stata logistic regression nomogram generator · 2015-06-24 · notice • nomogram generators for...
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Stata logistic regressionnomogram generator
Alexander Zlotnik, Telecom.Eng.Víctor Abraira Santos, PhD
Ramón y Cajal University Hospital
WORK IN PROGRESS PAPER
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NOTICE
• Nomogram generators for logistic and Coxregression models have been updated since this presentation.
• Download links to the latest program versions (nomolog & nomocox), examples, tutorialsand methodological notes are available on this webpage:http://www.zlotnik.net/stata/nomograms/
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Introduction
• Nomograms are one of the simplest, easiest and cheapestmethods of mechanical calculus. (…) precision is similar to that of a logarithmic ruler (…). Nomogramscan be used for research purposes (…) sometimes leading to new scientific results.
Source: “Nomography and its applications”G.S.Jovanovsky, Ed. Nauka, 1977
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Introduction
• Examples
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Logistic regression predictive models
• Logistic regression‐based predictive models are used in many fields, clinical research being one of them.
• Problems:– Variable importance is not obvious for some clinicians.
– Calculating an output probability with a set of input variable values can be laborious for these models, which hinders their adoption.
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Logistic regression predictive models
Source: YanSun, 2011
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• A nomogram could make this calculation much easier. Ex: Kattan nomograms for prostate cancer.
Logistic regression nomograms
Source: prostate-cancer.org
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• Output probability calculations are much easier.
• Variable importance is clear at a glance (longer the line => more important variable).
Logistic regression nomograms
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Logistic regression nomograms
• Logistic regression nomogram generation– Plot all possible scores/points (α1 xi) for each variable (X1..N).
– Get constant (α0).
– Transform into probability of event given the formula
)( 011
TPep +−+= α
Total points = TP = α1 X1+ α2 X2+…
Logistic regression nomograms
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Logistic regression nomograms
• Nomogram usage for a given case– Get input variable values, i.e. X1 =x1 , X2 =x2 …
– Obtain scores for all variables.
– Add all scores.
– Get probability (on a scale adjusted by the constant α0).
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Risk of death for a 40 year old woman, LOS (length of stay) = 20 days, Dialysis time = 75 months
Dialysis time
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Risk of death for a 40 year old woman, LOS (length of stay) = 20 days, Dialysis time = 75 months
40 years old => ~ 2.6 pointswoman => ~ 0 pointsLOS = 20 days => ~ 0.3 pointsDialisis time = 75 m => ~ 0.5 points--------------------------Total score ≈ 3.4Probability ≈ 0.05 ≈ 5%
Dialysis time
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Objectives
• Build a general‐purpose nomogram generator made entirely in Stata without external module dependence. Executable after arbitrary “logistic” or “logit” Stata commands.
• Automatic (or imposed) variable and data labeling.
• Automatic (or imposed) variable min/max, divisions, variable labels, dummy data labels.
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Stata programming Gotchas
• Macro string variables limited to 244 chars.
Solution: strL? Stata 13?
• Hard‐to‐grasp macro nesting syntax.
• Lack of built‐in data structures (non‐numeric arrays, dictionaries, lists, etc).
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• Lack of decent debugger (set trace on/off is not enough).
• Steep learning curve for error interpretation.
• Unit testing is hard to implement.
Stata programming Gotchas
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Programming techniques
• Time series graph hacks.
• logit & logistic outputs.
• Variable & data labels.
• Macro nesting.
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Programming techniques
• Time series graph hacks
Actual data point
Fictitious data points
myTime
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Programming techniques
• Logit & logistic outputs
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Programming techniques
• Custom data structures
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Programming techniques
• Variable & data labels
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Programming techniques
• Macro nesting
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Execution example
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Variablelabels are used if defined
Variablelabels are used if defined
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Positive coefficients
• Usually, positive coefficients are required in these nomograms in order to ease calculations (no substractions to get total score).
• Due to the linear nature of the TP term, it is easy to make all coefficients positive.
)( 011
TPep +−+= α
TP = α1 X1+ α2 X2+…
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Positive coefficients
• This can be done manually.
• Let’s see an example…logit muerto edadr ib1.Gtrata tpodial ib2.hbsagdon
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(Gtrata)
(hbsagdon)
Some dummy coefficients are negative
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Positive coefficients
• The most negative coefficient in Gtrata is “‐(3) Tacro”, i.e. data value 3.
• Hence, instead oflogit muerto edadr ib1.Gtrata tpodial ib2.hbsagdon
we use…logit muerto edadr ib3.Gtrata tpodial ib2.hbsagdon
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Now all dummy coefficients are positive(Gtrata)
(hbsagdon)
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• The program also can perform this operation automatically (work in progress).
• Since coefficients are linearly related, they do not need to be recalculated.
Positive coefficients
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Results
• Supports any kind of variable ordering.
• Supports negative coefficients.
• Supports omitted variables due to collinearity.
• Works after an almost arbitrary regression command.
• Let’s see execution modes & parameters…
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Remember the custom data structure
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Execution modes
• Automatic: everything is determined automatically.
• Manual: define all parameters manually (laborious).
• Hybrid: get some stuff automatically and refine it manually. For example: variable range is 14 to 81 and we want to make it 10 to 100 leaving all other variables as they are.
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Hybrid mode
The “edadr” coefficient does not change
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• Since the output is a standard Stata graph, it may be edited for further adjustments.
By the way…
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Other execution options
• iMaxVarLabelLen = 30 //Max N of chars to display in variable labels
• iMaxDataLabelLen = 30 //Max N of chars to display in data value labels
• iVarLabDescr = 0//Use variable description as variable label when possible (0=no; 1=yes)
• iDummyLabWithValues = 1 //Show data values on dummy data value labels (0=no; 1=yes)
• iCoefForcePositive = 0 //Force positive coefs (0=no; 1=yes)
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Limitations
• Dummy syntax must be “bx.var”.
• No interaction operators (“#”, “##”) allowed.
• Maximum of 15 variables (xtline command options overflow). Suggestions?
• Categorical variables have a limit of with 40 dummys each (easy to supersede if needed).
• Several performance improvements possible (max. string length).
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Structure of Presentation
• Introduction• Logistic regression nomograms• Objectives• Stata programming Gotchas• Programming techniques• Results• Limitations• Future work
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Future work
• Overcoming Stata limits: string variables, xtline command.
• Better drawing adjustments (fonts, axis, etc).
• Interaction operators support.
• Cox regression nomograms.
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Questions?
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Backup slides
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Dummy coefficient re‐adjustment
• Given a categorical variable “A” with N cátegoriesand a regression constant α0
z = α0 + αA1 ∙ D1 + αA2 ∙ D2 + … + αAN ∙ DN
If αAi i=1..N< 0,
we set as reference the most negative coefficienti.e. min(αAi i=1..N
)
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Dummy coefficient re‐adjustment
)( 011
TPep +−+= α
TP = αA1 · D1 + αA2 · D2 + …
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Dummy coefficient re‐adjustment
• And then
z = β0 + βA1 ∙D1 + βA2∙D2 + … + βAN∙DN
whereβ0 = α0 ‐min(αAi i=1..N
)β1 = α1 ‐min(αAi i=1..N
)…βN = αN ‐min(αAi i=1..N
)
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Some dummy coefficients are negative
Normal execution
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All coefficients are forced to be positive
This causes a displacement in the Total score to Prob conversion (due to α0)
Execution with forced positive coefficients