorithm(MaCH v1.0.18.c)[23]was used to impute untyped markers.The 1000 Genomes Phase I Integrated Release Version 2 served as reference panel for the genotype imputation.For the present study we use 55 genetic variants(51 SNPs and 4 indels).These variants are taken from the CAD genome-wide association meta-analysis performed by the CARDIoGRAMplusC4D Consortium[11].Using an additive genetic model,these variants represent the lead CARDIo-GRAMplusC4D variants on 47(out of 48)loci previously identified at genome-wide significance and 8 novel CAD loci found by this consortium.Out of the 48 loci examined[11],rs6903956 was not nominally significant and is not used in our analyses.All SNPs and indels are used as allele dosages,that is,the expected number of copies of specified allele is used in the analyses.

    After exclusion of missing values,the dataset consists of 1731 individuals,209 incident events and a median follow-up time of 5.7 years(with a maximum of 7.6 years).

    Design of simulations

    We adopted the simulation design used by Ambler and colleagues[14]by considering two main scenarios.For scenario 1,we consider clinical variables(age,gender,BMI,HDL over LDL cholesterol ratio,current smoking,diabetes,and hypertension)and blood-based biomarkers(C-reactive protein and creatinine)as predictors.For scenario 2,we added information on 55 genetic variants to these variables.On each scenario,we fit a Weibull ridge model from which we simulate the survival time using the methods of Bender and colleagues[24].Since the fitted Weibull model is used to simulate the survival time,this model provides the data generating mechanism,and as such it plays the role of the true underlying model.The resulting values of the survival time are then right-censored with help of a uniform random variable U on the interval(0,δ),that is,if the simulated time exceeds U,the(censored)time is set to U.The δs are chosen to achieve an EPV of 2.5,5,or 10(lower δ values produce a higher percentage of censored time and therefore fewer observed events).We generate 1000 simulated datasets. For each scenario and EPV,and on each one of them we fit a standard Cox model via partial likelihood,two BE models,with α=0.05 and α=0.5,a lasso model,a ridge model and elastic net model.

    Penalized models

    The Cox proportional hazards model assumes the hazard as follows,

    where(x1,x2,...,xp)is a vector of p predictor variables(e.g.,age,gender,and BMI)andβ1,β2,...,βpare the corresponding regression coefficients,which are the weights given to each variable by the model.These coefficients are obtained by maximizing the partiallog-likelihood function l(β),where β=(β1,β2,...,βp).

    For fixed non-negativeλ,maximization of the penalized partial log-likelihood function,

    produces the regression coefficients of the elastic net.The parameter λ controls the amount of shrinkage applied to the coefficients,higher values of lambda corresponding to lower coefficients.The parameter α is the elastic net mixing parameter and changes between 0 and 1[25,26].The lasso and ridge regression coefficients are obtained by setting α to 1 and 0 in Eq.(2),respectively,and maximizing the resulting expression.

    Selection of tuning parameters for penalized models

    For the lasso and the ridge,10-fold cross validation is used and the parameter that maximizes the cross-validated partial log likelihood[27]is used as the corresponding penalization parameter.For the elastic net,we consider a course grid from 0 to 1 in steps of length 0.05 for the mixing parameter α.As for the lasso and ridge,the cross-validated partial likelihood is maximized.

    Additional analyses were performed selecting the tuning parameters using(1)5-fold cross validation and(2)10-fold cross-validation.The folds for the latter were obtained as follows.The observations were clustered in 10 groups using the predictors and K-means[28].Then each fold was chosen randomly so that it would contain approximately one tenth of the individuals on each cluster.

    Comparison of methods

    The use of a Weibull model to generate the data allows us to compare the‘true”survival probabilities Si(t)of the i th individualat time t,to the survival probabilities^Si(t)estimated by the different models we considered.To compare survival probabilities,we used the same metrics as described previously[14]. RMSE for predictive accuracy is calculated as follows.

    For calibration,the calibration slopeα1is used,which is the slope of the model obtained by fitting a simple linear regression to y=logand x=log.Ideally α1should be 1(over fitting occurs if α1<1 and under fitting occurs if α1>1). For discrimination the concordance,the proportion of pairs of patients where individuals with the higher predicted event probability also have the higher‘true”event probabilities is used.It has a similar interpretation as the C-index and is related to Kendall’s rank correlation τ[29]according to the formula τ=2(concordance-0.5).For the RMSE and calibration slope the predicted survival probabilities are computed at time points 0.08,0.17,and 0.25 years,respectively,for scenario 1 and of 1,2.5,and 5 years,respectively,for scenario 2.The concordance is computed for only one time point,since its value does not depend on the particular time point used to compute the predicted survival probabilities.

    Analysis of the clinical dataset

    The methods considered were applied to the Athero Gene dataset[10].As measures of performance,we computed the C-index Cτ[12]and the calibration slope.For the computation of the C-index,the first five years of the follow-up were used. Since estimating the performance of a model on the same dataset the model was developed may produce over-optimistic performance estimates,both the C-index and calibration slope were corrected for over-optimism with help of the 0.632 bootstrap estimator[30].1000 bootstrap replications were used in the correction.

    Software

    Allanalyses were performed with R Version 3.2.1.The glmnet package[25,26]was used to fit the penalized Cox regressions(lasso,ridge,and elastic net).BE was performed with the package rms[4].The survival package[2]was used to fit the standard Cox model.The survC1 package was used to compute Cτ.

    Authors’contributions

    FMO performed the simulations and data analyses.RBS provided the clinical perspective and information on the Athero Gene study.TZ performed genotyping and provided genetic information.CM and DB provided code and support for the data analyses.AS performed genotype calling and provided statistical advice.DAT performed genotype imputation.MH provided statistical advice.FMO drafted the manuscript.All authors critically revised and approved the final manuscript.

    Competing interests

    The authors have declared no competing interests.

    Acknowledgments

    This work was performed in the context of the‘symAtrial”Junior Research Alliance funded by the German Ministry of Research and Education(BMBF 01ZX1408A)e:Med-Systems Medicine program.The Athero Gene study was supported by a grant of the‘Stiftung Rheinland-Pfalz fu¨r Innovation”,Ministry for Science and Education(AZ 15202-386261/545),Mainz,and European Union Seventh Framework Programme(FP7/2007-2013)under grant agreement No.HEALTH-F2-2011-278913(BiomarCaRE).RBS is funded by Deutsche Forschungsgemeinschaft(German Research Foundation)Emmy Noether Program SCHN 1149/3-1.This project has received funding from the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation programme(Grant No.648131).

    Supplementary material

    Supplementary material associated with this article can be found,in the online version,at http://dx.doi.org/10.1016/j. gpb.2016.03.006.

    [1]Moons K,Royston P,Vergouwe Y,Grobbee D,Altman D. Prognosis and prognostic research:what,why,and how?BMJ 2009;338:b375.

    [2]Therneau TM,Grambsch PM.Modeling survival data:extending the Cox model.New York:Springer Science&Business Media;2000.

    [3]Peduzzi P,Concato J,F(xiàn)einstein AR,Holford TR.Importance of events per independent variable in proportional hazards regression analysis II.Accuracy and precision of regression estimates.J Clin Epidemiol 1995;48:1503-10.

    [4]Harrell FE.Regression modeling strategies:with applications to linear models,logistic and ordinal regression,and survival analysis.New York:Springer Science&Business Media;2015.

    [5]Tibshirani R,Taylor J.Degrees of freedom in lasso problems. Ann Stat 2012;40:1198-232.

    [6]Verweij PJM,van Houwelingen HC.Penalized likelihood in Cox regression.Stat Med 1994;13:2427-36.

    [7]Tibshirani R.The lasso method for variable selection in the Cox model.Stat Med 1997;16:385-95.

    [8]Zou H,Hastie T.Regularization and variable selection via the elastic net.J R Stat Soc Ser B 2005;67:301-20.

    [9]Steyerberg E.Clinical prediction models:a practical approach to development,validation,and updating.New York:Springer Science&Business Media;2009.

    [10]Schnabel RB,Schulz A,Messow CM,Lubos E,Wild PS,Zeller T,et al.Multiple marker approach to risk stratification in patients with stable coronary artery disease.Eur Heart J 2010;31:3024-31.

    [11]CARDIoGRAMplusC4D Consortium.A comprehensive 1000 genomes-based genome-wide association meta-analysis of coronary artery disease.Nat Genet 2015;47:1121-30.

    [12]Uno H,Cai T,Pencina MJ,D’Agostino RB,Wei LJ.On the C-statistics for evaluating overall adequacy of risk prediction procedures with censored survival data.Stat Med 2011;30:1105-17.

    [13]Pencina M,D’Agostino R.Overall C as a measure of discrimination in survival analysis:model specific population value and confidence interval estimation.Stat Med 2004;23:2109-23.

    [14]Ambler G,Seaman S,Omar RZ.An evaluation of penalised survival methods for developing prognostic models with rare events.Stat Med 2012;31:1150-61.

    [15]Porzelius C,Schumacher M,Binder H.Sparse regression techniques in low-dimensional survival data settings.Stat Comput 2009;20:151-63.

    [16]Benner A,Zucknick M,Hielscher T,Ittrich C,Mansmann U. High-dimensional Cox models:the choice of penalty as part of the model building process.Biom J 2010;52:50-69.

    [17]Steyerberg E,Eijkemans M,Habbema J.Application of shrinkage techniques in logistic regression analysis:a case study.Stat Neerl 2001;55:76-88.

    [18]Lin IF,Chang WP,Liao Y-N.Shrinkage methods enhanced the accuracy of parameter estimation using Cox models with small number of events.J Clin Epidemiol 2013;66:743-51.

    [19]Heinze G,Schemper M.A solution to the problem of monotone likelihood in Cox regression.Biometrics 2001:114-9.

    [20]Van Houwelingen HC,Bruinsma T,Hart AAM,Van’t Veer LJ,Wessels LFA.Cross-validated Cox regression on microarray gene expression data.Stat Med 2006;25:3201-16.

    [21]Goeman JJ,Van De Geer SA,De Kort F,Van Houwelingen HC. A global test for groups of genes:testing association with a clinical outcome.Bioinformatics 2004;20:93-9.

    [22]Ishwaran H,Kogalur UB,Blackstone EH,Lauer MS.Random survival forests.Ann Appl Stat 2008:841-60.

    [23]Li Y,Willer CJ,Ding J,Scheet P,Abecasis GR.MaCH:using sequence and genotype data to estimate haplotypes and unobserved genotypes.Genet Epidemiol 2010;34:816-34.

    [24]Bender R,Augustin T,Blettner M.Generating survival times to simulate Cox proportional hazards models.Stat Med 2005;24:1713-23.

    [25]Friedman J,Hastie T,Tibshirani R.Regularization paths for generalized linear models via coordinate descent.J Stat Software 2010;33:1.

    [26]Simon N,F(xiàn)riedman J,Hastie T,Tibshirani R.Regularization paths for Cox’s proportional hazards model via coordinate descent.J Stat Software 2011;39:1-13.

    [27]Verweij PJM,Van Houwelingen HC.Cross-validation in survival analysis.Stat Med 1993;12:2305-14.

    [28]Hartigan JA,Wong MA.Algorithm AS 136:a k-means clustering algorithm.J R Stat Soc Ser C 1979;28:100-8.

    [29]Kendall MG.A new measure of rank correlation.Biometrika 1938;30:81-93.

    [30]Efron B.Estimating the error rate of a prediction rule:improvement on cross-validation.J Am Stat Assoc 1983;78:316-31.

    *Corresponding author.

    E-mail:f.ojeda-echevarria@uke.de(Ojeda FM).

    aORCID:0000-0003-4037-144X.

    bORCID:0000-0002-9449-6865.

    cORCID:0000-0002-7370-2033.

    dORCID:0000-0001-9084-7800.

    eORCID:0000-0002-8170-6632.

    fORCID:0000-0002-5612-1720.

    gORCID:0000-0003-3379-2641.

    hORCID:0000-0001-7170-9509.

    Peer review under responsibility of Beijing Institute of Genomics,Chinese Academy of Sciences and Genetics Society of China.

    http://dx.doi.org/10.1016/j.gpb.2016.03.006

    1672-0229?2016 The Authors.Production and hosting by Elsevier B.V.on behalf of Beijing Institute of Genomics,Chinese Academy of Sciences and Genetics Society of China.

    This is an open access article under the CC BY license(http://creativecommons.org/licenses/by/4.0/).

    亚洲美女视频黄频| 国产亚洲精品久久久com| 成人国产一区最新在线观看| 又黄又粗又硬又大视频| 久久久久久久久中文| 夜夜躁狠狠躁天天躁| 免费看日本二区| 1024手机看黄色片| 国产精品 国内视频| 一个人观看的视频www高清免费观看| 最近视频中文字幕2019在线8| 国产一区二区激情短视频| 亚洲18禁久久av| 国产精品一及| 高清日韩中文字幕在线| 丰满的人妻完整版| 久久久成人免费电影| 久久精品国产亚洲av香蕉五月| 中文字幕人成人乱码亚洲影| 亚洲国产精品999在线| 精品一区二区三区人妻视频| 亚洲中文字幕日韩| 全区人妻精品视频| 又紧又爽又黄一区二区| 又紧又爽又黄一区二区| 欧美区成人在线视频| 欧美最新免费一区二区三区 | 亚洲美女视频黄频| 精品国产三级普通话版| av欧美777| 久久亚洲精品不卡| www.色视频.com| 亚洲自拍偷在线| 久久人人精品亚洲av| 亚洲精品一区av在线观看| 日本五十路高清| 午夜免费成人在线视频| 国产三级中文精品| 日韩精品青青久久久久久| 国产爱豆传媒在线观看| 日韩免费av在线播放| 91字幕亚洲| 在线天堂最新版资源| 九九在线视频观看精品| 日本黄色视频三级网站网址| 久久精品国产综合久久久| 一区二区三区国产精品乱码| 亚洲av中文字字幕乱码综合| 一区二区三区国产精品乱码| 久久精品国产综合久久久| 好看av亚洲va欧美ⅴa在| 欧美日本视频| 日日夜夜操网爽| 国产av麻豆久久久久久久| 一区二区三区国产精品乱码| 在线观看舔阴道视频| 一本综合久久免费| 又黄又粗又硬又大视频| 成人国产综合亚洲| 老熟妇乱子伦视频在线观看| 成人高潮视频无遮挡免费网站| 亚洲色图av天堂| 看免费av毛片| 精品午夜福利视频在线观看一区| 亚洲第一欧美日韩一区二区三区| 午夜福利成人在线免费观看| 欧美日韩亚洲国产一区二区在线观看| 午夜福利成人在线免费观看| 99久久成人亚洲精品观看| 亚洲一区高清亚洲精品| 少妇的丰满在线观看| 在线看三级毛片| 99久久综合精品五月天人人| 欧美中文综合在线视频| 精品人妻一区二区三区麻豆 | 两个人视频免费观看高清| 亚洲国产精品成人综合色| 色精品久久人妻99蜜桃| 日本一二三区视频观看| 亚洲精品久久国产高清桃花| 亚洲最大成人手机在线| 在线观看日韩欧美| 欧美色欧美亚洲另类二区| 久久草成人影院| 黄色丝袜av网址大全| 中文在线观看免费www的网站| 中文字幕人妻熟人妻熟丝袜美 | 精品一区二区三区视频在线观看免费| www日本在线高清视频| 婷婷精品国产亚洲av| 夜夜看夜夜爽夜夜摸| 日韩欧美 国产精品| 神马国产精品三级电影在线观看| 国产男靠女视频免费网站| 成人三级黄色视频| 久久亚洲精品不卡| 亚洲18禁久久av| 欧美性猛交黑人性爽| 91在线精品国自产拍蜜月 | 日韩高清综合在线| 欧美日韩福利视频一区二区| 免费观看的影片在线观看| 好男人在线观看高清免费视频| 精品欧美国产一区二区三| 无人区码免费观看不卡| 国产成人欧美在线观看| 蜜桃久久精品国产亚洲av| 精品午夜福利视频在线观看一区| 精品人妻一区二区三区麻豆 | 高清毛片免费观看视频网站| 久久久久久久精品吃奶| www.www免费av| 一级作爱视频免费观看| xxxwww97欧美| 99热这里只有精品一区| 观看免费一级毛片| 18+在线观看网站| 亚洲最大成人中文| 精品国产亚洲在线| 全区人妻精品视频| 亚洲精品一区av在线观看| 国产精品久久久人人做人人爽| 五月玫瑰六月丁香| 嫩草影院精品99| 国产精品久久久久久人妻精品电影| 欧美成人一区二区免费高清观看| 精品欧美国产一区二区三| 桃色一区二区三区在线观看| 内地一区二区视频在线| 脱女人内裤的视频| 熟女电影av网| av欧美777| 亚洲欧美一区二区三区黑人| 热99re8久久精品国产| 真实男女啪啪啪动态图| 两性午夜刺激爽爽歪歪视频在线观看| 好男人电影高清在线观看| 亚洲国产欧洲综合997久久,| 中国美女看黄片| 亚洲久久久久久中文字幕| 无限看片的www在线观看| 好男人电影高清在线观看| 免费高清视频大片| 日本免费a在线| 超碰av人人做人人爽久久 | aaaaa片日本免费| 成人亚洲精品av一区二区| 真实男女啪啪啪动态图| 韩国av一区二区三区四区| 激情在线观看视频在线高清| 国产高清视频在线播放一区| 欧美av亚洲av综合av国产av| 午夜免费观看网址| 色综合站精品国产| 亚洲av熟女| 1024手机看黄色片| 免费看日本二区| 高潮久久久久久久久久久不卡| 男女那种视频在线观看| 国产熟女xx| 又黄又爽又免费观看的视频| 精品一区二区三区人妻视频| 精华霜和精华液先用哪个| 久久久久久久午夜电影| 国产精品久久久人人做人人爽| 欧美日韩中文字幕国产精品一区二区三区| 国产一区二区激情短视频| 久久6这里有精品| 亚洲欧美日韩高清专用| 免费看日本二区| 99精品在免费线老司机午夜| 看黄色毛片网站| www日本在线高清视频| 成年女人看的毛片在线观看| 男女午夜视频在线观看| 亚洲av美国av| 噜噜噜噜噜久久久久久91| 免费搜索国产男女视频| 在线观看免费午夜福利视频| 成熟少妇高潮喷水视频| 人妻丰满熟妇av一区二区三区| 亚洲va日本ⅴa欧美va伊人久久| 日韩中文字幕欧美一区二区| 欧美日韩黄片免| 亚洲国产精品999在线| 国产成年人精品一区二区| 国产国拍精品亚洲av在线观看 | tocl精华| 亚洲一区高清亚洲精品| 淫妇啪啪啪对白视频| 一个人看视频在线观看www免费 | 欧美性猛交╳xxx乱大交人| 亚洲黑人精品在线| 51国产日韩欧美| 亚洲国产精品久久男人天堂| 好看av亚洲va欧美ⅴa在| 在线观看免费视频日本深夜| 欧美又色又爽又黄视频| 久久精品国产清高在天天线| 久久久精品欧美日韩精品| 亚洲aⅴ乱码一区二区在线播放| а√天堂www在线а√下载| 亚洲最大成人手机在线| 老司机午夜福利在线观看视频| 九色国产91popny在线| 在线播放无遮挡| 在线观看免费视频日本深夜| 午夜免费成人在线视频| 亚洲18禁久久av| 一个人观看的视频www高清免费观看| 18禁裸乳无遮挡免费网站照片| 三级毛片av免费| 欧美国产日韩亚洲一区| 国产熟女xx| 成人av一区二区三区在线看| av欧美777| 黄色女人牲交| 制服丝袜大香蕉在线| 久久久色成人| svipshipincom国产片| 精品久久久久久久久久免费视频| 国产精品99久久久久久久久| 精品一区二区三区视频在线观看免费| 久久久久亚洲av毛片大全| 一进一出好大好爽视频| 观看美女的网站| 在线观看日韩欧美| 中文在线观看免费www的网站| 韩国av一区二区三区四区| 麻豆久久精品国产亚洲av| 最新中文字幕久久久久| 国产一区二区在线av高清观看| 99国产精品一区二区蜜桃av| 97超级碰碰碰精品色视频在线观看| 免费人成在线观看视频色| 国产探花极品一区二区| 久久久久久九九精品二区国产| 国产伦精品一区二区三区视频9 | 精品免费久久久久久久清纯| 久久久国产成人免费| 国产精品一区二区免费欧美| 欧美日韩瑟瑟在线播放| 免费在线观看影片大全网站| 国产不卡一卡二| 久久久精品欧美日韩精品| 麻豆国产av国片精品| 亚洲国产精品久久男人天堂| av专区在线播放| 亚洲成人免费电影在线观看| 欧美在线黄色| 国产精品爽爽va在线观看网站| 美女cb高潮喷水在线观看| 18禁黄网站禁片午夜丰满| 真实男女啪啪啪动态图| 看片在线看免费视频| 婷婷精品国产亚洲av| 亚洲自拍偷在线| 久久久久久久精品吃奶| 欧美黄色淫秽网站| 色综合婷婷激情| 国产99白浆流出| 亚洲片人在线观看| 狠狠狠狠99中文字幕| aaaaa片日本免费| 国产在线精品亚洲第一网站| 欧美精品啪啪一区二区三区| 亚洲精品在线观看二区| 国产成人福利小说| 男人的好看免费观看在线视频| 精品久久久久久成人av| 国产伦在线观看视频一区| 男人舔奶头视频| 国产av不卡久久| 一本久久中文字幕| 熟女少妇亚洲综合色aaa.| 国产成+人综合+亚洲专区| 91字幕亚洲| 变态另类丝袜制服| 99热精品在线国产| 欧美不卡视频在线免费观看| 国产午夜精品久久久久久一区二区三区 | 国产高清有码在线观看视频| 美女 人体艺术 gogo| 精品国内亚洲2022精品成人| av天堂在线播放| 深爱激情五月婷婷| 国产精品久久电影中文字幕| 夜夜看夜夜爽夜夜摸| 亚洲无线在线观看| 美女高潮的动态| 又黄又爽又免费观看的视频| 精品乱码久久久久久99久播| 美女 人体艺术 gogo| 色老头精品视频在线观看| 丰满人妻一区二区三区视频av | 麻豆一二三区av精品| 一级a爱片免费观看的视频| 国产成人影院久久av| 美女被艹到高潮喷水动态| 亚洲精品日韩av片在线观看 | 国产精品野战在线观看| 欧美av亚洲av综合av国产av| 十八禁人妻一区二区| 中文字幕av在线有码专区| 在线观看一区二区三区| 真人一进一出gif抽搐免费| 在线播放无遮挡| 黄色女人牲交| 精品一区二区三区视频在线 | а√天堂www在线а√下载| 国产aⅴ精品一区二区三区波| 国产乱人视频| 欧美激情在线99| 怎么达到女性高潮| 无遮挡黄片免费观看| 十八禁人妻一区二区| 在线国产一区二区在线| 草草在线视频免费看| 可以在线观看的亚洲视频| 99久久久亚洲精品蜜臀av| 欧美一区二区亚洲| www.熟女人妻精品国产| 日韩免费av在线播放| 丝袜美腿在线中文| 国内精品久久久久精免费| 国产真实伦视频高清在线观看 | 日韩欧美一区二区三区在线观看| 亚洲成人久久爱视频| 少妇高潮的动态图| 中文字幕人妻丝袜一区二区| 久久久久性生活片| 99视频精品全部免费 在线| 九九热线精品视视频播放| 亚洲不卡免费看| ponron亚洲| 99久久无色码亚洲精品果冻| 免费一级毛片在线播放高清视频| 91av网一区二区| 天天躁日日操中文字幕| 国产av麻豆久久久久久久| 男人舔女人下体高潮全视频| 精品熟女少妇八av免费久了| 成年版毛片免费区| 久久精品综合一区二区三区| 日韩欧美在线二视频| 成人国产一区最新在线观看| 亚洲五月天丁香| 欧美高清成人免费视频www| 国产精品久久久久久精品电影| 国内精品久久久久久久电影| 波野结衣二区三区在线 | 婷婷丁香在线五月| 日韩欧美 国产精品| 啪啪无遮挡十八禁网站| 少妇的逼水好多| 香蕉av资源在线| 99久久精品国产亚洲精品| 女同久久另类99精品国产91| 国产精品女同一区二区软件 | 男人的好看免费观看在线视频| 一本综合久久免费| 国产成年人精品一区二区| 国产69精品久久久久777片| 欧美区成人在线视频| 国产精品女同一区二区软件 | 桃红色精品国产亚洲av| 熟妇人妻久久中文字幕3abv| 天堂动漫精品| 亚洲avbb在线观看| 欧美又色又爽又黄视频| 国产亚洲精品久久久com| 国产精品乱码一区二三区的特点| 国产国拍精品亚洲av在线观看 | 日本黄大片高清| 欧美在线一区亚洲| 亚洲国产欧美网| 亚洲av美国av| 欧美日韩亚洲国产一区二区在线观看| 久久精品人妻少妇| 久久久久九九精品影院| 亚洲va日本ⅴa欧美va伊人久久| 99在线人妻在线中文字幕| 中出人妻视频一区二区| 国产高清视频在线播放一区| 亚洲五月天丁香| 成人永久免费在线观看视频| 国产高清视频在线观看网站| 亚洲av电影不卡..在线观看| 99国产极品粉嫩在线观看| 毛片女人毛片| 国语自产精品视频在线第100页| 乱人视频在线观看| 国产成人a区在线观看| 五月伊人婷婷丁香| 精品无人区乱码1区二区| 成年女人看的毛片在线观看| 欧美在线一区亚洲| 国产午夜精品论理片| 19禁男女啪啪无遮挡网站| 日韩欧美国产在线观看| av国产免费在线观看| 一级黄片播放器| 不卡一级毛片| 欧美成人一区二区免费高清观看| 欧美绝顶高潮抽搐喷水| 久久久国产精品麻豆| 国产成人啪精品午夜网站| 人人妻人人澡欧美一区二区| 亚洲欧美日韩高清专用| 精品不卡国产一区二区三区| 最近最新中文字幕大全免费视频| 亚洲av中文字字幕乱码综合| 亚洲精品色激情综合| 狂野欧美激情性xxxx| 日韩免费av在线播放| 国产亚洲精品久久久com| 婷婷精品国产亚洲av| 男女之事视频高清在线观看| 日本五十路高清| 亚洲av熟女| 国产精品亚洲美女久久久| 国产一区二区激情短视频| 国产高清三级在线| 国产精品av视频在线免费观看| 国产中年淑女户外野战色| 国产一区二区三区视频了| 18美女黄网站色大片免费观看| 无限看片的www在线观看| 成人特级av手机在线观看| 亚洲在线观看片| 午夜免费观看网址| 国产成人啪精品午夜网站| 丁香欧美五月| 中文字幕精品亚洲无线码一区| 动漫黄色视频在线观看| 久久精品91无色码中文字幕| 日韩国内少妇激情av| 亚洲精品国产精品久久久不卡| 亚洲人成网站高清观看| 日韩欧美一区二区三区在线观看| 亚洲国产精品成人综合色| 看黄色毛片网站| 床上黄色一级片| 精品一区二区三区av网在线观看| 国产不卡一卡二| 精品电影一区二区在线| 国产精品嫩草影院av在线观看 | 黄片大片在线免费观看| 国产乱人伦免费视频| 欧美成人性av电影在线观看| 精品久久久久久久人妻蜜臀av| 国产欧美日韩精品亚洲av| 男女那种视频在线观看| 婷婷六月久久综合丁香| 亚洲成a人片在线一区二区| 嫩草影视91久久| 久99久视频精品免费| 我的老师免费观看完整版| 午夜免费激情av| 在线观看66精品国产| 亚洲国产精品成人综合色| 国产成+人综合+亚洲专区| 欧美性猛交黑人性爽| 亚洲avbb在线观看| 美女免费视频网站| 一级黄片播放器| 日韩精品青青久久久久久| 国产成人aa在线观看| 国内精品美女久久久久久| 亚洲最大成人手机在线| 亚洲电影在线观看av| 黄片大片在线免费观看| 国产亚洲精品久久久久久毛片| 在线观看午夜福利视频| 又紧又爽又黄一区二区| 午夜福利在线观看吧| 欧美最新免费一区二区三区 | 最近视频中文字幕2019在线8| 看黄色毛片网站| 淫秽高清视频在线观看| 国产欧美日韩精品一区二区| 亚洲内射少妇av| 中文字幕久久专区| 波多野结衣高清作品| 高潮久久久久久久久久久不卡| 国产高清视频在线观看网站| 淫妇啪啪啪对白视频| 99精品欧美一区二区三区四区| 久久人妻av系列| 国产私拍福利视频在线观看| www.熟女人妻精品国产| 99久久精品热视频| 精品久久久久久久久久久久久| 国产免费av片在线观看野外av| 国产成人啪精品午夜网站| 久久这里只有精品中国| 国产精品永久免费网站| 他把我摸到了高潮在线观看| 久久伊人香网站| 午夜免费观看网址| 九色国产91popny在线| 男女床上黄色一级片免费看| 亚洲在线观看片| 哪里可以看免费的av片| 可以在线观看毛片的网站| 国产一区二区亚洲精品在线观看| 精品国内亚洲2022精品成人| 亚洲精品国产精品久久久不卡| 天堂av国产一区二区熟女人妻| 国产精品日韩av在线免费观看| 国产探花在线观看一区二区| 波多野结衣高清作品| 啦啦啦观看免费观看视频高清| 变态另类丝袜制服| 成人精品一区二区免费| 丰满乱子伦码专区| 在线观看舔阴道视频| 欧美日韩乱码在线| 亚洲国产精品合色在线| 一个人观看的视频www高清免费观看| 免费av不卡在线播放| 亚洲精品久久国产高清桃花| 成人特级黄色片久久久久久久| 亚洲av免费高清在线观看| 亚洲中文字幕一区二区三区有码在线看| 一本一本综合久久| 国内少妇人妻偷人精品xxx网站| 非洲黑人性xxxx精品又粗又长| 人人妻,人人澡人人爽秒播| 国产精品亚洲av一区麻豆| 美女免费视频网站| 法律面前人人平等表现在哪些方面| 日韩欧美一区二区三区在线观看| 观看免费一级毛片| 久久精品影院6| 在线国产一区二区在线| 国产精品女同一区二区软件 | 成人性生交大片免费视频hd| 国产乱人视频| bbb黄色大片| 村上凉子中文字幕在线| 婷婷丁香在线五月| 黄色女人牲交| 亚洲在线观看片| 亚洲av日韩精品久久久久久密| 香蕉久久夜色| 亚洲aⅴ乱码一区二区在线播放| 麻豆成人av在线观看| 久久午夜亚洲精品久久| 91字幕亚洲| 首页视频小说图片口味搜索| avwww免费| 尤物成人国产欧美一区二区三区| 亚洲18禁久久av| 久久久久久久久中文| 一个人免费在线观看电影| 白带黄色成豆腐渣| 亚洲五月婷婷丁香| 午夜福利高清视频| 两人在一起打扑克的视频| 中文字幕人成人乱码亚洲影| 高清在线国产一区| 国产欧美日韩精品亚洲av| 久久久久久久久中文| 一个人免费在线观看电影| 黄色日韩在线| 久久久久九九精品影院| 亚洲成人久久性| 国产麻豆成人av免费视频| 人人妻人人澡欧美一区二区| 欧美极品一区二区三区四区| 宅男免费午夜| 免费一级毛片在线播放高清视频| 国产精品女同一区二区软件 | 人妻久久中文字幕网| 高清日韩中文字幕在线| 成人一区二区视频在线观看| av在线天堂中文字幕| 网址你懂的国产日韩在线| 嫁个100分男人电影在线观看| 国内少妇人妻偷人精品xxx网站| 亚洲一区高清亚洲精品| 男女做爰动态图高潮gif福利片| 精品一区二区三区av网在线观看| 国产一区二区在线av高清观看| 欧美+日韩+精品| 成人无遮挡网站| 日韩免费av在线播放| 亚洲精品456在线播放app | 久久精品亚洲精品国产色婷小说| 免费搜索国产男女视频| 999久久久精品免费观看国产| 美女 人体艺术 gogo| 国产一区在线观看成人免费| 99热这里只有精品一区| 美女高潮喷水抽搐中文字幕| 色综合婷婷激情| 日韩av在线大香蕉| 日韩中文字幕欧美一区二区| 午夜激情福利司机影院| 国产精品香港三级国产av潘金莲| 国产aⅴ精品一区二区三区波| 国产亚洲欧美在线一区二区| 亚洲无线观看免费| 久久精品91无色码中文字幕| 午夜福利高清视频| 精品日产1卡2卡| 久久中文看片网| 99久久99久久久精品蜜桃| 欧美激情在线99| 我的老师免费观看完整版| 日本撒尿小便嘘嘘汇集6| 精华霜和精华液先用哪个| 国产高清三级在线| 欧美性猛交╳xxx乱大交人|