| Title: | A package for survival time prediction based on a piecewise baseline hazard Cox regression model. |
|---|---|
| Description: | The package is the R-version of the C-based software \bold{CASPAR} (Kaderali,2006: \url{http://bioinformatics.oxfordjournals.org/content/22/12/1495}). It is meant to help predict survival times in the presence of high-dimensional explanatory covariates. The model is a piecewise baseline hazard Cox regression model with an Lq-norm based prior that selects for the most important regression coefficients, and in turn the most relevant covariates for survival analysis. It was primarily tried on gene expression and aCGH data, but can be used on any other type of high-dimensional data and in disciplines other than biology and medicine. |
| Authors: | Douaa Mugahid, Lars Kaderali |
| Maintainer: | Douaa Mugahid <[email protected]>, Lars Kaderali <[email protected]> |
| License: | GPL (>=3) |
| Version: | 1.51.0 |
| Built: | 2024-07-03 05:47:03 UTC |
| Source: | https://github.com/bioc/RCASPAR |
This function plots the survival curve for the provided data set as a Kaplan Meier plot. It can only be used for visualization and returns no numeric values.
kmplt(data, title)kmplt(data, title)
data |
A data frame containing at least the two columns “censored” and “True_STs”. Where “censored” contains the censorship status of the subject as either “0/F” for ‘uncensored subjects’ or “$1$/T” for ‘censored subjects’. This information is essential to be able to plot the KM curve. |
title |
A string of characters denoting the title of the plot produced. |
Note that this function was intended only for visualization and does not return any numerical values as such.
A plot of the survival function “S(t)” against the survival times (unit-less) as calculated for the provided data set.
Douaa Mugahid
Bland JM, Altman DG. Survival probabilities (the Kaplan-Meier method). BMJ 1998;317;1572\ http://www.bmj.com/statsbk/12.dtl
censored <- c(1, 0, 1, 1, 1, 0, 1, 0, 0, 0) True_STs <- c(1, 4, 5, 4, 6, 3, 2, 1, 3, 4) dat <- as.data.frame(cbind(True_STs, censored)) kmplt(dat, "test")censored <- c(1, 0, 1, 1, 1, 0, 1, 0, 0, 0) True_STs <- c(1, 4, 5, 4, 6, 3, 2, 1, 3, 4) dat <- as.data.frame(cbind(True_STs, censored)) kmplt(dat, "test")
The package is the R-version of the C-based software CASPAR (Kaderali,2006). It is meant to help predict survival times in the presence of high-dimensional explanatory co-variates. The model is a piecewise baseline hazard Cox regression model with an Lq-norm based prior that selects for the most important regression coefficients, and in turn the most relevant co-variates for survival analysis. It was primarily tried on gene expression and aCGH data, but can be used on any other type of high-dimensional data and in disciplines other than biology and medicine.
| Package: | RCASPAR |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2010-08-23 |
| License: GPL(>=3) LazyLoad: | yes |
Douaa Mugahid
Maintainer: Douaa Mugahid <[email protected]>, Lars Kaderali <[email protected]>
The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer. as well as Kaderali, Lars.(2006) A Heirarchial Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker The prior on the regression coefficients was adopted from: Mazur, J., Ritter,D.,Reinelt, G. & Kaderali, L. (2009). Reconstructing Non-Linear dynamic Models of Gene Regulation using Stochastic Sampling. BMC Bioinformatics, 10(448).
## Eg.(1): A simple example performed with a training and validation set: data(Bergamaschi) data(survData) ## Generate prediction: result <- STpredictor_BLH(geDataS=Bergamaschi[1:27, 1:2], survDataS=survData[1:27, 9:10], geDataT=Bergamaschi[28:82, 1:2], survDataT=survData[28:82, 9:10], q = 1, s = 1, a = 1.558, b = 0.179 , cut.off=15, groups = 3, method = "CG", noprior = 1, extras = list(reltol=1)) ## Plot a KM plot with both long and short survivors: kmplt_svrl(long=result$long_survivors, short=result$short_survivors,title="KM plot of long and short survivors") ## Determine the area under the curve of AUROC curves vs. time to see the performance of the predictor given the chosen parameters and the current partitioning into training ## and validation sets: survivAURC(Stime=result$predicted_STs$True_STs,status=result$predicted_STs$censored, marker=result$predicted_STs$Predicted_STs, time.max=20) ## Perform a log-rank test to see if the difference between the long and short survivors is significant: logrnk(dataL=result$long_survivors, dataS=result$short_survivors) ## Eg.(2): A simple example performed with cross validation: data(Bergamaschi) data(survData) ## Generate prediction: STpredictor_xvBLH(geData=Bergamaschi[1:40,1:2], survData=survData[1:40,9:10], k = 10, cut.off = 10, q = 1, s = 1, a = 1.558, b = 0.179, groups = 3, method = "BFGS", noprior = 1, extras = list(reltol=1)) ## Plot a KM plot with both long and short survivors: kmplt_svrl(long=result$long_survivors, short=result$short_survivors,title="KM plot of long and short survivors") ## Determine the area under the curve of AUROC curves vs. time to see the performance of the predictor given the chosen parameters and the current partitioning into training ## and validation sets: survivAURC(Stime=result$predicted_STs$True_STs,status=result$predicted_STs$censored, marker=result$predicted_STs$Predicted_STs, time.max=20) ## Perform a log-rank test to see if the difference between the long and short survivors is significant: logrnk(dataL=result$long_survivors, dataS=result$short_survivors)## Eg.(1): A simple example performed with a training and validation set: data(Bergamaschi) data(survData) ## Generate prediction: result <- STpredictor_BLH(geDataS=Bergamaschi[1:27, 1:2], survDataS=survData[1:27, 9:10], geDataT=Bergamaschi[28:82, 1:2], survDataT=survData[28:82, 9:10], q = 1, s = 1, a = 1.558, b = 0.179 , cut.off=15, groups = 3, method = "CG", noprior = 1, extras = list(reltol=1)) ## Plot a KM plot with both long and short survivors: kmplt_svrl(long=result$long_survivors, short=result$short_survivors,title="KM plot of long and short survivors") ## Determine the area under the curve of AUROC curves vs. time to see the performance of the predictor given the chosen parameters and the current partitioning into training ## and validation sets: survivAURC(Stime=result$predicted_STs$True_STs,status=result$predicted_STs$censored, marker=result$predicted_STs$Predicted_STs, time.max=20) ## Perform a log-rank test to see if the difference between the long and short survivors is significant: logrnk(dataL=result$long_survivors, dataS=result$short_survivors) ## Eg.(2): A simple example performed with cross validation: data(Bergamaschi) data(survData) ## Generate prediction: STpredictor_xvBLH(geData=Bergamaschi[1:40,1:2], survData=survData[1:40,9:10], k = 10, cut.off = 10, q = 1, s = 1, a = 1.558, b = 0.179, groups = 3, method = "BFGS", noprior = 1, extras = list(reltol=1)) ## Plot a KM plot with both long and short survivors: kmplt_svrl(long=result$long_survivors, short=result$short_survivors,title="KM plot of long and short survivors") ## Determine the area under the curve of AUROC curves vs. time to see the performance of the predictor given the chosen parameters and the current partitioning into training ## and validation sets: survivAURC(Stime=result$predicted_STs$True_STs,status=result$predicted_STs$censored, marker=result$predicted_STs$Predicted_STs, time.max=20) ## Perform a log-rank test to see if the difference between the long and short survivors is significant: logrnk(dataL=result$long_survivors, dataS=result$short_survivors)
A dataframe:\ ”Bergamaschi:" A dataframe of 10 covariates (in the columns) for 82 patients (in the rows)\
data(Bergamaschi)data(Bergamaschi)
The format is: num [1:82, 1:10] 0.654 0.701 0.126 0.899 0.267 ... - attr(*, "dimnames")=List of 2 ..$ : chr [1:82] "1" "2" "3" "4" ... ..$ : chr [1:10] "IMAGE:753234" "IMAGE:50794" "IMAGE:302190" "IMAGE:51408" ...
A subset of the data set used in Bergamaschi, A., & al., e. (2006). Distinct Patterns of DNA Copy NumberAlteration are associated with different clinicopathological features and gene expression subtypes of breast cancer. Genes, Chromosomes and cancer , 45, 1033-1040.
Bergamaschi, A., & al., e. (2006). Distinct Patterns of DNA Copy NumberAlteration are associated with different clinicopathological features and gene expression subtypes of breast cancer. Genes, Chromosomes and cancer , 45, 1033-1040.
Bergamaschi, A., & al., e. (2006). Distinct Patterns of DNA Copy NumberAlteration are associated with different clinicopathological features and gene expression subtypes of breast cancer. Genes, Chromosomes and cancer , 45, 1033-1040.
data(Bergamaschi) colnames(Bergamaschi)data(Bergamaschi) colnames(Bergamaschi)
Given the necessary data, this function calculates the derivative of the objective function without a w.r.t. the baseline hazards and weights(regression coefficients) in the model to be used in gradient-based optimization algorithms.
deriv_weight_estimator_BLH(geDataT, survDataT, weights_baselineH, q, s, a, b, groups)deriv_weight_estimator_BLH(geDataT, survDataT, weights_baselineH, q, s, a, b, groups)
geDataT |
The co-variate data (gene expression or aCGH, etc...) of the patient set passed on by the user. It is a matrix with the co-variates in the columns and the subjects in the rows. Each cell corresponds to that rowth subject's columnth co-variate's value. |
survDataT |
The survival data of the patient set passed on by the user. It takes on the form of a data frame with at least have the following columns “True_STs” and “censored”, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a “1” while patients who experience an event are assigned “1”. |
weights_baselineH |
A single vector with the initial values of the baseline hazards followed by the weights(regression coefficients) for the co-variates. |
q |
One of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
s |
The second of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights\_baselineH” argument. |
A vector of the same length as the “weights\_baselineH” argument corresponding to the calculated derivatives of the objective with respect to every component of “weights\_baselineH”.
This function is in itself not ver useful to the user, but is used within the function weights\_BLH
Douaa Mugahid
The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer. as well as Kaderali, Lars.(2006) A Hierarchial Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker The prior on the regression coefficients was adopted from: Mazur, J., Ritter,D.,Reinelt, G. & Kaderali, L. (2009). Reconstructing Non-Linear dynamic Models of Gene Regulation using Stochastic Sampling. BMC Bioinformatics, 10(448).
weight_estimator_BLH, codederiv_weight_estimator_BLH_noprior
data(Bergamaschi) data(survData) deriv_weight_estimator_BLH(survDataT=survData[1:10, 9:10], geDataT=Bergamaschi[1:10, 1:2], weights_baselineH=c(0.1,0.2,0.3,rep(0,2)), q=1, s=1, a=1.5, b=0.3, groups=3)data(Bergamaschi) data(survData) deriv_weight_estimator_BLH(survDataT=survData[1:10, 9:10], geDataT=Bergamaschi[1:10, 1:2], weights_baselineH=c(0.1,0.2,0.3,rep(0,2)), q=1, s=1, a=1.5, b=0.3, groups=3)
Given the necessary data, this function calculates the derivative of the objective function without a prior on the regression coefficients w.r.t. the baseline hazards and weights(regression coefficients) in the model to be used in gradient-based optimization algorithms. This is sometimes necessary to get the optimization algorithm out of a peaked origin where it could start.
deriv_weight_estimator_BLH_noprior(survDataT, geDataT, weights_baselineH, a, b, groups)deriv_weight_estimator_BLH_noprior(survDataT, geDataT, weights_baselineH, a, b, groups)
survDataT |
The survival data of the patient set passed on by the user. It takes on the form of a data frame with at least have the following columns “True\_STs” and “censored”, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a “1” while patients who experience an event are assigned “1”. |
geDataT |
The co-variate data (gene expression or aCGH, etc...) of the patient set passed on by the user. It is a matrix with the co-variates in the columns and the subjects in the rows. Each cell corresponds to that rowth subject's columnth co-variate's value. |
weights_baselineH |
A single vector with the initial values of the baseline hazards followed by the weights(regression coefficients) for the co-variates. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights\_baselineH” argument. |
A vector of the same length as the “weights\_baselineH” argument corresponding to the calculated derivatives of the objective with respect to every component of “weights\_baselineH”.
This function is in itself not very useful to the user, but is used within the function
weights\_BLH.
Douaa Mugahid
The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer. as well as Kaderali, Lars.(2006) A Hierarchial Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker
weight_estimator_BLH_noprior, deriv_weight_estimator_BLH
data(Bergamaschi) data(survData) deriv_weight_estimator_BLH_noprior(survDataT=survData[1:10, 9:10], geDataT=Bergamaschi[1:10, 1:2], weights_baselineH=c(0.1,0.2,0.3,rep(0,2)), a=1.5, b=0.3, groups=3)data(Bergamaschi) data(survData) deriv_weight_estimator_BLH_noprior(survDataT=survData[1:10, 9:10], geDataT=Bergamaschi[1:10, 1:2], weights_baselineH=c(0.1,0.2,0.3,rep(0,2)), a=1.5, b=0.3, groups=3)
This function can plot the KM curves estimated for $2-3$ patients simultaneously for sake of easier comparison.
kmplt_svrl(all, long, short, title)kmplt_svrl(all, long, short, title)
all |
Data for the first set of patients; usually the complete set of patients, but could be any other.It is a data frame containing at least the two columns “censored” and “True_STs”. Where “censored” contains the censorship status of the subject as either “0/F” for uncensored subjects or “1/T” for censored subjects. This information is essential to be able to plot the KM curve. |
long |
Data for the second set of patients; in our case the group of patients who survived at least up to the cut off value passed to the predictor. It has essentially the same structure as “all” |
short |
Data for the third and last set of patients; in our case the group of patients who survived less than the cut off value passed on to the predictor. It essentially has the same structure as the two other arguments. |
title |
The main title for the plot. |
This function essentially is the same as kmplt but does the same for up to $3$ plots simultaneously.
A plot with all $2-3$ KM curves.
Douaa Mugahid
http://www.bmj.com/statsbk/12.dtl
censored <- c(1, 0, 1, 1, 1, 0, 1, 0, 0, 0) True_STs <- c(1, 4, 5, 4, 6, 3, 2, 1, 3, 4) dat1 <- as.data.frame(cbind(True_STs, censored)) censored <- c(1, 0, 1, 0, 1, 0, 1, 0, 1, 1) True_STs <- c(7, 7, 8, 5, 9, 11, 8, 11, 10, 6) dat2 <- as.data.frame(cbind(True_STs, censored)) censored <- c(1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1) True_STs <- c(1, 4, 5, 4, 6, 3, 2, 1, 3, 4, 7, 7, 8, 5, 9, 11, 8, 11, 10, 6) dat3 <- as.data.frame(cbind(True_STs, censored)) kmplt_svrl(all=dat3, long=dat2, short=dat1, title="KM of predictions")censored <- c(1, 0, 1, 1, 1, 0, 1, 0, 0, 0) True_STs <- c(1, 4, 5, 4, 6, 3, 2, 1, 3, 4) dat1 <- as.data.frame(cbind(True_STs, censored)) censored <- c(1, 0, 1, 0, 1, 0, 1, 0, 1, 1) True_STs <- c(7, 7, 8, 5, 9, 11, 8, 11, 10, 6) dat2 <- as.data.frame(cbind(True_STs, censored)) censored <- c(1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1) True_STs <- c(1, 4, 5, 4, 6, 3, 2, 1, 3, 4, 7, 7, 8, 5, 9, 11, 8, 11, 10, 6) dat3 <- as.data.frame(cbind(True_STs, censored)) kmplt_svrl(all=dat3, long=dat2, short=dat1, title="KM of predictions")
This function performs a Chi-square test on the long and short subject sets to determine if their is a significant difference between the survival times in both sets. It returns the p-value.
logrnk(dataL, dataS)logrnk(dataL, dataS)
dataL |
The set of subjects predicted to fall into the long-survivor set. A data frame containing at least the following columns: “PatientOrderValidation” (the number/order of the subject); “group” (the group into which the patient falls L (for long) or S(for short)); “censored” (the censorship status of the patient $1$ for uncensored and $0$ for censored). |
dataS |
Same as “dataL” but for the set of short survivors. |
Note that the typical arguments to be passed are the results of the “STpredict” functions “long\_survivors” and “long\_survivors”
The estimated p-value is returned
Douaa AS Mugahid
Bland JM, Altman DG. Survival probabilities (the Kaplan-Meier method). BMJ 2004;328;1073 http://www.bmj.com/statsbk/12.dtl
PatientOrderValidation_L <- c(1, 2, 3, 5, 7) PatientOrderValidation_S <- c(4, 6, 8) group_L <- rep("L", 5) group_S <- rep("S", 3) censored_L <- c(0, 0, 1, 1, 0) censored_S <- c(0, 0, 1) True_STs_L <- c(5, 6, 6 ,7, 8) True_STs_S <- c(2, 3, 2) short <- as.data.frame(cbind(PatientOrderValidation_S, group_S, censored_S, True_STs_S)) long <- as.data.frame(cbind(PatientOrderValidation_L, group_L, censored_L, True_STs_L)) names(short) <- c("PatientOrderValidation", "group", "censored", "True_STs") names(long) <- c("PatientOrderValidation", "group", "censored", "True_STs") logrnk(dataL=long, dataS=short)PatientOrderValidation_L <- c(1, 2, 3, 5, 7) PatientOrderValidation_S <- c(4, 6, 8) group_L <- rep("L", 5) group_S <- rep("S", 3) censored_L <- c(0, 0, 1, 1, 0) censored_S <- c(0, 0, 1) True_STs_L <- c(5, 6, 6 ,7, 8) True_STs_S <- c(2, 3, 2) short <- as.data.frame(cbind(PatientOrderValidation_S, group_S, censored_S, True_STs_S)) long <- as.data.frame(cbind(PatientOrderValidation_L, group_L, censored_L, True_STs_L)) names(short) <- c("PatientOrderValidation", "group", "censored", "True_STs") names(long) <- c("PatientOrderValidation", "group", "censored", "True_STs") logrnk(dataL=long, dataS=short)
This function allows the user to visualize the shape of the gamma distribution used as a prior on the baseline hazards in the functions ending with "_BLH"
pltgamma(a, b)pltgamma(a, b)
a |
Is the shape parameter for the gamma distribution. |
b |
Is the scale parameter for the gamma distribution |
A plot of the gamma distribution with the given parameters.
Douaa Mugahid
pltgamma(a=2,b=2)pltgamma(a=2,b=2)
This function helps visualize the effect of the parameters q and s on the prior distribution used on the weights.
pltprior(q, s)pltprior(q, s)
q |
One of the two parameters used to determine the prior on the weights. |
s |
The second of two parameters used to determine the prior on the weights. |
The prior assumed on the weights in the objective function takes on the following formulation:
A 3D plot of the value of the prior taking into consideration only two weights
Douaa Mugahid
Mazur J., et al. Reconstructing nonlinear dynamic models of gene regulation using stochastic sampling. BMC Bioinformatics 2009;10;448
pltprior(q=1,s=1)pltprior(q=1,s=1)
A function that calculates the approximate value of the definite integral of a continuous function. In other words, it can help plot the area under the curve of the plotted function between two limits.
simpson(x, y)simpson(x, y)
x |
A vector of the values at which the function is to be plotted. |
y |
A vector with the values of the function at the corresponding x-values. |
A single numerical value of the approximate area under the curve generated with the x and y values.
Compared to the trapezoidal algorithm, this is usually more accurate.
Douaa Mugahid
Hennion, P.E.(1962). Algorithm 84: Simpson's integration. Communications of ACM. 5(4), 208
x <- seq(0:20) y <- seq(0, 100, 1) simpson(x,y)x <- seq(0:20) y <- seq(0, 100, 1) simpson(x,y)
This function uses the training set to estimated the best regression coefficients, and baseline hazards describing the data according to the piecewise baseline hazard Cox regression model. It then takes them and uses them to predict the survival times of the validation set, which are determined as the mean value of the p.d.f. of the survival time, as a continuous random variable, given the co-variate values of that subject.
STpredictor_BLH(geDataS, survDataS, cut.off, file = paste(getwd(), "STpredictor_results", sep = "/"), geDataT, survDataT, groups = NULL, a = 2, b = 2, q = 1, s = 1, BLHs = NULL, geneweights = NULL, method = "BFGS", noprior = 1, extras = list())STpredictor_BLH(geDataS, survDataS, cut.off, file = paste(getwd(), "STpredictor_results", sep = "/"), geDataT, survDataT, groups = NULL, a = 2, b = 2, q = 1, s = 1, BLHs = NULL, geneweights = NULL, method = "BFGS", noprior = 1, extras = list())
geDataS |
The co-variate data of the validation set passed on by the user. It is a matrix with the co-variates in the columns and the subjects in the rows. Each cell corresponds to that rowth subject's columnth co-variate's value. |
survDataS |
The survival data of the validation set passed on by the user. It takes on the form of a data frame with at least have the following columns “True\_STs” and “censored”, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a “1” while patients who experience an event are assigned “1”. |
cut.off |
The value of the separator around which the patients are grouped according to their predicted survival times. |
file |
The path of the file to which the log file of this session is saved. |
geDataT |
The co-variate data of the kth training set passed on by the user. |
survDataT |
The survival data of the kth training set passed on by the user. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights\_baselineH” argument. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
q |
One of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
s |
The second of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
BLHs |
A vector with the initial values for the baseline hazards. Should be of length groups. The default is NULL, in which case a vector of length |
geneweights |
A vector with the initial values of the weights(regression coefficients) for the co-variates. The default is NULL, in which case a vector of zeros the same length as
|
method |
The preferred optimization method. It can be one of the following:\
|
noprior |
An integer indicating the number of iterations to be done without assuming a prior on the regression coefficients. |
extras |
The extra arguments to passed to the optimization function optim. For further details on them, see the documentation for the |
log_optimization |
The result of the optimization performed on the training set as is described in the documentation for the |
short_survivors |
A data frame of results for the patients living less than the cut off value; with the columns True\_STs (the observed survival times), Predicted\_STs (the predicted survival times), censored(the censoring status of the patient, absolute\_error(the sign-less difference between the predicted and observed survival times), PatientOrderValidation (The patient's number) |
long_survivors |
A data frame with the results for the patients living at least as long as the cut off value; with columns True\_STs (the observed survival times), Predicted\_STs (the predicted survival times), censored(the censoring status of the patient,absolute\_error(the sign-less difference between the predicted and observed survival times), PatientOrderValidation (The patient's number) |
Douaa Mugahid
The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer. as well as Kaderali, Lars.(2006) A Hierarchical Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker The prior on the regression coefficients was adopted from: Mazur, J., Ritter,D.,Reinelt, G. & Kaderali, L. (2009). Reconstructing Non-Linear dynamic Models of Gene Regulation using Stochastic Sampling. BMC Bioinformatics, 10(448).
data(Bergamaschi) data(survData) result <- STpredictor_BLH(geDataS=Bergamaschi[1:27, 1:2], survDataS=survData[1:27, 9:10], geDataT=Bergamaschi[28:82, 1:2], survDataT=survData[28:82, 9:10], q = 1, s = 1, a = 1.558, b = 0.179, cut.off=3, groups = 3, method = "CG", noprior = 1, extras = list(reltol=1))data(Bergamaschi) data(survData) result <- STpredictor_BLH(geDataS=Bergamaschi[1:27, 1:2], survDataS=survData[1:27, 9:10], geDataT=Bergamaschi[28:82, 1:2], survDataT=survData[28:82, 9:10], q = 1, s = 1, a = 1.558, b = 0.179, cut.off=3, groups = 3, method = "CG", noprior = 1, extras = list(reltol=1))
Using the full data provided by the user, this function splits the data set k times, into a smaller validation set, and a much bigger training set. The regression coefficients of the model are estimated from the training set and used to predict the survival times of the validation set. The patients can then be split into patients two groups around a cut off value also specified by the user.
STpredictor_xvBLH(geData, survData, k = 10, cut.off, file = paste(getwd(), "STpredictor.xv.BLH_results", sep = "/"), q = 1, s = 1, a = 2, b = 2, groups = 3, geneweights = NULL , BLHs = NULL, method = "BFGS", noprior = 1, extras = list())STpredictor_xvBLH(geData, survData, k = 10, cut.off, file = paste(getwd(), "STpredictor.xv.BLH_results", sep = "/"), q = 1, s = 1, a = 2, b = 2, groups = 3, geneweights = NULL , BLHs = NULL, method = "BFGS", noprior = 1, extras = list())
geData |
A matrix with the co-variate data of the full set of subjects. It is constructed with the co-variate in the columns and the subjects in the rows.Each cell corresponds to that rowth subject's column th co-variate's value. |
survData |
The survival data of the entire set of subjects. It takes on the form of a data frame with at least have the following columns “True_STs” and “censored”, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a “1” while patients who experience an event are assigned “1”. |
k |
The number of times the cross-validation is. |
cut.off |
The value of the separator around which the patients are grouped according to their predicted survival times. |
file |
The path of the file to which the log file of this session is saved. |
q |
One of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
s |
The second of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights_baselineH” argument |
geneweights |
A vector with the initial values of the weights(regression coefficients) for the co-variates. The default is NULL, in which case a vector of zeros the same length as
|
BLHs |
A vector with the initial values for the baseline hazards. Should be of length groups. The default is NULL, in which case a vector of length |
method |
The preferred optimization method. It can be one of the following:
|
noprior |
An integer indicating the number of iterations to be done without assuming a prior on the regression coefficients. |
extras |
The extra arguments to passed to the optimization function optim. For further details on them, see the documentation for the optim function. |
predicted_STs |
A data frame of the results for all patients, with the columns True_STs (the observed survival times), Predicted_STs (the predicted survival times), censored(the censoring status of the patient,absolute_error(the signless difference between the predicted and oberved survival times), PatientOrderValidation (The patient's number) |
short_survivors |
A data frame of results for the patients living less than the cut off value; with the columns True_STs (the observed survival times), Predicted_STs (the predicted survival times), censored(the censoring status of the patient,absolute_error(the signless difference between the predicted and oberved survival times), PatientOrderValidation (The patient's number) |
long_survivors |
A data frame with the results for the patients living at least as long as the cut off value; with columns True_STs (the observed survival times), Predicted_STs (the predicted survival times), censored(the censoring status of the patient,absolute_error(the sign-less difference between the predicted and observed survival times), PatientOrderValidation (The patient's number) |
weights |
A vector with the mean value of the regression coefficients obtained from the k training sets |
baselineHs |
A vector with the mean value of the baseline hazards returned from the k training sets |
Douaa Mugahid
The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer.// as well as Kaderali, Lars.(2006) A Hierarchial Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker The prior on the regression coefficients was adopted from: Mazur, J., Ritter,D.,Reinelt, G. & Kaderali, L. (2009). Reconstructing Non-Linear dynamic Models of Gene Regulation using Stochastic Sampling. BMC Bioinformatics, 10(448).
data(Bergamaschi) data(survData) STpredictor_xvBLH(geData=Bergamaschi[1:20, 1:2], survData=survData[1:20, 9:10], k = 10, cut.off=3, file = paste(getwd(), "STpredictor.xv.BLH_results", sep = "/"), q = 1, s = 1, a = 2, b = 2, groups = 3, geneweights = NULL, BLHs = NULL, method = "CG", noprior = 1, extras = list(reltol=1))data(Bergamaschi) data(survData) STpredictor_xvBLH(geData=Bergamaschi[1:20, 1:2], survData=survData[1:20, 9:10], k = 10, cut.off=3, file = paste(getwd(), "STpredictor.xv.BLH_results", sep = "/"), q = 1, s = 1, a = 2, b = 2, groups = 3, geneweights = NULL, BLHs = NULL, method = "CG", noprior = 1, extras = list(reltol=1))
A dataframe ”survData:" A dataframe containing the survival information of the 82 patients the relevant columns of which are "True_STs", "censored" indicating the recorded survival times of the patients, and their censorship status simultaneously. In the "censored" column "0" indicates a non-censored patient, and "1" indicates a censored patient\
data(survData)data(survData)
A data frame with 82 observations on the following 10 variables.
Array.IDThe array IDs of the patients
Sample.ID.Bauke.The array IDs of the patients as annotated in one source
Experiment.Jon.The array IDs of the patients as annotated in a third source (in essence the same as the previous two)
ExptIDThe Experiment ID
OrderThe number/order of the patient
Overall.survival..mons.undividedthe overall survival time of the patients in months
Relapse.free.survival..mons.the relapse free survival time of the patients in months
Status.0.A..1.AWD..2.DOD..3.DOCthe status of the tumour (as abbreviated in the publication)
censoredthe status of censorship with ”0" corresponding to a ”non-censored" patient and ”1" to a ”censored patient"
True_STsThe survival/censorship times of the patient in years
A subset of the data set used in Bergamaschi, A., & al., e. (2006). Distinct Patterns of DNA Copy NumberAlteration are associated with different clinicopathological features and gene expression subtypes of breast cancer. Genes, Chromosomes and cancer , 45, 1033-1040.
Bergamaschi, A., & al., e. (2006). Distinct Patterns of DNA Copy NumberAlteration are associated with different clinicopathological features and gene expression subtypes of breast cancer. Genes, Chromosomes and cancer , 45, 1033-1040.
Bergamaschi, A., & al., e. (2006). Distinct Patterns of DNA Copy NumberAlteration are associated with different clinicopathological features and gene expression subtypes of breast cancer. Genes, Chromosomes and cancer , 45, 1033-1040.
data(survData) colnames(survData)data(survData) colnames(survData)
This function plots the individual area under the ROC curves of different time points against the time at which they were evaluated, and calculates the area under that curve.
survivAURC(Stime, status, marker, entry = NULL, cut.values = NULL, time.max = 20, by = 1)survivAURC(Stime, status, marker, entry = NULL, cut.values = NULL, time.max = 20, by = 1)
Stime |
The observed survival times of the patients. |
status |
The censoring status of the patient. 1 for a censored patient, and 0 for a patient who has an event. |
marker |
The predicted survival time of the patients. |
entry |
The time of entry of the patients, set to NULL by default. |
cut.values |
The cut off values for which the ROC curves are to be constructed. |
time.max |
The maximum time point for which the area under a ROC curve is to be plotted. |
by |
The step size between every ROC curve estimated and the next. |
The calculations for the Area under the ROC curves at each time point is done according to Patrick Heagerty's survivalROC function in the survivalROC package in R. It is a value indicating the performance of the predictor when used on the results of both functions STpredictor.BLH and STpredictor.xv.BLH.
AUC |
The value of the area under the curve generated |
AUeachROC |
A vector with the values of the area under the individual ROC curves |
A plot of the Area under the ROC curves against their corresponding time points.
Douaa Mugahid
Heagerty,P., Lumely T. & Pepe M.(2000). Time-dependent ROC curves for censored survival data & a diagnostic marker. Biometrics, 56(2), 337-344.
True_STs <- c(1.416667,2.75,2.416667,2.583333,2.166667,2.5,2.5,1.833333,1.25,0.6666667,1,6.583333,6.5,6.666667,2.75,1.666667,1.166667,2.833333,3.583333,6.166667,6.166667, 3.416667,6.083333,1.833333,5.583333,0.75,5.75,5.5,0.5833333,7.666667,5,2.833333,1.333333,5.083333,0.8333333,1.5,4.75,3.416667,4.666667,1.916667,4.666667,7.416667,0.9166667, 1.083333,3.75,3.25,3,2.416667,2.75,2.5,2.666667,4.5,4.416667,1.5,0.8333333,3.166667,3.833333,3.833333,0.4166667,3.333333,2.75,3.083333,0.3333333,0.25,0.6666667,1.833333, 2.333333,3.416667,3.416667,3,0.6666667,0.75,2.166667,1,1.416667,1.333333,1.166667,1.166667,0.4166667,1.25,1.166667,1.083333) Predicted_STs <- c(6.030591,6.014457,3.545584,5.414229,6.41576,9.393992,5.542331,6.890859,8.090213,4.98545,2.77357,6.275699,9.163978,7.511511,9.531218,7.63715,10.08977, 11.12364,3.982502,5.441881,12.61404,12.21851,17.05850,12.78141,16.22795,21.48544,6.281354,13.83925,8.859929,6.104142,8.255909,2.335526,6.564962,2.335761,9.33772,12.62540, 10.97276,15.63089,8.01967,5.817267,5.59897,4.340784,32.40319,33.74123,27.45024,26.31024,26.88833,24.34707,32.06541,38.90473,17.37102,15.11059,8.772035,14.24816,7.852889, 7.79996,5.601459,2.802408,35.77047,24.34717,30.65796,25.93927,20.64544,22.04807,19.15037,23.83430,1.876557,3.937208,6.526354,5.886377,9.301074,12.4657,14.49783,15.41502, 2.860931,2.541947,4.543111,4.525553,4.148272,3.986912,6.246755,6.89523) censored <- c(0,1,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1,1,1,1,1,1, 1) survivAURC(Stime=True_STs,status=censored, marker=Predicted_STs,time.max=5)True_STs <- c(1.416667,2.75,2.416667,2.583333,2.166667,2.5,2.5,1.833333,1.25,0.6666667,1,6.583333,6.5,6.666667,2.75,1.666667,1.166667,2.833333,3.583333,6.166667,6.166667, 3.416667,6.083333,1.833333,5.583333,0.75,5.75,5.5,0.5833333,7.666667,5,2.833333,1.333333,5.083333,0.8333333,1.5,4.75,3.416667,4.666667,1.916667,4.666667,7.416667,0.9166667, 1.083333,3.75,3.25,3,2.416667,2.75,2.5,2.666667,4.5,4.416667,1.5,0.8333333,3.166667,3.833333,3.833333,0.4166667,3.333333,2.75,3.083333,0.3333333,0.25,0.6666667,1.833333, 2.333333,3.416667,3.416667,3,0.6666667,0.75,2.166667,1,1.416667,1.333333,1.166667,1.166667,0.4166667,1.25,1.166667,1.083333) Predicted_STs <- c(6.030591,6.014457,3.545584,5.414229,6.41576,9.393992,5.542331,6.890859,8.090213,4.98545,2.77357,6.275699,9.163978,7.511511,9.531218,7.63715,10.08977, 11.12364,3.982502,5.441881,12.61404,12.21851,17.05850,12.78141,16.22795,21.48544,6.281354,13.83925,8.859929,6.104142,8.255909,2.335526,6.564962,2.335761,9.33772,12.62540, 10.97276,15.63089,8.01967,5.817267,5.59897,4.340784,32.40319,33.74123,27.45024,26.31024,26.88833,24.34707,32.06541,38.90473,17.37102,15.11059,8.772035,14.24816,7.852889, 7.79996,5.601459,2.802408,35.77047,24.34717,30.65796,25.93927,20.64544,22.04807,19.15037,23.83430,1.876557,3.937208,6.526354,5.886377,9.301074,12.4657,14.49783,15.41502, 2.860931,2.541947,4.543111,4.525553,4.148272,3.986912,6.246755,6.89523) censored <- c(0,1,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1,1,1,1,1,1, 1) survivAURC(Stime=True_STs,status=censored, marker=Predicted_STs,time.max=5)
The function generates the Receiver-Operator Curve (ROC) at the specified time point using predicted and observed data in the presence of censored subjects. It so plots (1 - specificity) against the (specificity) at the designated cut off points. It is based on Patrick Heagerty's survivalROC function in the survivalROC package.
survivROC(Stime, status, marker, entry = NULL, predict.time, cut.values = NULL, plot = TRUE)survivROC(Stime, status, marker, entry = NULL, predict.time, cut.values = NULL, plot = TRUE)
Stime |
The observed survival times of the patients. |
status |
The censoring status of the patient. 1 for a censored patient, and 0 for a patient who has an event. |
marker |
The predicted survival time of the patients. |
entry |
The time of entry of the patients, set to NULL by default. |
predict.time |
The time point for which the ROC curve is to be plotted. |
cut.values |
The cut off values for which the ROC curves are to be constructed. |
plot |
A logical argument that specifies whether a plot is to be generated (TRUE) or not (FALSE). The argument is set to TRUE by default. |
This function is basically the survivROC function in Patrick Heagerty's survivROC package, with slight modifications to it to better suit our purpose. Unlike Heagerty's function it only performs the calculations using the KM estimator and does not provide any other methods as options.
cut.values |
the cut off values for which the sensitivity and (1-specificity) were calculated |
Comp.Specificity |
(1 - Specificity) as was calculated for every cut off value. |
Sensitivity |
The Sensitivity as was calculated for every cut off value |
predict.time |
The time point for which the ROC curve is calculated |
Survival |
The value of the estimated survivor function (using the KM estimator) at "predict.time" |
AUC |
The value of the area under the estimated ROC curve |
It is important to note that using the Kaplan-Meier estimator as the method for estimating the survival function results in non-monotonous curves in some instances.
Douaa Mugahid
Heagerty,P., Lumely T. & Pepe M.(2000). Time-dependent ROC curves for censored survival data & a diagnostic marker. Biometrics, 56(2), 337-344.
True_STs <- c(1.416667,2.75,2.416667,2.583333,2.166667,2.5,2.5,1.833333,1.25,0.6666667,1,6.583333,6.5,6.666667,2.75,1.666667,1.166667,2.833333,3.583333,6.166667,6.166667, 3.416667,6.083333,1.833333,5.583333,0.75,5.75,5.5,0.5833333,7.666667,5,2.833333,1.333333,5.083333,0.8333333,1.5,4.75,3.416667,4.666667,1.916667,4.666667,7.416667,0.9166667, 1.083333,3.75,3.25,3,2.416667,2.75,2.5,2.666667,4.5,4.416667,1.5,0.8333333,3.166667,3.833333,3.833333,0.4166667,3.333333,2.75,3.083333,0.3333333,0.25,0.6666667,1.833333, 2.333333,3.416667,3.416667,3,0.6666667,0.75,2.166667,1,1.416667,1.333333,1.166667,1.166667,0.4166667,1.25,1.166667,1.083333) Predicted_STs <- c(6.030591,6.014457,3.545584,5.414229,6.41576,9.393992,5.542331,6.890859,8.090213,4.98545,2.77357,6.275699,9.163978,7.511511,9.531218,7.63715,10.08977, 11.12364,3.982502,5.441881,12.61404,12.21851,17.05850,12.78141,16.22795,21.48544,6.281354,13.83925,8.859929,6.104142,8.255909,2.335526,6.564962,2.335761,9.33772,12.62540, 10.97276,15.63089,8.01967,5.817267,5.59897,4.340784,32.40319,33.74123,27.45024,26.31024,26.88833,24.34707,32.06541,38.90473,17.37102,15.11059,8.772035,14.24816,7.852889, 7.79996,5.601459,2.802408,35.77047,24.34717,30.65796,25.93927,20.64544,22.04807,19.15037,23.83430,1.876557,3.937208,6.526354,5.886377,9.301074,12.4657,14.49783,15.41502, 2.860931,2.541947,4.543111,4.525553,4.148272,3.986912,6.246755,6.89523) censored <- c(0,1,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1,1,1,1,1,1, 1) survivROC(Stime=True_STs,status=censored, marker=Predicted_STs,predict.time=5)True_STs <- c(1.416667,2.75,2.416667,2.583333,2.166667,2.5,2.5,1.833333,1.25,0.6666667,1,6.583333,6.5,6.666667,2.75,1.666667,1.166667,2.833333,3.583333,6.166667,6.166667, 3.416667,6.083333,1.833333,5.583333,0.75,5.75,5.5,0.5833333,7.666667,5,2.833333,1.333333,5.083333,0.8333333,1.5,4.75,3.416667,4.666667,1.916667,4.666667,7.416667,0.9166667, 1.083333,3.75,3.25,3,2.416667,2.75,2.5,2.666667,4.5,4.416667,1.5,0.8333333,3.166667,3.833333,3.833333,0.4166667,3.333333,2.75,3.083333,0.3333333,0.25,0.6666667,1.833333, 2.333333,3.416667,3.416667,3,0.6666667,0.75,2.166667,1,1.416667,1.333333,1.166667,1.166667,0.4166667,1.25,1.166667,1.083333) Predicted_STs <- c(6.030591,6.014457,3.545584,5.414229,6.41576,9.393992,5.542331,6.890859,8.090213,4.98545,2.77357,6.275699,9.163978,7.511511,9.531218,7.63715,10.08977, 11.12364,3.982502,5.441881,12.61404,12.21851,17.05850,12.78141,16.22795,21.48544,6.281354,13.83925,8.859929,6.104142,8.255909,2.335526,6.564962,2.335761,9.33772,12.62540, 10.97276,15.63089,8.01967,5.817267,5.59897,4.340784,32.40319,33.74123,27.45024,26.31024,26.88833,24.34707,32.06541,38.90473,17.37102,15.11059,8.772035,14.24816,7.852889, 7.79996,5.601459,2.802408,35.77047,24.34717,30.65796,25.93927,20.64544,22.04807,19.15037,23.83430,1.876557,3.937208,6.526354,5.886377,9.301074,12.4657,14.49783,15.41502, 2.860931,2.541947,4.543111,4.525553,4.148272,3.986912,6.246755,6.89523) censored <- c(0,1,1,1,1,0,1,1,0,1,0,1,1,1,1,0,0,0,0,1,1,1,1,0,1,0,1,1,0,1,1,0,0,1,0,0,1,0,1,0,1,1,0,0,1,1,1,0,1,1,1,1,1,0,1,1,1,1,0,1,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1,1,1,1,1,1, 1) survivROC(Stime=True_STs,status=censored, marker=Predicted_STs,predict.time=5)
A function that calculates the approximate value of the definite integral of a continuous function. In other words, it can help plot the area under the curve of the plotted function between two limits.
trapezoid(x, y)trapezoid(x, y)
x |
The values to be used along the x-axis while plotting the curve of the function. The x in f(x)=y |
y |
The values to be used along the y-axis while plotting the curve of the function. The y in the f(x)=y. |
The area under the curve plotted with the x and y values provided as arguments.
Using this method is slightly less accurate than using the simpson integration method
Douaa Mugahid
Weisstein, Eric W. "Trapezoidal Rule." From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/TrapezoidalRule.html
x <- seq(0:20) y <- seq(0, 100, 1) trapezoid(x,y)x <- seq(0:20) y <- seq(0, 100, 1) trapezoid(x,y)
Given the arguments, it can evaluate the value of the objective function used by the optimization algorithms for determining the optimal regression parameters and baseline hazard values.
weight_estimator_BLH(survDataT, geDataT, weights_baselineH, q, s, a, b, groups)weight_estimator_BLH(survDataT, geDataT, weights_baselineH, q, s, a, b, groups)
survDataT |
The survival data of the patient set passed on by the user. It takes on the form of a data frame with at least have the following columns “True_STs” and “censored”, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a “1” while patients who experience an event are assigned “1”. |
geDataT |
The co-variate data (gene expression or aCGH, etc...) of the patient set passed on by the user. It is a matrix with the co-variates in the columns and the subjects in the rows. Each cell corresponds to that rowth subject's columnth co-variate's value. |
weights_baselineH |
A single vector with the initial values of the baseline hazards followed by the weights(regression coefficients) for the co-variates. |
q |
One of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
s |
The second of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights_baselineH” argument. |
A single numerical value corresponding to the value of the objective function with the given regression coefficients and baseline hazard values.
This function is in itself not useful to the user, but is used within the function weights.BLH
Douaa Mugahid
The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer. as well as Kaderali, Lars.(2006) A Hierarchial Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker The prior on the regression coefficients was adopted from: Mazur, J., Ritter,D.,Reinelt, G. & Kaderali, L. (2009). Reconstructing Non-Linear dynamic Models of Gene Regulation using Stochastic Sampling. BMC Bioinformatics, 10(448).
weight_estimator_BLH_noprior, deriv_weight_estimator_BLH_noprior
data(Bergamaschi) data(survData) weight_estimator_BLH(survDataT=survData[1:10, 9:10], geDataT=Bergamaschi[1:10 , 1:2],weights_baselineH=c(0.1,0.2,0.3,rep(0,ncol(Bergamaschi))), q=1, s=1, a=1.5, b=0.3, groups=3)data(Bergamaschi) data(survData) weight_estimator_BLH(survDataT=survData[1:10, 9:10], geDataT=Bergamaschi[1:10 , 1:2],weights_baselineH=c(0.1,0.2,0.3,rep(0,ncol(Bergamaschi))), q=1, s=1, a=1.5, b=0.3, groups=3)
Given the arguments, it can evaluate the value of the objective function used by the optimization algorithms for determining the optimal regression parameters and baseline hazard values without including the prior on the regression coefficients, which can be necessary if the starting conditions are set to the origin, which is very peaked in case of inclusion of the prior distribution.
weight_estimator_BLH_noprior(geDataT, survDataT, weights_baselineH, a, b, groups)weight_estimator_BLH_noprior(geDataT, survDataT, weights_baselineH, a, b, groups)
survDataT |
The survival data of the patient set passed on by the user. It takes on the form of a data frame with at least have the following columns “True_STs” and “censored”, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a “1” while patients who experience an event are assigned “1”. |
geDataT |
The co-variate data (gene expression or aCGH, etc...) of the patient set passed on by the user. It is a matrix with the co-variates in the columns and the subjects in the rows. Each cell corresponds to that rowth subject's columnth co-variate's value. |
weights_baselineH |
A single vector with the initial values of the baseline hazards followed by the weights(regression coefficients) for the co-variates. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights_baselineH” argument. |
A vector of the same length as the "weights_baselineH" argument corresponding to the calculated derivatives of the objective with respect to every component of "weights_baselineH".
This function is in itself not useful to the user, but is used within the function weights.BLH
Douaa Mugahid
The basic model is based on the Cox regression model as first introduced by Sir David Cox in: Cox,D.(1972).Regression models & life tables. Journal of the Royal Society of Statistics, 34(2), 187-220. The extension of the Cox model to its stepwise form was adapted from: Ibrahim, J.G, Chen, M.-H. & Sinha, D. (2005). Bayesian Survival Analysis (second ed.). NY: Springer. as well as Kaderali, Lars.(2006) A Hierarchial Bayesian Approach to Regression and its Application to Predicting Survival Times in Cancer Patients. Aachen: Shaker
weight_estimator_BLH, deriv_weight_estimator_BLH_noprior
data(Bergamaschi) data(survData) weight_estimator_BLH_noprior(geDataT=Bergamaschi[1:10, 1:2], survDataT=survData[1:10, 9:10], weights_baselineH=c(0.1,0.2,0.3,rep(0,2)), a=1.5, b=0.3, groups=3)data(Bergamaschi) data(survData) weight_estimator_BLH_noprior(geDataT=Bergamaschi[1:10, 1:2], survDataT=survData[1:10, 9:10], weights_baselineH=c(0.1,0.2,0.3,rep(0,2)), a=1.5, b=0.3, groups=3)
This function is a wrapper around the optimization function optim to allow the optimization for the regression coefficients and baseline
hazards appropriate for the data set at hand. It is where the functions weight_estimator_BLH, weight_estimator_BLH_noprior,
deriv_weight_estimator_BLH, deriv_weight_estimator_BLH_noprior are required.
weights_BLH(geDataT, survDataT, q, s, a, b, groups, par, method = c("Nelder-Mead", "L-BFGS-B", "CG", "BFGS", "SANN"), noprior = 1, extras = list(), dist = NULL)weights_BLH(geDataT, survDataT, q, s, a, b, groups, par, method = c("Nelder-Mead", "L-BFGS-B", "CG", "BFGS", "SANN"), noprior = 1, extras = list(), dist = NULL)
geDataT |
A matrix with the co-variate in the columns and the subjects in the rows.Each cell corresponds to that rowth subject's columnth co-variate's value. |
survDataT |
A data frame with the survival data of the set of subjects at hand. It should at least have the following columns “True_STs” and “censored”, corresponding to the observed survival times and the censoring status of the subjects consecutively. Censored patients are assigned a “1” while patients who experience an event are assigned “1”. |
q |
One of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
s |
The second of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights_baselineH” argument. |
par |
A single vector with the initial values of the baseline hazards followed by the weights(regression coefficients) for the co-variates. |
method |
The preferred optimization method. It can be one of the following:
|
noprior |
An integer indicating the number of iterations to be done without assuming a prior on the regression coefficients. |
extras |
The extra arguments to passed to the optimization function optim. For further details on them, see the documentation for the |
dist |
The distribution function to be passed to the optimization algorithm in case of using SANN to generate a new candidate point. |
The same value as the optim function. See it's documentation for details.
Note that this function is just a wrapper around the optim function to serve our purpose, and it's main purpose is to be called within the main functions of this package
STpredictor_BLH and weights_xvBLH
Douaa Mugahid
http://sekhon.berkeley.edu/stats/html/optim.html
data(Bergamaschi) data(survData) weights_BLH(geDataT=Bergamaschi[1:10,1:2], survDataT=survData[1:10, 9:10], q=1, s=1, a=1.56, b=0.17, groups=3, par=c(0.1,0.2,0.3,rep(0,ncol(Bergamaschi))), method = "CG", noprior = 1, extras = list(reltol=1), dist = NULL)data(Bergamaschi) data(survData) weights_BLH(geDataT=Bergamaschi[1:10,1:2], survDataT=survData[1:10, 9:10], q=1, s=1, a=1.56, b=0.17, groups=3, par=c(0.1,0.2,0.3,rep(0,ncol(Bergamaschi))), method = "CG", noprior = 1, extras = list(reltol=1), dist = NULL)
This function is an “incomplete” version of STpredictor.BLH used within the cross validation function STpredictor_xvBLH to predicted the survival times of the
subset of patients in the kth partitioning. It is not meant for use outside that function.
weights_xvBLH(geDataS, survDataS, geDataT, survDataT, q = 1, s = 1, a = 2, b = 2, groups = 3, par, method = "BFGS", noprior = 1, extras = list())weights_xvBLH(geDataS, survDataS, geDataT, survDataT, q = 1, s = 1, a = 2, b = 2, groups = 3, par, method = "BFGS", noprior = 1, extras = list())
geDataS |
The co-variate data of the kth validation set passed on by |
survDataS |
The survival data of the kth validation set passed on by |
geDataT |
The co-variate data of the kth training set passed on by |
survDataT |
The survival data of the kth training set passed on by |
q |
One of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
s |
The second of the two parameters on the prior distribution used on the weights (regression coefficients) in the model. |
a |
The shape parameter for the gamma distribution used as a prior on the baseline hazards. |
b |
The scale parameter for the gamma distribution used as a prior on the baseline hazards. |
groups |
The number of partitions along the time axis for which a different baseline hazard is to be assigned. This number should be the same as the number of initial values passed for the baseline hazards in the beginning of the “weights_baselineH” argument. |
par |
A single vector with the initial values of the baseline hazards followed by the weights(regression coefficients) for the co-variates. |
method |
The preferred optimization method. It can be one of the following:
|
noprior |
An integer indicating the number of iterations to be done without assuming a prior on the regression coefficients. |
extras |
The extra arguments to passed to the optimization function optim. For further details on them, see the documentation for the |
prediction |
A data frame with the columns True_STs (the observed survival times), Predicted_STs (the predicted survival times), censored(the censoring status of the patient,absolute_error(the sign-less difference between the predicted and observed survival times), PatientOrderValidation (The patient's number) |
est.geneweight |
The estimated regression coefficients from the kth training set (geDataT,survDataT) |
est.baselineH |
The estimated baseline hazards from the kth training set (geDataT, survDataT) |
This function is not meant to be used outside its wrapper.
Douaa Mugahid
data(Bergamaschi) data(survData) weights_xvBLH(geDataS=Bergamaschi[21:31, 1:2], survDataS=survData[21:31, 9:10],geDataT=Bergamaschi[1:20, 1:2], survDataT=survData[1:20, 9:10], q = 1, s = 1, a = 2, b = 2, groups = 3, par = c(0.1, 0.1, 0.1,rep(0,2)), method = "CG", noprior = 1, extras = list(reltol=1))data(Bergamaschi) data(survData) weights_xvBLH(geDataS=Bergamaschi[21:31, 1:2], survDataS=survData[21:31, 9:10],geDataT=Bergamaschi[1:20, 1:2], survDataT=survData[1:20, 9:10], q = 1, s = 1, a = 2, b = 2, groups = 3, par = c(0.1, 0.1, 0.1,rep(0,2)), method = "CG", noprior = 1, extras = list(reltol=1))