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CoxModel […]

represents the symbolic proportional hazards model obtained from CoxModelFit .

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Options  
ConfidenceLevel  
ConfidenceRange  
ConfidenceTransform  
See Also
Related Guides
History
Cite this Page

CoxModel […]

represents the symbolic proportional hazards model obtained from CoxModelFit .

Details and Options

  • Properties of a Cox model are obtained from CoxModel […]["property"].
  • CoxModel […][{prop1,prop2,…}] gives several properties.
  • CoxModel[…][x0][t] gives the value of the best-fit function at a particular point t for covariate levels x0.
  • Normal gives the expression for the baseline survival function in a CoxModel .
  • CoxModel […][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 CoxModelFit that generate the model.
  • CoxModel takes the following options:
  • ConfidenceLevel confidence level to use for parameters and predictions
    ConfidenceRange All range for simultaneous confidence bands
    ConfidenceTransform "LogLog" confidence transform to use

Examples

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Basic Examples  (1)

Create a CoxModel from some right-censored data:

Wolfram Language code: data = EventData[{1, 2, 3, 4}, {0, 0, 1, 0}];
Wolfram Language code: mod = CoxModelFit[data]

Extract a property from the model:

Wolfram Language code: mod["EventTimes"]

Evaluate the baseline survival function at 3:

Wolfram Language code: mod[3]

Scope  (6)

Extract a property from a CoxModel object:

Wolfram Language code: mod = CoxModelFit[{1, 2, 3, 4}]

The standard errors for the baseline survival function:

Wolfram Language code: mod["StandardErrors"][]

Extract multiple properties:

Wolfram Language code: mod = CoxModelFit[{1, 2, 3, 4}]
Wolfram Language code: mod[{"MartingaleResiduals", "CoxSnellResiduals"}]

Obtain a list of available properties:

Wolfram Language code: mod = CoxModelFit[{1, 2, 3, 4}]
Wolfram Language code: mod["Properties"]

Evaluate the baseline survival function at a point:

Wolfram Language code: mod = CoxModelFit[{1, 2, 3, 4}];
Wolfram Language code: mod[2]

Map over several points:

Wolfram Language code: mod /@ {1, 2, 3, 4}

Use Normal to obtain an expression for the baseline survival function:

Wolfram Language code: mod = CoxModelFit[{1, 2, 3, 4}];
Wolfram Language code: Normal[mod]

Annotate a property:

Wolfram Language code: mod = CoxModelFit[{1, 2, 3, 4}];
Wolfram Language code: Table[Row[{i, ": ", mod["BaselineList", i]}], {i, {"Description", "LongDescription"}}]//TableForm

Options  (5)

ConfidenceLevel  (3)

The confidence level can be changed after fitting:

Wolfram Language code: ξ = {{67, 1}, {11, 0}, {32, 0}, {50, 1}, {65, 1}, {44, 1}, {20, 1}, {26, 0}, {69, 1}, {50, 1}, {25, 1}, {18, 0}, {63, 1}, {41, 0}, {30, 0}, {32, 1}, {46, 1}, {35, 0}, {33, 0}, {22, 0}}; e = EventData[Automatic, {{8, 22, 6, 4, 12, 11, 2, 34, 25, 15, 8, 6, 34, 6, 32, 1, 15, 9, 9, 6}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0}, None}];
Wolfram Language code: model = CoxModelFit[{ξ, e}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[x, 1], Subscript[x, 2]}]

Plots of baseline survival with pointwise confidence bands:

Wolfram Language code: Table[Plot[Evaluate@{model["SF"][][t], model["PointwiseBands", "SF", ConfidenceLevel -> i][][t]}, {t, 0, 35}, PlotLabel -> i], {i, {.9, .95, .99}}]

Change the confidence level for parameter confidence intervals:

Wolfram Language code: ξ = {{67, 1}, {11, 0}, {32, 0}, {50, 1}, {65, 1}, {44, 1}, {20, 1}, {26, 0}, {69, 1}, {50, 1}, {25, 1}, {18, 0}, {63, 1}, {41, 0}, {30, 0}, {32, 1}, {46, 1}, {35, 0}, {33, 0}, {22, 0}}; e = EventData[Automatic, {{8, 22, 6, 4, 12, 11, 2, 34, 25, 15, 8, 6, 34, 6, 32, 1, 15, 9, 9, 6}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0}, None}];

Use default confidence level:

Wolfram Language code: model = CoxModelFit[{ξ, e}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[x, 1], Subscript[x, 2]}];
Wolfram Language code: model["ParameterConfidenceIntervals"]

The level can be changed after fitting:

Wolfram Language code: Table[model["ParameterConfidenceIntervals", ConfidenceLevel -> i], {i, {.85, .9, .95}}]

Specify confidence level in summary tables:

Wolfram Language code: ξ = {{67, 1}, {11, 0}, {32, 0}, {50, 1}, {65, 1}, {44, 1}, {20, 1}, {26, 0}, {69, 1}, {50, 1}, {25, 1}, {18, 0}, {63, 1}, {41, 0}, {30, 0}, {32, 1}, {46, 1}, {35, 0}, {33, 0}, {22, 0}};
Wolfram Language code: model = CoxModelFit[{ξ, EventData[Automatic, {{8, 22, 6, 4, 12, 11, 2, 34, 25, 15, 8, 6, 34, 6, 32, 1, 15, 9, 9, 6}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0}, None}]}, {Subscript[x, 1], Subscript[x, 2]}, {Subscript[x, 1], Subscript[x, 2]}]

Summarize the cumulative hazard function with 90% confidence limits:

Wolfram Language code: model["EventTable", "CHF", ConfidenceLevel -> .90][{50, 1}]

ConfidenceRange  (1)

Set the confidence range for simultaneous intervals and bands:

Wolfram Language code: model = CoxModelFit[EventData[Automatic, {{{2081, Infinity}, {1602, Infinity}, {1496, Infinity}, {1462, Infinity}, {1433, Infinity}, {1377, Infinity}, {1330, Infinity}, {996, Infinity}, {226, Infinity}, {1199, Infinity}, {1111, Infinity}, {530, Infinity}, {1182, Infinity}, {1167, Infinity}, 418, 383, 276, 104, 609, 172, 487, 662, 194, 230, 526, 122, 129, 74, 122, 86, 466, 192, 109, 55, 1, 107, 110, 332}, None, None}]]

The bands are only defined over the confidence range:

Wolfram Language code: Plot[Evaluate@{model["SF"][][x], model["EqualPrecisionBands", ConfidenceRange -> {172, 383}][][x]}, {x, 100, 500}, PlotRange -> {0, 1}]

By default, the range is set to All :

Wolfram Language code: Plot[Evaluate@{model["SF"][][x], model["EqualPrecisionBands", ConfidenceRange -> All][][x]}, {x, 0, 2081}, PlotRange -> {0, 1}]

Set the range to Full :

Wolfram Language code: Plot[Evaluate@{model["SF"][][x], model["EqualPrecisionBands", ConfidenceRange -> Full][][x]}, {x, 0, 2081}, PlotRange -> {0, 1}]

ConfidenceTransform  (1)

Apply transformations to confidence intervals and bands:

Wolfram Language code: ξ = {1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0};
Wolfram Language code: model = CoxModelFit[{ξ, EventData[Automatic, {{8, 22, 6, 4, 12, 11, 2, 34, 25, 15, 8, 6, 34, 6, 32, 1, 15, 9, 9, 6}, {0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0}, None}]}, x, x]

A collection of available transforms:

Wolfram Language code: tr = {"Linear", "LogLog", "ArcSinSqrt", "Log", "Logit"};

Bands for survival function at time 15:

Wolfram Language code: Table[{i, model["PointwiseBands", "SF", ConfidenceTransform -> i][][15]}, {i, tr}]//Grid

Visualize the bands:

Wolfram Language code: Table[Plot[Evaluate@{model["SF"][][t], model["PointwiseBands", "SF", ConfidenceTransform -> i][][t]}, {t, 0, 35}, PlotLabel -> i], {i, tr}]

"LogLog" bands and intervals are used by default:

Wolfram Language code: model["PointwiseBands", ConfidenceTransform -> "LogLog"][{0}][15]
Wolfram Language code: model["PointwiseBands"][{0}][15]
Wolfram Research (2012), CoxModel, Wolfram Language function, https://reference.wolfram.com/language/ref/CoxModel.html.

Text

Wolfram Research (2012), CoxModel, Wolfram Language function, https://reference.wolfram.com/language/ref/CoxModel.html.

CMS

Wolfram Language. 2012. "CoxModel." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/CoxModel.html.

APA

Wolfram Language. (2012). CoxModel. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/CoxModel.html

BibTeX

@misc{reference.wolfram_2026_coxmodel, author="Wolfram Research", title="{CoxModel}", year="2012", howpublished="\url{https://reference.wolfram.com/language/ref/CoxModel.html}", note=[Accessed: 14-August-2026]}

BibLaTeX

@online{reference.wolfram_2026_coxmodel, organization={Wolfram Research}, title={CoxModel}, year={2012}, url={https://reference.wolfram.com/language/ref/CoxModel.html}, note=[Accessed: 14-August-2026]}
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