# Nomograms

## Nomograms are predictive tools that give relative contexts and probabilities of clinical outcomes

Nomograms are visual and mathematical tools that allow clinicians, researchers, patients, and members of a population to give relative context and probabilities related to developing clinical outcomes. Nomograms can predict for the probability of a clinical outcome based upon the presence of pertinent risk factors, confounders, and predictor variables. All nomograms are based on

__that are used to predict for outcomes. The type of regression model used for a nomogram depends upon the scale of measurement of the outcome.__**regression models**__,__**Logistic regression**__, and__**multinomial logistic regression**__are used to build nomograms for categorical and ordinal outcomes. If the "time-to-event" for developing an outcome is the basis for creating a nomogram, then__**proportional odds regression**__or__**Kaplan-Meier**__analysis can be used.__**Cox regression**__, when statistical assumptions are met, is used to build nomograms for continuous outcomes.__**Multiple regression**__or__**Poisson regression**__can be used to build nomograms for count outcomes (naturally skewed distributions).__**negative binomial regression**### Steps for creating a nomogram

This methodology was published by Iasonos et al.*:

1. The first step in creating a nomogram is to explicitly define the population of interest that the nomogram will be applied to in clinical practice. The population should be defined in an

2. The second step in creating a nomogram is to operationally define the outcome of interest. Describing the outcome in a precise and accurate fashion is important when creating nomograms. Remember, the whole purpose of a nomogram is to be able to predict for the probability of an outcome occurring. Therefore, the outcome needs to be as precise and accurate as possible and be easily understood by both clinicians and patients.

3. The third step in creating a nomogram is to select several covariates that have a pathophysiological link to the outcome of interest. When building a nomogram, all potential covariates associated with an outcome should be included in the model, so long as they all fit in the pathophysiology of developing the outcome. The covariates should be selected in an

4. The fourth step in creating a nomogram is to select a prediction model, the covariates to be entered into the model, and make sure that all of the statistical assumptions of the prediction model (regression) are met. The type of regression to be used for a nomogram is based upon the scale of measurement of the outcome. The covariates are chosen based on the available data, the pathophysiological framework associated with the disease state, and clinical evidence. The types of statistical assumptions that are tested in all regression models such as multicollinearity, interactions, normality, homoscedasticity, and model fit (residual analysis).

5. The fifth step is to finalize the prediction model using validation, discrimination, and calibration methods. Validation methods include cross-validation (

6. The sixth step is to interpret the final nomogram that has been validated and assessed for concordance and model fit. The relative effects of each covariate are converted into a point scale ranging from 0 to 100. These "scores" for each covariate are added together and correspond to the predicted probability of a patient having the outcome of interest. The scoring method is as follows:

Take the covariate with the highest beta value (regardless of statistical significance) and assign it 100 points. With the rest of the covariates, divide their respective beta values by the highest beta value to yield the amount of points they represent in the nomogram. By doing this, researchers are assigning points to other covariates proportionally based on their effect size in relation to the largest beta value. Add up all the points from all of the covariates in the model and match them to the corresponding predicted probability yielded from the regression model.

7. The seventh and final step is to correctly apply and/or generalize the nomogram in clinical practice. Clinicians should ask themselves the following: Does the patient have clinical and prognostic similarities to the population used when validating the nomogram? Are all the pertinent/correct covariates accounted for in the nomogram as it relates to your patient? Do the point estimates of the regression model make sense in your current clinical context? What degree of uncertainty do you have with the nomogram and its underlying regression model? Can you provide patients with a probability that contains uncertainty or varying effects from patient to patient?

1. The first step in creating a nomogram is to explicitly define the population of interest that the nomogram will be applied to in clinical practice. The population should be defined in an

*a priori*fashion with thorough inclusion and exclusion criteria. It is preferable to have population-level data when building nomograms because it allows for the model to be more generalizable. The ability of clinicians to correctly apply the predicted probabilities of a nomogram is entirely dependent upon how well they understand the population of interest that the nomogram was based upon.2. The second step in creating a nomogram is to operationally define the outcome of interest. Describing the outcome in a precise and accurate fashion is important when creating nomograms. Remember, the whole purpose of a nomogram is to be able to predict for the probability of an outcome occurring. Therefore, the outcome needs to be as precise and accurate as possible and be easily understood by both clinicians and patients.

3. The third step in creating a nomogram is to select several covariates that have a pathophysiological link to the outcome of interest. When building a nomogram, all potential covariates associated with an outcome should be included in the model, so long as they all fit in the pathophysiology of developing the outcome. The covariates should be selected in an

*a priori*fashion and should be grounded in clinical evidence rather than statistical significance.4. The fourth step in creating a nomogram is to select a prediction model, the covariates to be entered into the model, and make sure that all of the statistical assumptions of the prediction model (regression) are met. The type of regression to be used for a nomogram is based upon the scale of measurement of the outcome. The covariates are chosen based on the available data, the pathophysiological framework associated with the disease state, and clinical evidence. The types of statistical assumptions that are tested in all regression models such as multicollinearity, interactions, normality, homoscedasticity, and model fit (residual analysis).

5. The fifth step is to finalize the prediction model using validation, discrimination, and calibration methods. Validation methods include cross-validation (

__and__**split-group validation**__) and external validation (seeing if the model holds up with a new population or dataset). Predictive accuracy of discrimination is how well a model differentiates between patients with and without the outcome of interest. Discrimination is assessed by the concordance index (or c-index) that is yielded from__**bootstrap validation**__(c-statistics or area under the curve, "AUC"). Calibration of regression models is measured by plotting the predicted probabilities of the model against the actual probabilites. This is also known as residual analysis. Calibration is essential a measure of model fit.__**ROC analyses**6. The sixth step is to interpret the final nomogram that has been validated and assessed for concordance and model fit. The relative effects of each covariate are converted into a point scale ranging from 0 to 100. These "scores" for each covariate are added together and correspond to the predicted probability of a patient having the outcome of interest. The scoring method is as follows:

Take the covariate with the highest beta value (regardless of statistical significance) and assign it 100 points. With the rest of the covariates, divide their respective beta values by the highest beta value to yield the amount of points they represent in the nomogram. By doing this, researchers are assigning points to other covariates proportionally based on their effect size in relation to the largest beta value. Add up all the points from all of the covariates in the model and match them to the corresponding predicted probability yielded from the regression model.

7. The seventh and final step is to correctly apply and/or generalize the nomogram in clinical practice. Clinicians should ask themselves the following: Does the patient have clinical and prognostic similarities to the population used when validating the nomogram? Are all the pertinent/correct covariates accounted for in the nomogram as it relates to your patient? Do the point estimates of the regression model make sense in your current clinical context? What degree of uncertainty do you have with the nomogram and its underlying regression model? Can you provide patients with a probability that contains uncertainty or varying effects from patient to patient?

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*Iasonos A, Schrag D, Raj GV, Panageas KS. How to build and interpret a nomogram for cancer prognosis.

*Journal of Clinical Oncology*, 2008; 26; 1364-1370.
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