BUILT-IN MATHEMATICA SYMBOL

# SurvivalModelFit

SurvivalModelFit[{e1, e2, ...}]
creates a survival model for event times.

## Details and OptionsDetails and Options

• SurvivalModelFit is used in survival, reliability, and duration analysis. It gives a nonparametric survival distribution as well as measures of confidence directly from incomplete data.
• SurvivalModelFit returns a symbolic SurvivalModel object to represent the survival model it constructs. The properties and diagnostics of the model can be obtained from model["property"].
• The form of events follows the form used in EventData.
• Different functional forms of the survival model can be obtained by specifying the form h in . The following forms can be used:
•  "CDF" cumulative distribution function "CHF" cumulative hazard function "SF" survival function
• The value of the fitted function h from SurvivalModelFit at a particular time t can be found from . is equivalent to .
• Specifying Normal[model] gives a pure function form of the estimated survival function.
• A list of available model properties can be obtained using model["Properties"].
• Properties of a fitted function h of the model can be obtained using . The expression model["property"] is equivalent to .
• Some properties related to the fitted function that can be obtained using model["property"]:
•  "EventTable" formatted table summarizing the fitted function "EventTableEntries" entries from the event table "FittedFunction" pure functional form of the fitted function "FullEventTable" extended event table "FullEventTableEntries" entries from the full event table "MeanSurvival" the mean survival time "MedianSurvival" the median survival time "StandardErrorFunction" functional form of standard errors of the fitted function "StandardErrors" a list of standard errors for each time point "SurvivalDistribution" the DataDistribution object used in the fitting
• Confidence intervals about the fitted function are given as a list of paired values corresponding to each time point given by model["EstimationPoints"].
• Confidence bands are given as pure functions that are equivalent to confidence intervals when evaluated at all time points in model["EstimationPoints"].
• Properties related to confidence intervals and bands include:
•  "PointwiseBands" pointwise confidence bands "PointwiseIntervals" pointwise confidence intervals "EqualPrecisionBands" simultaneous confidence bands "EqualPrecisionIntervals" simultaneous confidence intervals "HallWellnerBands" simultaneous Hall-Wellner confidence bands "HallWellnerIntervals" simultaneous Hall-Wellner confidence intervals
• Properties related to the event data:
•  "EstimationPoints" time points used in the estimation "EventData" EventData object used in the estimation "EventMatrix" matrix indicating possible event locations "EventMatrixPlot" a custom matrix plot of the event matrix "TruncationMatrix" matrix indicating where units are observable "TruncationMatrixPlot" a custom matrix plot of the truncation matrix
• Properties related to counts of different types of observations:
•  "AtRisk" number of individuals at risk at each time point "EventCounts" number of events for each time point "LeftCensoringCounts" number of left-censored events for each time point "ObservationCount" effective number of experimental units "RightCensoringCounts" number of right-censored events for each time point
• SurvivalModelFit takes the following options:
•  ConfidenceLevel 95/100 level to use for intervals and bands ConfidenceRange All range for simultaneous confidence bands ConfidenceTransform "LogLog" confidence transform to use Method Automatic method to use for model fitting
• With , probability-p confidence intervals and bands are computed for the various functional forms.
• ConfidenceRange->{tmin, tmax} gives probability-p simultaneous confidence intervals and bands for the fitted function between and .
• Possible settings for ConfidenceTransform include , , , , , or a pure function g.
• SurvivalModelFit automatically chooses the method most appropriate to the data. The Kaplan-Meier estimator is used for right-censored data. For other types of censoring, the estimate is constructed using a self-consistency approach. Different methods may only support some types of censoring or truncation.
• The setting Method->estimator specifies an estimator to use for distribution functions. Possible settings include:
•  "KaplanMeier" product limit estimator for right-censored data "NelsonAalen" based on the Nelson-Aalen cumulative hazard estimator "Turnbull" Turnbull algorithm for interval-censored data "Noncensored" censoring is ignored and interval midpoints are used "SelfConsistency" Turnbull algorithm for doubly censored data
• Additional method settings can be found in the Options section of Examples.

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Fit a survival model to some right-censored data:

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Evaluate the model at a point:

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Obtain a functional representation of the model:

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Visualize a 95% pointwise confidence region about the survival function:

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