bigSurvSGD {bigSurvSGD} | R Documentation |

## Big survival data analysis using stochastic gradient descent

### Description

Fits Cox model via stochastic gradient descent (SGD). This implementation avoids computational instability of the standard Cox Model when datasets are large. Furthermore, it scales up with very large datasets that do not fit the memory. It also handles large sparse datasets using the proximal stochastic gradient descent algorithm. For more details about the method, please see Aliasghar Tarkhan and Noah Simon (2020) <arXiv:2003.00116v2>.

### Usage

```
bigSurvSGD(
formula = Surv(time = time, status = status) ~ .,
data,
norm.method = "standardize",
features.mean = NULL,
features.sd = NULL,
opt.method = "AMSGrad",
beta.init = NULL,
beta.type = "averaged",
lr.const = 0.12,
lr.tau = 0.5,
strata.size = 20,
batch.size = 1,
num.epoch = 100,
b1 = 0.9,
b2 = 0.99,
eps = 1e-08,
inference.method = "plugin",
num.boot = 1000,
num.epoch.boot = 100,
boot.method = "SGD",
lr.const.boot = 0.12,
lr.tau.boot = 0.5,
num.sample.strata = 1000,
sig.level = 0.05,
beta0 = 0,
alpha = NULL,
lambda = NULL,
nlambda = 100,
num.strata.lambda = 10,
lambda.scale = 1,
parallel.flag = FALSE,
num.cores = NULL,
bigmemory.flag = FALSE,
num.rows.chunk = 1e+06,
col.names = NULL
)
## S3 method for class 'bigSurvSGD'
print(x, ...)
## S3 method for class 'bigSurvSGD'
plot(x, ...)
```

### Arguments

`formula` |
a formula in format of Surv(time=time, status=status)~feature1+feature2+... describing time-to-event variable, status variable, and features to be included in model. Default is "Surv(time, status)~." that regresses on all the features included in the dataset. |

`data` |
survival dataset. It can be in form of data.frame or a path to a .csv file if we aim not to read data off the memory. If we aim to read data off the memory, it must be a path to a .csv data. |

`norm.method` |
normalization method before starting the analysis. "center" only centers the features by subtracting the mean, "scale" only scales the features by dividing features to their standard deviation, "normalization" does both centering and scaling, and "none" does not perform any pre-processing. The default is "normalization". |

`features.mean` |
mean vector of features used for normalization. The default is NULL where our alorithm calculates it. |

`features.sd` |
standard deviation vector of features used for normalization. The default is NULL where our alorithm calculates it. |

`opt.method` |
optimization algorithm: "SGD" estimates the coefficients using the standard stochastic gradient descent; "ADAM" estimates the coefficients using ADAM optimizer; "AMSGrad" estimates the coefficients using AMSGrad optimizer. The default is "AMSGrad". |

`beta.init` |
initialization for coefficient. The default is NULL where our algorithm starts with an all-zero vector. |

`beta.type` |
type of coefficient to be returned. If specified as "single", the last updated coefficient is returned. If specified as "averaged", the Polyak-Ruppert (i.e., average over iterates) is returned. The default is "averaged". |

`lr.const` |
proportional constant for the learning rate. The higher values give faster but noisier estimates and vice versa. The default is 0.12 for "AMSGrad" optimizer. |

`lr.tau` |
the power of iteration index in the learning rate. The bigger value represents the faster decay in the lerning rate and vice versa. The default is 0.5. |

`strata.size` |
strata size. The default is 20 patients per stratum. |

`batch.size` |
batch size. The default is 1 stratum per batch. |

`num.epoch` |
Number of epochs for the SGD-based algorithms. The default is 100. |

`b1` |
hyper parameter for "AMSGrad" and "ADAM". The default is 0.9. See https://arxiv.org/abs/1412.6980 for "ADMA" and https://arxiv.org/abs/1904.03590 for "AMSGrad". |

`b2` |
hyper parameter for "AMSGrad" and "ADAM". The default is 0.99. |

`eps` |
hyper parameter for "AMSGrad" and "ADAM". The default is 1e-8. |

`inference.method` |
method for inference, i.e., constructing confidence interval (CI): "bootstrap" constructs CI usin non-parametric bootstrap; "plugin": constructs CI using asymptotic properties of U-statistics; The default is "plugin" which returns estimates, confidence intervals, test statistics, and p-values. |

`num.boot` |
number of boostrap resamples. Default is 1000. |

`num.epoch.boot` |
number of epochs for each boorstrap resamples. Default is 100. |

`boot.method` |
optimization method for bootstrap. Default is "SGD". |

`lr.const.boot` |
proportional constant for the learning rate for bootstrap resamples. Defauls is "0.12" |

`lr.tau.boot` |
power of iteration index in the learning rate for bootstrap resamples. Defauls is "0.5" |

`num.sample.strata` |
number of sample strata per observation to estimate standard error using plugin method. Default value is 1000. |

`sig.level` |
significance level for constructing (1-sig.level) confidence interval. Default is 0.05. |

`beta0` |
null vector of coefficients for calculating p-value using plugin method. Default is zero vector. |

`alpha` |
penalty coeficient between 0 and 1. alpha=0 only considers the ridge penlaty and alpha=1 only considers the lasso penalty. Otherwise, it considers a convex combination of these two penalties. Defualt is NULL, i.e., no penalty. |

`lambda` |
coeficient for the elastic net penalty. There are three possible scenarios: (1) If alpha is defined NULL, no penalty (ridge or lasso) is considered regardless of values of lambda; (2) If alpha is not NULL but lambda is NULL, it first calculates the largest value of lambda (lambda.max) for which all coefficients become zero. Then it considers an exponentially decreasing sequence of lambda starting from lambda.max ges toward lambda.min (lambda.min=0.01*lambda.max if p>n, otherewise lambda.min=0.0001*lambda.max) and return their corresponding coefficients. (3) If a value for lambda is specified, our algorithm returns coefficients for specified pair of (lambda, alpha). The default is NULL. |

`nlambda` |
number of elements to be considered for scenario (2) above. Default is 100. |

`num.strata.lambda` |
number of sample strata to estimate maximum lambda (lambda.max) when alpha is not NULL and lambda=NULL (see lambda). |

`lambda.scale` |
we scale lambda.max to make sure we start with a lambda for which we get all coefficients equal to 0. Default is 1. |

`parallel.flag` |
to specify if we want to use parallel computing for inference. Default is "F", i.e., no parallel computing. |

`num.cores` |
number of cores for parallel computing. The default is "NULL" for which if parallel.flag=T, it uses all available cores on your system. |

`bigmemory.flag` |
determins if data needs to be read off the memory in case data does not fit memory. Default is F, not to use bigmemoty package. |

`num.rows.chunk` |
maximum number of rows per chunk to be read off the memory. This is crucial for the large datasets that do not fit memory. Use fewer number of rows for the large number of features, especially if you receive an error due to lack of memory. The default value is 1e6 rows. |

`col.names` |
a vector of characters for column names of data. If NULL, the column names of dataset "data" will be selected. The default is NULL (i.e., reads columns of given dataset). |

`x` |
a 'bigSurvSGD' object |

`...` |
additional argument used |

### Value

coef: Log of hazards ratio. If no inference is used, it returns a vector for estimated coefficients: If inference is used, it returns a matrix including estimates and confidence intervals of coefficients. In case of penalization, it resturns a matrix with columns corresponding to lambdas.

coef.exp: Exponentiated version of coef (hazards ratio).

lambda: Returns lambda(s) used for penalizarion.

alpha: Returns alpha used for penalizarion.

features.mean: Returns means of features, if given or calculated

features.sd: Returns standard deviations of features, if given or calculated.

### Examples

```
# Simulated survival data - just estimation and no confidence interval
data(survData) # a dataset with 1000 observations (rows) and 10 features (columns)
resultsBig <- bigSurvSGD(formula=Surv(time, status)~.,data=survData, inference.method="none",
parallel.flag=TRUE, num.cores=2)
resultsBig
# Simulated survival data
data(survData) # a dataset with 1000 observations (rows) and 10 features (columns)
resultsBig <- bigSurvSGD(formula=Surv(time, status)~.,data=survData, inference="none",
parallel.flag=TRUE, num.cores=2)
resultsBig
# Simulated survival data to be read off the memory
data(survData) # a dataset with 1000 observations (rows) and 10 features (columns)
# Save dataset survSGD as bigSurvSGD to be read chunk-by-chunk off the memory
write.csv(survData, file.path(tempdir(), "bigSurvData.csv"), row.names = FALSE)
dataPath <- file.path(tempdir(), "bigSurvData.csv") # path to where data is
resultsBigOffMemory <- bigSurvSGD(formula=Surv(time, status)~., data=dataPath,
bigmemory.flag=TRUE, parallel.flag=TRUE, num.cores=2)
resultsBigOffMemory
# Simulated sparse survival data
data(sparseSurvData) # a sparse data with 100 observations (rows) and 150 features (columns)
resultsBigSparse <- bigSurvSGD(formula=Surv(time, status)~.,data=sparseSurvData,
alpha=0.9, lambda=0.1)
resultsBigSparse
```

*bigSurvSGD*version 0.0.1 Index]