The advantage of nomograms is that they incorporate all relevant continuous predictive factors for individual patients, thus providing a more accurate prediction than models based on risk grouping. They usually also surpass clinical experts at outcome’s prediction by calculating probabilities in a uniform fashion. The superior performance has been shown by several studies comparing nomograms to risk-grouping schemata, in part, due to substantial heterogeneity within risk group categories. A good example of the heterogeneity inherent in risk groups is shown in Fig. 7.2 where the 5-year progression-free probability (PFP) after radical prostatectomy was calculated for patients classified as low-, medium-, and high-risk using the criteria by D’Amico et al. [5]. The graph shows a substantial distribution of intermediate- and high-risk patients across the spectra of nomogram probabilities; clearly, it would be incorrect to call a patient “high-risk” if their likelihood of being free of cancer progression at 5 years exceeded 90 %. This highlights the substantial heterogeneity within risk group’s categories and as such, is useful for gauging the prognosis for that specific group of patients, not necessarily the individual patient. A nomogram should be able to be tailored to an individual patient, as this is what is most important to the patient, that is his individual prognosis not that of a group.

A nomogram can be used to personalize the prediction of outcomes for an individual based on his unique characteristics. The complexity of nomograms over risk groups enhances the predictive accuracy for both the patient and the physician. While cumbersome to use in paper form (and nearly impossible to calculate in one’s head!), the availability of the nomograms in on-line web format in the public domain facilitates their use in the setting of a busy clinic (http://​www.​nomograms.​org or htttp://www.​clinicriskcalcul​ators.​org).

One way to illustrate the superior predictive performance of nomograms relative to risk groups is to compare several staging nomograms to the “Partin Tables.” The Partin tables take into account serum PSA (four categories), clinical stage (seven categories), and biopsy Gleason sum (five categories) to predict pathological stage of prostate cancer. Then the patient is assigned to one of the four mutually exclusive groups (organ confined, established extraprostatic extension (EPE), seminal vesicle invasion (SVI), or lymph node involvement (LNI)). In a review of our institution’s prostate cancer database, the predictive accuracy of the “Partin Tables” for predicting organ-confined disease, SVI, and LNI was 0.71, 0.72, and 0.74, respectively [6]. These tables underestimate the probability of EPE, since a substantial proportion of patients with lymph node metastases and SVI will also have EPE. A more accurate predictive model is done with having each variable as a continuous variable. Thus, PSA, clinical stage, and Gleason sum when modeled as a continuous variable had a concordance index for predicting organ-confined disease, SVI, and LNI of 0.74, 0.84, and 0.76, respectively (Bianco FJ Jr et al., unpublished data).

Some general principles need to be taken into consideration with designing a predictive model. First is discrimination, the model should accurately predict which patients will and will not reach the endpoint. Next calibration, the model should be able to make predictions that reflect actual outcomes. And finally, validation, the model should perform consistently when applied to different data sets. Careful consideration should be taken when determining the patient population that the model will be based on. The model should have an index patient that is representative of the general population to whom the model will be applied. The treatments being received by the cohort population should mirror those of the general population. There should be a built-in broad applicability to the model. Trying to define a very specific population or to model after a population with uncommon treatment modalities will limit the model’s application to future patients. A good predictive model should not only be based on enough cases to be able to reach specific endpoints, but also have an appropriate number of variables. The model should include variables that are statistically significant and those that are not statistically significant (if there is a strong clinical rationale for including them). Including only significant variables will result in falsely narrowed confidence intervals (CI) that make the model appear more accurate than it is, secondary to the inappropriately large influence exerted by these variables. A well-constructed model will repeatedly perform with similar accuracy when applied to heterogeneous novel populations, hence exemplify generalizability. Factors that diminish this concept are when a prognostic model’s data set is too small, not all the variables are recorded correctly or large portions missing, or too many variables are used. In the clinical setting, the value of a nomogram is when it is easy to use and it uses parameters that are routinely employed and reliable. The ease of use is important, because even though a model may be very accurate, if it proves cumbersome to use, then it loses its practicality in the clinical setting.

Kattan and colleagues developed nomograms based on Cox proportional hazards or logistic regression analysis modified by restricted cubic splines. The use of cubic splines has the benefit of being able to use continuous variable while maintaining a nonlinear relationship. When using unmodified regression models, they require variables to assume linear relationships, which is not ideal because it assumes that the weight assigned to incremental changes is the same across the spectrum. For example, a rise in PSA from 3 to 6 ng/mL would have the same impact as a rise from 303 to 306 ng/mL. In theory, machine learning modeling methods (e.g., artificial neural networks) may lead to enhanced predictive accuracy as they offer greater flexibility than traditional statistical methods. This is especially true if data sets contain highly predictive nonlinear or interactive effects. In spite of this, traditional statistical methods seem to perform as well as machine learning methods and provide the added advantage of reproducibility and interpretability through the generation of hazard ratios and tests of significance for the predictors.

A benefit of nomograms is that they maximize the available information in a data set, in return obtaining the most value out of each variable. An example is when looking at a Gleason score, as it may be further defined by the primary and secondary Gleason grades and then each may be used as independent variables, rather than using the Gleason score alone, especially since various combinations of primary/secondary Gleason grades can result in the same Gleason score (e.g., 3 + 4 = 7 and 4 + 3 = 7) yet reflect quite different disease states with different prognoses [7].

Many nomograms that predict cancer recurrence incorporate an important concept of how patients who receive secondary treatment before demonstrating disease progression are classified as treatment failures. As the secondary treatment was most likely triggered by an adverse feature associated with a high risk of recurrence or some evidence of recurrence, therefore it is presumed that the treatment is given shortly before the recurrence would have declared itself [8]. One could exclude these patients from the nomogram, but censoring (or excluding) them would bias the nomogram towards improved outcomes. Including these patients but assigning treatment failure at the time of adjuvant therapy may lead to overly pessimistic predictions. A different and favored approach is to view the use of secondary therapy as a time-dependent covariate instead of as a fixed parameter like pathological stage.

Rather than the area under the receiver operator characteristic curve (AUC), the discrimination of these nomograms is measured using the concordance index (or c-index). The c-index functions in the presence of case censoring and is more appropriate for analyzing survival or time-to-event data, while the AUC requires binary outcomes (e.g., yes/no).

Nomograms are calibrated and then validated to determine accuracy. If an external validation (i.e., the gold standard) is not possible for evaluating accuracy and reproducibility, then internal validation methods may be used, such as jackknife, leave-one-out cross-validation, and bootstrapping. These are considered legitimate alternatives that can be used alone or together with external validation to assess the nomograms accuracy.