SurvivalModel
represents the symbolic survival model obtained from functions like SurvivalModelFit.
Details and Options
- Properties of a survival model are obtained from SurvivalModel[…]["property"].
- SurvivalModel[…][{prop1,prop2,…}] gives several properties.
- SurvivalModel[…][x1,…] gives the value of the best-fit function at a particular point x1, … .
- Normal gives the expression for the default fitted function in a SurvivalModel.
- SurvivalModel objects are returned by fitting functions such as SurvivalModelFit.
- SurvivalModel[…][prop,ann] gives the annotation ann associated with the property prop.
- Possible properties available for a given type of fitted model are listed on the pages for functions such as SurvivalModelFit that generate the model.
- SurvivalModel 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 »
Examples
open all close allBasic Examples (1)
Create a SurvivalModel from some right-censored data:
data = EventData[{1, 2, 3, 4}, {0, 0, 1, 0}];mod = SurvivalModelFit[data]Extract a property from the model:
mod["EstimationPoints"]Evaluate the survival function at 
:
mod[3]Use Normal to obtain the survival function:
Normal[mod]Obtain a list of available properties:
mod["Properties"]Scope (5)
Extract a property from a SurvivalModel object:
mod = SurvivalModelFit[{1, 2, 3, 4}]The standard errors for the survival function:
mod["StandardErrors"]mod = SurvivalModelFit[{1, 2, 3, 4}]mod[{"StandardErrors", "EstimationPoints"}]Evaluate the fitted function at a point:
mod = SurvivalModelFit[{1, 2, 3, 4}];mod[2]mod /@ {1, 2, 3, 4}Obtain an expression for the default fitted function:
mod = SurvivalModelFit[{1, 2, 3, 4}];Normal[mod]mod = SurvivalModelFit[{1, 2, 3, 4}];ann = mod["StandardErrors", "Properties"]Table[Row[{i, ":
", mod["StandardErrors", i]}], {i, ann}]//TableFormOptions (7)
ConfidenceLevel (3)
Set the confidence level used for computing confidence intervals and bands:
data = {30, 32, 26, {37, ∞}, 29, {32, ∞}, 24, {31, ∞}, {31, ∞}, 42};𝒮 = SurvivalModelFit[data]A set of 90% intervals corresponding to the time points in the model:
𝒮["PointwiseIntervals", ConfidenceLevel -> .9]The confidence level can also be set before the model has been fitted:
𝒮 = SurvivalModelFit[data, ConfidenceLevel -> .9];
𝒮["PointwiseIntervals"]By default, the confidence level is set to 95/100:
data = {30, 32, 26, {37, ∞}, 29, {32, ∞}, 24, {31, ∞}, {31, ∞}, 42};𝒮 = SurvivalModelFit[data]𝒮["PointwiseIntervals"] === 𝒮["PointwiseIntervals", ConfidenceLevel -> 95 / 100]Compute confidence intervals for the survival probability at a point:
data = {{10, 12}, {11, 13}, {15, 18}, 16, {18, 20}, 20, 21};𝒮 = SurvivalModelFit[data]clev = {.7, .75, .8, .85, .9, .95};Confidence intervals about the survival function at 16 for a range of confidence levels:
Grid[Table[{i, 𝒮["PointwiseBands", ConfidenceLevel -> i][16]}, {i, clev}], Alignment -> Left]ConfidenceRange (1)
Set the confidence range for simultaneous intervals and bands:
data = {{2081, ∞}, {1602, ∞}, {1496, ∞}, {1462, ∞}, {1433, ∞}, {1377, ∞}, {1330, ∞}, {996, ∞}, {226, ∞}, {1199, ∞}, {1111, ∞}, {530, ∞}, {1182, ∞}, {1167, ∞}, 418, 383, 276, 104, 609, 172, 487, 662, 194, 230, 526, 122, 129, 74, 122, 86, 466, 192, 109, 55, 1, 107, 110, 332};𝒮 = SurvivalModelFit[data]The bands are only defined over the confidence range:
Plot[{𝒮[x], 𝒮["EqualPrecisionBands", ConfidenceRange -> {172, 383}][x]}, {x, 100, 500}, PlotRange -> {0, 1}]By default, the range is set to All:
Plot[{𝒮[x], 𝒮["EqualPrecisionBands", ConfidenceRange -> All][x]}, {x, 0, 2081}, PlotRange -> {0, 1}]Set the range to Full:
Plot[{𝒮[x], 𝒮["EqualPrecisionBands", ConfidenceRange -> Full][x]}, {x, 0, 2081}, PlotRange -> {0, 1}]ConfidenceTransform (3)
Apply transformations to confidence intervals and bands:
data = {30, 32, 26, {37, ∞}, 29, {32, ∞}, 24, {31, ∞}, {31, ∞}, 42};𝒮 = SurvivalModelFit[data]A collection of named transforms:
tr = {"Linear", "LogLog", "ArcSinSqrt", "Log", "Logit"};Grid[Table[{i, 𝒮["PointwiseBands", ConfidenceTransform -> i][40]}, {i, tr}], Alignment -> Left]"LogLog" bands and intervals are used by default:
𝒮["PointwiseBands", ConfidenceTransform -> "LogLog"] === 𝒮["PointwiseBands"]Transformations can ensure that intervals and bands are appropriately bounded:
data = {30, 32, 26, {37, ∞}, 29, {32, ∞}, 24, {31, ∞}, {31, ∞}, 42};𝒮 = SurvivalModelFit[data]Notice that the upper 95% limit is larger than 1.0 for some event times:
𝒮["EventTable", ConfidenceTransform -> "Linear"]Using a "LogLog" transform corrects this issue:
𝒮["EventTable", ConfidenceTransform -> "LogLog"]Define custom transformations:
data = {30, 32, 26, {37, ∞}, 29, {32, ∞}, 24, {31, ∞}, {31, ∞}, 42};𝒮 = SurvivalModelFit[data]Explicit definitions for the various named transforms:
tr = {"Linear", "LogLog", "ArcSinSqrt", "Log", "Logit"};
trans = {#&, Log[Log[#]]&, ArcSin[Sqrt[#]]&, Log[#]&, Log[(#/1 - #)]&};Grid[(ints = MapThread[{#1, 𝒮["PointwiseBands", ConfidenceTransform -> #2][40]}&, {tr, trans}]), Alignment -> Left]Verify that the definitions are equivalent to the named transforms:
ints[[All, 2]] == Table[𝒮["PointwiseBands", ConfidenceTransform -> i][40], {i, tr}]Text
Wolfram Research (2012), SurvivalModel, Wolfram Language function, https://reference.wolfram.com/language/ref/SurvivalModel.html.
CMS
Wolfram Language. 2012. "SurvivalModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SurvivalModel.html.
APA
Wolfram Language. (2012). SurvivalModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SurvivalModel.html