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help.Rmd
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---
title: 'geneSurv: an interactive tool for survival analysis in genomics research'
author: "Selcuk Korkmaz"
date: "February 3, 2017"
output:
html_document:
theme: united
toc: yes
toc_float: yes
pdf_document:
toc: yes
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```
## Abstract
Survival analysis is often used in cancer studies. It has been shown that combination of clinical data with genomics increases predictive performance of survival analysis methods. This tool provides a wide range of survival analysis methods for genomics research, especially in cancer studies. The tool includes analysis methods including Kaplan-Meier, Cox regression, Penalized Cox regression and Random Survival Forests. It also offers methods for optimal cutoff point determination for continuous markers.
Each procedure includes following features:
Kaplan-Meier: descriptive statistics, survival table, mean and median life time, hazard ratios, comparison tests including Log-rank, Gehan-Breslow, Tarone-Ware, Peto-Peto, Modified Peto-Peto, Flemington-Harrington, and interactive plots such as Kaplan-Meier curves and hazard plots.
Cox regression: coefficient estimates, hazard ratios, goodness of fit test, analysis of deviance, save predictions, save residuals, save Martingale residuals, save Schoenfeld residuals, save dfBetas, proportional hazard assumption test, and interactive plots including Schoenfeld residual plot and Log-Minus-Log plot.
Penalized Cox regression: feature selection using ridge, elastic net and lasso penalization. A cross-validation to investigate the relationship between partial likelihood devaince and lambda values.
Random survival forests: overall survival predictions (Nelson-Aalen estimator, overall ensemble), individual survival predictions (with OOB), individual cumulative hazard predictions (with OOB), error rate, feature selection, and interactive plots including random survival plot, cumulative hazard plot, error rate plot, Cox vs RSF plot
Optimal cutoff: determination of optimal cutoff value by maxmizing test statistics, including log-rank, Gehan-Breslow, Tarone-Ware, Peto-Peto, modified Peto-Peto, Flemington-Harrington.
---
output:
html_document: default
pdf_document: default
---
## 1.Data upload
This tool requires a dataset in `*.txt` format, which is seperated by `comma`, `semicolon`, `space` or `tab` delimiter. First row of dataset must include header. When the appropriate file is uploaded, the dataset will be appear immediately on the main page of the tool. Alternatively users can upload one of the example datasets provided within the tool for testing and understanding the operating logic of the tool.
<img src="images/dataUpload.jpg" alt="Data upload" align="middle" style="width:800px; height:200px;"/>
<img src="images/dataUploadHelp.jpg" alt="Data upload help" align="middle" style="width:800px; height:251px;"/>
### 1.1. Data Pre-processing
An important step of the data analysis in statistics is the data pre-processing. Users can perform some basic data pre-processing steps using this tool, including near zero filtering, centering, scaling and log-transformation (natural logarithm). To perform a data pre-processing; (1) check the "Pre-processing" box, (2) select "Survival time", "Status variable" and variables you wish to exclude from pre-processing (i.e. categorical variables), (3) select one or more pre-processing methods, including near zero filtering, centering, scaling and log-transformation, (4) click "Run pre-process" button to perform the pre-processing.
<img src="images/dataPreProcess2.jpg" alt="Data pre-processing" align="middle" style="width:800px; height:400px;"/>
After the pre-processing, all the selected pre-processing steps will be applied to the dataset and new data set will appear on the main panel of the tool. If there are any variables which have near zero variances, they will be excluded from the dataset and will appear in a new table.
<img src="images/dataPreProcess.jpg" alt="Data pre-processing" align="middle" style="width:800px; height:400px;"/>
## 2. Analysis Methods
### 2.1. Kaplan-Meier
#### Concept
Kaplan-Meier is a non-paranetric statistical method that is used to estimate survival probabilities and hazard ratios for a cohort study group. In clinical trials, it is often used to measure the part of patients living for a certain period of time after a treatment.
#### Variables
* `Survival time`: Time until an event occurs (i.e. days, weeks, months, years)
* `Status variable`: The event (i.e. death, disease, remission, recovery)
* `Category value for status variable`: Category value of the event of interest (i.e. 1, yes)
* `Factor variable`: A categorical variable which indicates different study groups (i.e. treatment, gender)
#### Usage
A Kaplan-Meier analysis can be conducted by applying the following steps:
1. Select the analysis method as `Kaplan Meier` from `Analysis` tab.
2. Select suitable variables for the analysis, such as `survival time`, `status variable`, `category value for status variable` and `factor variable`, if exists.
3. In advanced options, one can change confidence interval type, as log, log-log or plain, variance estimation method, as Greenwood or Tsiatis, Flemington-Harrington weights, confidence level and reference category, as first or last.
4. Click `Run` button to run the analysis.
<img src="images/survivalHelp.jpg" alt="Survival help" align="middle" style="width:800px; height:450px;"/>
#### Outputs
*Desired outputs can be selected by clicking Outputs checkbox. Available outputs are;*
```{r kaplanMeier, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE, include=FALSE}
setwd("~/Dropbox/GSD/Studies/Web-Tools(Devel)/geneSurv/")
library("survival")
library("KMsurv")
library("survMisc")
source("kaplanMeier.R")
library("highcharter")
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
km = kaplanMeier (survivalTime = "dmfs_time", statusVariable = "dmfs_event", status = 1, factors= "ER_IHC", survivalTable = TRUE, data = data)
```
#####a. Case summary
Summary statistics, such as number and percent of observations, events and censored cases can be obtained.
```{r kaplanMeierDescriptives, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE, include=TRUE}
desc = km$tableResult$caseSummary
descs = do.call(rbind.data.frame, desc)
DT::datatable(descs, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(
dom = 'Bfrtip',
buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE
))
```
*
#####b. Survival table
A survival table can be created. First column in the table represents factor group and number of time points (i.e. 1.2 means second time point in the first factor group, likewise 2.1 means first time point in the second group). Second column is survival time, third column gives number of subjects at risk, fourth column is the number of events, fifth column represents the cumulative probability of surviving, sixth, seventh and eight columns are associated standard error, lower and upper limits, respectively.
```{r kaplanMeier2, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
stResult = km$testResult$survivalTable
stResults = do.call(rbind.data.frame, stResult)
DT::datatable(stResults, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip',buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE
))
```
#####c. Survival plot
A forest plot can be created for each level of factor group using survival probabilites at each end point.
```{r survivalPlot, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
surv = km$testResult$survivalTable[[names(km$testResult$hazardRatio)[1]]]
highchart() %>% hc_exporting(enabled = TRUE, filename = "survivalPlot") %>%
hc_add_series(name = "Survival", type = "line", data = surv$`Cumulative probability of surviving`, showInLegend = FALSE, zIndex = 1, marker = list(lineColor = "black", lineWidth = 1), lineWidth = 0, id = "survival") %>%
hc_add_series(name = "CI", data = as.matrix(cbind(surv$`Lower limit`, surv$`Upper limit`)),type = "errorbar", names = "Limits", showInLegend = FALSE, zIndex = 0, lineWidth = 1.5, linkedTo = "survival") %>%
hc_chart(zoomType = "xy", inverted = TRUE) %>%
hc_xAxis(categories = as.character(surv$Time), title = list(text = "Time")) %>%
hc_yAxis(startOnTick = FALSE, endOnTick = FALSE, title = list(text = "Survival")) %>%
#hc_plotOptions(tooltip = list(headerFormat = "<b>Time: </b>{point.x}")) %>%
hc_tooltip(crosshairs = TRUE, shared = TRUE, headerFormat = "<b>Time: </b>{point.x} <br>") %>%
hc_plotOptions(line = list(tooltip = list(pointFormat = "<b>{series.name}: </b>{point.y:.3f} ")),
errorbar = list(tooltip = list(pointFormat = "({point.low} - {point.high})"))) %>%
hc_add_theme(hc_theme_google())
```
*
#####d. Mean and Median life time
Mean and median life time and their associated confidence levels can be calculated for each level of factor group.
```{r medianAndMedianLifeTime, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
mst = km$tableResult$meanMedianSurvivalTimes
rownames(mst) = mst$Factor
mstResults = mst[-1]
DT::datatable(mstResults, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(
dom = 'Bfrtip',
buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE
))
```
*
#####e. Hazard ratio
Hazard ratios and their respective lower and upper limits can be calculated for each factor group at each end point.
```{r hazardRatioKaplanMeier, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
hrResult = km$testResult$hazardRatio
hrResults = do.call(rbind.data.frame, hrResult)
DT::datatable(hrResults, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(
dom = 'Bfrtip',
buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE
))
```
*
#####f. Hazard plot
A forest plot can be created for each level of factor group using hazard ratios at each end point.
```{r hazardPlot, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
hazard = km$testResult$hazardRatio[[names(km$testResult$hazardRatio)[1]]]
highchart() %>% hc_exporting(enabled = TRUE, filename = "hazardPlot") %>%
hc_add_series(name = "Hazard", type = "line", data = hazard$Hazard.Ratio, showInLegend = FALSE, zIndex = 1, marker = list(lineColor = "black", lineWidth = 1), lineWidth = 0, id = "hazard") %>%
hc_add_series(name = "CI", data = as.matrix(cbind(hazard$Lower, hazard$Upper)),type = "errorbar", names = "Limits", showInLegend = FALSE, zIndex = 0, lineWidth = 1.5, linkedTo = "hazard") %>%
hc_chart(zoomType = "xy", inverted = TRUE) %>%
hc_xAxis(categories = as.character(hazard$Time), title = list(text = "Time")) %>%
hc_yAxis(startOnTick = FALSE, endOnTick = FALSE, title = list(text = "Hazard Ratio")) %>%
#hc_plotOptions(tooltip = list(headerFormat = "<b>Time: </b>{point.x}")) %>%
hc_tooltip(crosshairs = TRUE, shared = TRUE, headerFormat = "<b>Time: </b>{point.x} <br>") %>%
hc_plotOptions(line = list(tooltip = list(pointFormat = "<b>{series.name}: </b>{point.y:.3f} ")),
errorbar = list(tooltip = list(pointFormat = "({point.low} - {point.high})"))) %>%
hc_add_theme(hc_theme_google())
```
#####g. Comparison tests
Six different comparison tests can be calculated for testing the differences in survival probability estimations between factor groups.
```{r comparisonTestsKaplanMeier, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
compTestResult = km$testResult$testResults
DT::datatable(compTestResult, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(
dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
*
#####h. Plots
<img src="images/survivalHelpKMplots.jpg" alt="Survival plots help" align="middle" style="width:800px; height:450px;"/>
```{r coxPlots, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE, include=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
km = kaplanMeier (survivalTime = "dmfs_time", statusVariable = "dmfs_event", status = 1, factors= "ER_IHC", survivalTable = TRUE, data = data)
survivalTime = "dmfs_time"
statusVariable = "dmfs_event"
status = 1
fctr = "ER_IHC"
ci = "log"
varianceEstimation = "greenwood"
confidenceLevel = 95
factors = fctr
if(!is.null(survivalTime)){
survivalTime = as.matrix(data[, survivalTime, drop = FALSE])
}
if(!is.null(factors)){
factors = as.factor(data[, factors])
}
if(!is.null(factors)){
factorsName = data[, factors, drop = FALSE]
}
if(!is.null(statusVariable)){
statusVariable = data[, statusVariable]
}
if(!is.null(status)){
if(is.numeric(status)){status = as.numeric(status)}else{status = as.factor(status)}
}
if(!is.null(factors)){
newData = data.frame(id =seq(1,dim(survivalTime)[1], 1), survivalTime= survivalTime,
statusVar=statusVariable,factor = factors)
newData = newData[complete.cases(newData),]
colnames(newData) = c("id","time","statusVar", "factor")
}else{
newData = data.frame(id =seq(1,dim(survivalTime)[1], 1), survivalTime= survivalTime,
statusVar=statusVariable)
newData = newData[complete.cases(newData),]
colnames(newData) = c("id", "time", "statusVar")
}
newData$statusVar = newData$statusVar%in%status
#data[,input$survivalTimeKM] = as.numeric(data[,input$survivalTimeKM])
#data[,input$factorVarKM] = as.factor(data[,input$factorVarKM])
if(!is.null(fctr)){
compareCurves <- survfit(Surv(time, statusVar == TRUE) ~ factors, data = newData, conf.type = ci, error = varianceEstimation, conf.int = confidenceLevel/100)
for(i in 1:length(names(compareCurves$strata))) {
names(compareCurves$strata)[i] = gsub("factors", "ER_IHC", names(compareCurves$strata)[i])
}
}else{
compareCurves <- survfit(Surv(time, statusVar == TRUE) ~ 1, data = newData, conf.type = ci, error = varianceEstimation, conf.int = confidenceLevel/100)
}
enabledLegend = TRUE
is.even <- function(x) x %% 2 == 0
ranges = TRUE
```
##### i. Kaplan-Meier curve
Kaplan-Meier curves can be created. A number of edit options is also available for plots.
```{r kmPlots, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
p = hchart(compareCurves, ranges = ranges, type = "line", markTimes = TRUE,
animation = TRUE)
p %>% hc_title(text = "Kaplan-Meier Plot") %>%
hc_xAxis(title = list(text = "Time"), tickInterval=NULL, tickLength = 5, lineWidth = 1) %>%
hc_yAxis(title = list(text = "Survival Probability"), lineWidth = 1, tickLength = 5, tickWidth= 1, labels = list(format = "{value:.2f}")) %>%
#hc_colors("#440154") %>%
hc_add_theme(hc_theme_gridlight()) %>%
hc_chart(backgroundColor = "white", zoomType = "xy") %>%
hc_legend(enabled = TRUE) %>%
hc_plotOptions(line = list(dashStyle = "Solid"), area = list(zIndex = 15), series = list(enableMouseTracking = TRUE)) %>%
hc_tooltip(shared = TRUE, crosshairs = TRUE, valueDecimals = 3, followTouchMove = FALSE, headerFormat = "<b>Time</b>: {point.key} <br>")#, pointFormat = "{series.name}: {point.y}")
```
##### j. Hazard plot
Hazard plot can be created. A number of edit options is also available for plots.
```{r hazardPlots, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
p <- hchart(compareCurves, fun = "cumhaz", ranges = ranges, type = "line", markTimes = TRUE,
animation = TRUE)
p %>% hc_title(text = "Hazard Plot") %>%
hc_xAxis(title = list(text = "Time"), tickInterval=NULL, tickLength = 5, lineWidth = 1) %>%
hc_yAxis(title = list(text = "Cumulative Hazard"), lineWidth = 1, tickLength = 5, tickWidth= 1, labels = list(format = "{value:.2f}")) %>%
#hc_colors("#440154") %>%
hc_add_theme(hc_theme_gridlight()) %>%
hc_chart(backgroundColor = "white", zoomType = "xy") %>%
hc_legend(enabled = TRUE) %>%
hc_plotOptions(line = list(dashStyle = "Solid"), area = list(zIndex = 15), series = list(enableMouseTracking = TRUE)) %>%
hc_tooltip(shared = TRUE, crosshairs = TRUE, valueDecimals = 3, followTouchMove = FALSE, headerFormat = "<b>Time</b>: {point.key} <br>")#, pointFormat = "{series.name}: {point.y}")
```
##### k. Log-Minus-Log plot
Log-Minus-Log plot can be created. A number of edit options is also available for plots.
```{r lmlPlots, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
p <- hchart(compareCurves, fun = "cloglog", ranges = ranges, type = "line", markTimes = TRUE,
animation = TRUE)
p %>% hc_title(text = "Log-Minus-Log Plot") %>%
hc_xAxis(title = list(text = "Time"), tickInterval=NULL, tickLength = 5, lineWidth = 1) %>%
hc_yAxis(title = list(text = "log(-log(survival))"), lineWidth = 1, tickLength = 5, tickWidth= 1, labels = list(format = "{value:.2f}")) %>%
#hc_colors("#440154") %>%
hc_add_theme(hc_theme_gridlight()) %>%
hc_chart(backgroundColor = "white", zoomType = "xy") %>%
hc_legend(enabled = TRUE) %>%
hc_plotOptions(line = list(dashStyle = "Solid"), area = list(zIndex = 15), series = list(enableMouseTracking = TRUE)) %>%
hc_tooltip(shared = TRUE, crosshairs = TRUE, valueDecimals = 3, followTouchMove = FALSE, headerFormat = "<b>Time</b>: {point.key} <br>")#, pointFormat = "{series.name}: {point.y}")
```
### 2.2. Cox Regression
#### Concept
Cox regression, also known as proportional hazard regression, is a method to investigate the effect of one or multiple factors (i.e. gene expressions) upon the time an event of interest occurs. In this model, the effect of a unit increase in a factor is multiplicative with respect to the hazard rate.
#### Usage
A Cox regression analysis can be conducted by applying the following steps:
1. Select the analysis method as `Cox Regression` from `Analysis` tab.
2. Select suitable variables for the analysis, such as `survival time`, `status variable`, `category value for status variable`, and categorical and continuous predictors for the model.
3. In advanced options, `interaction terms`, `strata terms` and `time dependent covariates` can be added to the model. Moreover, if there are multiple records for observations, users can specify it by clicking `Multiple ID` checkbox. Furthermore, one can choose model selection criteria, as `AIC` or `p-value`, model selection method, as `backward`, `forward` or `stepwise`, reference category, as `first` or `last`, and ties method, as `Efron`, `Breslow` or `exact` and change the `confidence level`.
4. Click `Run` button to run the analysis.
<img src="images/coxRegressionHelp.jpg" alt="Cox Regression help" align="middle" style="width:800px; height:350;"/>
#### Outputs
Desired outputs can be selected by clicking Outputs checkbox. Available outputs are coefficient estimates, hazard ratio, goodness of fit tests, analysis of deviance, predictions, residuals, Martingale residuals, Schoenfeld residuals and DfBetas.
```{r coxRegression, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE, include=FALSE}
setwd("~/Dropbox/GSD/Studies/Web-Tools(Devel)/geneSurv/")
library("DT")
library("survival")
library("KMsurv")
library("survMisc")
source("coxRegression.R")
source("getDescriptiveResultsCoxRegression.R")
source("stepwise.R")
source("plotLT.R")
require("ggplot2")
source("ggsurv.R")
source("ggsurv2.R")
source("plotSchoenfeld.R")
library("magrittr")
library("dplyr")
library("survminer")
library("highcharter")
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", data = data)
```
#####a. Coefficient Estimates
A coefficient estimation table, which includes variable names, coefficient estimates and their associated standard errors, z statistics and p values, can be created.
```{r displayCoefficientEstimatesResults, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
coeffResultsCox = cox$testResult$displayCoefficientEstimatesResults
DT::datatable(coeffResultsCox, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(
dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####b. Hazard ratio
A hazard ratio table, which includes variable names, hazard ratios and their associated lower and upper limits, can be created.
```{r hazardRatioReactiveCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
hrResultsCox = cox$testResult$hazardRatioResults
DT::datatable(hrResultsCox, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(
dom = 'Bfrtip',
buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE
))
```
#####c. Hazard plot
A forest plot can be created for hazard ratios to give them a visual inpection.
```{r hazardPlotCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
cox = cox$testResult$hazardRatioResults
if(nrow(cox)>1){
cox = cbind.data.frame("Variable" = levels(cox$Variable), apply(cox[,-1],2, as.numeric))
}else{
cox = cbind.data.frame("Variable" = levels(cox$Variable), as.data.frame(t(apply(cox[,-1],2, as.numeric))))
}
highchart() %>% hc_exporting(enabled = TRUE, filename = "hazardPlot") %>%
hc_add_series(name = "Hazard", type = "line", data = cox$`Hazard ratio`, showInLegend = FALSE, zIndex = 1, marker = list(lineColor = "black", lineWidth = 1), lineWidth = 0, id = "hazard") %>%
hc_add_series(name = "CI", data = as.matrix(cbind(cox$`Lower limit (95%)`, cox$`Upper limit (95%)`)),type = "errorbar", names = "Limits", showInLegend = FALSE, zIndex = 0, lineWidth = 1.5, linkedTo = "hazard") %>%
hc_chart(zoomType = "xy", inverted = TRUE) %>%
hc_xAxis(categories = matrix(cox$Variable, ncol = 1)) %>%
hc_yAxis(startOnTick = FALSE, endOnTick = FALSE, title = list(text = "Hazard Ratio"), plotLines = list(list(value = 1, width = 2, color = "green", dashStyle = "Dash"))) %>%
#hc_plotOptions(tooltip = list(headerFormat = "<b>Time: </b>{point.x}")) %>%
hc_tooltip(crosshairs = TRUE, shared = TRUE, headerFormat = "<b>Variable: </b>{point.x} <br>") %>%
hc_plotOptions(line = list(tooltip = list(pointFormat = "<b>{series.name}: </b>{point.y:.3f} ")),
errorbar = list(tooltip = list(pointFormat = "({point.low} - {point.high})"))) %>%
hc_add_theme(hc_theme_google())
```
#####d. Goodness of Fit Tests
Fitted Cox regression model can be tested with three tests: Likelihood ratio, Wald, Score.
```{r goodnessOfFitTestsCoxsss, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", data = data)
goodnessOfFit = cox$testResult$goodnessOfFitTestsResults
datatable(goodnessOfFit, rownames=FALSE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####e. Analysis of Deviance
A deviance analysis can be conducted for each variable in the fitted model.
```{r analysisOfDevianceCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", data = data)
aod = cox$testResult$analysisOfDevianceResults
datatable(aod, rownames=FALSE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####f. Predictions
Predictions from the fitted model can be obtained.
```{r storePredictionsCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", storePredictions = TRUE, data = data)
preds = cox$testResult$Store$Predictions
datatable(preds, rownames=TRUE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####g. Residuals
Residuals from the fitted model can be obtained.
```{r storeResidualsCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", storeResiduals = TRUE, data = data)
residuals = cox$testResult$Store$Residuals
datatable(residuals, rownames=TRUE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####h. Martingale Residuals
Martingale residuals from the fitted model can be obtained.
```{r storeMartingaleResidualsCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", storeMartingaleResiduals = TRUE, data = data)
martingaleResiduals = cox$testResult$Store$MartingaleResiduals
datatable(martingaleResiduals, rownames=TRUE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####i. Schoenfeld Residuals
Schoenfeld residuals from the fitted model can be obtained.
```{r storeSchoenfeldResidualsCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", storeSchoenfeldResiduals = TRUE, data = data)
storeSchoenfeldResiduals = cox$testResult$Store$SchoenfeldResiduals
datatable(storeSchoenfeldResiduals, rownames=TRUE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####j. DfBetas
DfBetas residuals from the fitted model can be obtained.
```{r storeDfBetasCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", storeDfBetas = TRUE, data = data)
DfBetas = cox$testResult$Store$DfBetas
datatable(DfBetas, rownames=TRUE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####k. Proportional Hazard Assumption
<img src="images/coxPhHelp.jpg" alt="Cox Regression help" align="middle" style="width:800px; height:350;"/>
#####l. Proportional Hazard Test
To check the proportionality assumption of Cox regression model, a proportional hazard test can be conducted both globally and for each variable in the fitted model.
```{r phTest, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
cox = coxRegression(survivalTime = "dmfs_time", categoricalInput = "ER_IHC", continuousInput = c("ESR1.205225_at", "PGR.208305_at"), statusVariable = "dmfs_event", status = 1, displayDescriptives = TRUE, displayCoefficientEstimates = TRUE, displayModelFit = TRUE, hazardRatio = TRUE, goodnessOfFitTests = TRUE, analysisOfDeviance = TRUE, ties = "efron", storeDfBetas = TRUE, data = data)
coxPhTest = cox$testResult$displayCoxPh
datatable(coxPhTest, rownames=TRUE, extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip', buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
#####m. Schoenfeld Plot
Beside a formal test for proportionality assumption, a Schoenfeld plot can be created to check the assumption visually.
```{r schoenfeldPlot, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
compareCurves = cox$model
x <- cox.zph(compareCurves, transform = 'rank')
resid = TRUE
se = TRUE
df = 4
nsmo = 40
ltyest = "Solid"
ltyci = "Solid"
col = 1
colorLine = "#204BD9"
colorLineCI = "#59A819"
lwd=1
lty = ltyest
xx <- x$x
yy <- x$y
d <- nrow(yy)
df <- max(df)
nvar <- ncol(yy)
pred.x <- seq(from=min(xx), to=max(xx), length=nsmo)
temp <- c(pred.x, xx)
lmat <- splines::ns(temp, df=df, intercept=TRUE)
pmat <- lmat[1:nsmo,]
xmat <- lmat[-(1:nsmo),]
qmat <- qr(xmat)
yvar = x$y
var = ncol(yvar)
if (qmat$rank < df) {stop("Spline fit is singular, try a smaller degrees of freedom")}
if (se) {
bk <- backsolve(qmat$qr[1:df, 1:df], diag(df))
xtx <- bk %*% t(bk)
seval <- d*((pmat%*% xtx) *pmat) %*% rep(1, df)
}
if (missing(var)) {var <- 1:nvar}else {
if (is.character(var)) {var <- match(var, dimnames(yy)[[2]])}
if (any(is.na(var)) || max(var)>nvar || min(var) <1) {stop("Invalid variable requested")}
}
if (x$transform == 'log') {
xx <- exp(xx)
pred.x <- exp(pred.x)
}
if(x$transform != 'identity') {
xtime <- as.numeric(dimnames(yy)[[1]])
indx <- !duplicated(xx)
apr1 <- approx(xx[indx], xtime[indx],
seq(min(xx), max(xx), length=17)[2*(1:8)])
temp <- signif(apr1$y,2)
apr2 <- approx(xtime[indx], xx[indx], temp)
xaxisval <- apr2$y
xaxislab <- rep("",8)
for (i in 1:8) {xaxislab[i] <- format(temp[i])}
}
col <- rep(col, length=2)
lwd <- rep(lwd, length=2)
lty <- rep(lty, length=2)
svar = "ESR1.205225_at"
for (i in 1:var) {
y <- yy[,svar]
yhat <- pmat %*% qr.coef(qmat, y)
if (resid) {yr <-range(yhat, y)}else{yr <-range(yhat)}
if (se) {
temp <- 2* sqrt(x$var[i,i]*seval)
yup <- yhat + temp
ylow<- yhat - temp
yr <- range(yr, yup, ylow)
newData2 = cbind.data.frame(pred.x,yhat, yup, ylow)
}
newData = cbind.data.frame(xx, y)
newData3 = cbind.data.frame(pred.x, yhat)
fn = paste0("function() {\n if (this.value == ", xaxisval[1], ") {return ",xaxislab[1], "}\n
if (this.value == ", xaxisval[2], ") {return ",xaxislab[2], "}\n
if (this.value == ", xaxisval[3], ") {return ",xaxislab[3], "}\n
if (this.value == ", xaxisval[4], ") {return ",xaxislab[4], "}\n
if (this.value == ", xaxisval[5], ") {return ",xaxislab[5], "}\n
if (this.value == ", xaxisval[6], ") {return ",xaxislab[6], "}\n
if (this.value == ", xaxisval[7], ") {return ",xaxislab[7], "}\n
if (this.value == ", xaxisval[8], ") {return ",xaxislab[8], "}\n
", "}"
)
ylabel = paste0("Scaled Schoenfeld residuals for ", svar)
sp = highchart() %>%
hc_add_series(name = "Curve", data = as.matrix(newData3), type = "line", enabled = FALSE, color = "#204BD9", marker = list(enabled = FALSE), id = "schoenLine")%>%
hc_xAxis(tickInterval=NULL, tickLength = 5, lineWidth = 1, tickPositions = xaxisval, labels = list(formatter = JS(fn), format = "{value:.2f}"), title = list(text = "Time"))%>%
hc_yAxis(tickInterval=NULL, tickLength = 5, lineWidth = 1, title = list(text = ylabel), labels = list(format = "{value:.2f}"))%>%
hc_title(text = "Schoenfeld Plot") %>%
hc_add_theme(hc_theme_google()) %>%
hc_plotOptions(line = list(dashStyle = "Solid")) %>%
hc_chart(backgroundColor = "#FFFFFF", zoomType = "xy") %>%
hc_tooltip(shared = TRUE, crosshairs = FALSE, valueDecimals = 2, followTouchMove = FALSE)
if (resid){
sp = sp %>% hc_add_series(name = "Residuals", data = as.matrix(newData), type="scatter", labels = list(format = "{value:.2f}"), color = "#000000", zIndex = 10, marker = list(symbol = "circle", radius = 4))
}
if (se){
sp = sp %>% hc_add_series(name = "CI", data = as.matrix(cbind(newData2$pred.x, newData2$ylow, newData2$yup)),
type = "arearange", fillOpacity = 0.4, showInLegend = FALSE, linkedTo = "schoenLine", color ="#59A819")
}
sp = sp %>% hc_exporting(enabled = TRUE, filename = "schoenfeldplot")
}
sp
```
#####n. Log-Minus-Log Plot
Another useful plot for checking proportionality assumption is log-minus-log plot. Lines should be parallel to each other to satisfy proportionality.
```{r lmlPlotCox, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
survivalTime = "dmfs_time"
statusVariable = "dmfs_event"
status = 1
rnames = colnames(data)
fctr = "ER_IHC"
fctr = rnames[which.max(RecordLinkage::levenshteinSim(fctr,rnames))]
#ci = input$ciKM
#varianceEstimation = input$varianceEstimationKM
#confidenceLevel = input$confidenceLevelKM
factors = fctr
if(!is.null(survivalTime)){
survivalTime = as.matrix(data[, survivalTime, drop = FALSE])
}
if(!is.null(factors)){
factors = as.factor(data[, factors])
}
if(!is.null(statusVariable)){
statusVariable = data[, statusVariable]
}
if(!is.null(status)){
if(is.numeric(status)){status = as.factor(status)}else{status = as.factor(status)}
}
if(!is.null(factors)){
newData = data.frame(id =seq(1,dim(survivalTime)[1], 1), survivalTime= survivalTime,
statusVar=statusVariable,factor = factors)
newData = newData[complete.cases(newData),]
colnames(newData) = c("id", "time", "statusVar", "factor")
}
newData$statusVar = newData$statusVar%in%status
if(!is.null(fctr)){
compareCurves <- survfit(Surv(time, statusVar == TRUE) ~ factors, data = newData)
for(i in 1:length(names(compareCurves$strata))) {
names(compareCurves$strata)[i] = gsub("factors", fctr, names(compareCurves$strata)[i])
}
}
p = hchart(compareCurves, fun = "cloglog", ranges = FALSE, type = "line", animation = TRUE, rangesOpacity = 0.4)
p %>% hc_exporting(enabled = TRUE, filename = "plot") %>%
hc_title(text = "Log-Minus-Log Plot") %>%
hc_xAxis(title = list(text = "Time"), tickInterval=NULL, tickLength = 5, lineWidth = 1) %>%
hc_yAxis(title = list(text = "log(-log(survival))"), lineWidth = 1, tickLength = 5, tickWidth= 1, labels = list(format = "{value:.2f}")) %>%
#hc_colors("#440154") %>%
hc_add_theme(hc_theme_google()) %>%
hc_chart(backgroundColor = "white", zoomType = "xy") %>%
hc_legend(enabled = TRUE) %>%
hc_plotOptions(line = list(dashStyle = "Solid"), area = list(zIndex = 15), series = list(enableMouseTracking = TRUE)) %>%
hc_tooltip(shared = TRUE, crosshairs = TRUE, valueDecimals = 3, followTouchMove = FALSE, headerFormat = "<b>Time</b>: {point.key} <br>")
```
### 2.3. Penalized Cox Regression
#### Concept
Feature selection is an useful strategy to avoid over-fitting, to obtain more reliable predictive results, and to provide more insights into the underlying casual relationships <a href ="https://www.ncbi.nlm.nih.gov/pubmed/18562478" target = "_blank" > (Ma and Huang, 2008)</a>. In this section, a feature selection can be performed using ridge, elastic net or lasso penalty, especially when there are too many predictors (e.g. `n<<p`). More information can be found in <a href ="http://users.stat.umn.edu/~zouxx019/Papers/elasticnet.pdf" target = "_blank" > Zou and Hastie, 2005</a>, <a href ="http://www.jstatsoft.org/v33/i01/" target = "_blank" > Freidman et al, 2008</a> and <a href ="http://www.jstatsoft.org/v39/i05/" target = "_blank" > Simon et al, 2011</a>.
#### Usage
A Penalized Cox regression analysis can be conducted by applying the following steps:
1. Select the analysis method as `Penalized Cox Regression` from `Analysis` tab.
2. Select suitable variables for the analysis, such as `survival time`, `status variable`
3. If all predictors are continious then one can check the `Select All Variables` option to include all variables in dataset to the feature selection process. If some predictors categorical and others are continious, then uncheck the `Select All Variables` option and select categorical and continuous variables seperately.
4. Define the penalty term using the `Penalty term` slider as follow:
`Penalty term = 0`: ridge penalty
`0 < Penalty term < 1`: elastic net penalty
`Penalty term = 1`: lasso penalty
5. Select the number of folds for cross-validation. Note that number of folds must be greater than 3.
6. Click `Run` button to run the analysis.
<img src="images/regCoxReg.jpg" alt="Cox Regression help" align="middle" style="width:800px; height:350;"/>
#### Outputs
#####a) Variables in the model
Variable selection is conducted with the selected penalized method (i.e. ridge, elasticnet, lasso) and results will be displayed as a table, which includes selected variables and their associated coefficient estimates.
```{r regCoxReg, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
library("glmnet")
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
data = data[,-1]
survivalTimerCox = "dmfs_time"
survivalStatusrCox = "dmfs_event"
regCoxList = list()
indx = !(colnames(data) %in% c(survivalTimerCox, survivalStatusrCox))
x = data.matrix(data[,indx, drop = FALSE])
y= Surv(data[,survivalTimerCox], data[,survivalStatusrCox])
set.seed(1234)
cvFit = cv.glmnet(x, y, family = "cox", alpha = 0.2)
coefficients = as.data.frame(as.matrix(coef(cvFit, s = cvFit$lambda.min)))
coefficients$`1` = as.numeric(formatC(coefficients$`1`, digits = 3, format = "f"))
coefficients2 = data.frame(rownames(coefficients), coefficients[,1])
coefficients3 = coefficients2[coefficients2[2] != 0,]
colnames(coefficients3) = c("Variable", "Coefficient estimate")
varsNotInTheModel = coefficients2[coefficients2[2] == 0,]
if(nrow(varsNotInTheModel) > 0){
varsNotInTheModel$coefficients...1. = formatC(varsNotInTheModel$coefficients...1., digits = 3, format = "f")
colnames(varsNotInTheModel) = c("Variable", "Coefficient estimate")
}else{
varsNotInTheModel = NULL
}
regCoxList = list(coefficients3, varsNotInTheModel)
datatable(regCoxList[[1]], extensions = c('Buttons','KeyTable', 'Responsive'), options = list(dom = 'Bfrtip',buttons = c('copy', 'csv', 'excel', 'pdf', 'print'), keys = TRUE))
```
*
#####b) Cross-validation curve
A cross-validation curve can be created to investigate the relationship between partial likelihood devaince and lambda values.
```{r regCoxRegPlot, echo=FALSE, eval = TRUE, message=FALSE, warning=FALSE}
library("glmnet")
data <- read.table("www/data/GSE2034.txt", header=TRUE, sep = "\t")
data = data[,-1]
survivalTimerCox = "dmfs_time"
survivalStatusrCox = "dmfs_event"