# Getting the optimal age cut off

I am working with a database of diseased and non-diseased patients. I would like to recommend an optimal age cut off for disease screening. The common problem with screening is that it creates a large number of false positive, which is directly related to the positive predictive (PPV). The PPV in turn, is affected by the prevalence.

In a nutshell, I would like to derive an age that provides the best trade-off where I will be able to:

1. retain a large percentage of the diseased patients and
2. drop a large percentage of non-diseased patients.

The central idea is to avoid unnecessary screening of patients who have relatively low probability of having the disease.

In this case, the independent variable is the age while the dependent variable diseased, non diseased.

I tried running an ROC curve to get the optimal balance by the comparing highest Youden statistic.

I'll like to know if there's a better way to do this or if what I am is acceptable. Please do let me know if you anything I've mentioned is unclear. Thank you very much.

• ROC curve is the standard way to get optimal cut-off values.
– rnso
Commented Mar 23, 2015 at 6:00
• This is the kind of situation where any reasonable meaning that can be given to "optimal" has to take into account the relative costs of false positive & false negative results, as well as the prevalence of the disease. Commented Mar 23, 2015 at 9:40
• I should also have mentioned that it's very likely the kind of situation in which it would be extremely inappropriate not to consult a medical statistician before making any final decision. Commented Mar 23, 2015 at 10:05
• In addition, what you are saying in effect is that age has a discontinuous effect on outcome and that the decision point for one patient depends on other patients. Neither of these assumptions is correct. ROC analysis plays no role in decision making except for mass one-time decisions where utilities are unknowable. Commented Mar 23, 2015 at 12:14
• @bluemudpie : you should post some details about your data / figure here for better analysis.
– rnso
Commented Mar 23, 2015 at 13:23

The easiest thing to do would be to first bin your data by age groups.

Then for disease and non disease I would go with using odds ratio and risk ratio calculations. Odds ratios are used to compare the relative odds of the occurrence.

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2938757/

You should be able to grab the data used in a two-by-two frequency table (diseased and non-diseased patients) (screened and no screened)

Then plug and chug in the odds ratio equation. The higher the odds ratio means higher odds of getting the disease.

Another way to do this is to use a Q-Q plot but it is not used as often in the medical field https://en.wikipedia.org/wiki/Q%E2%80%93Q_plot

• This will cause a great many problems and result in misleading interpretations of what are truly continuous age effects. Better is to model age as a smooth nonlinear effect using for example a regression spline. Commented Mar 24, 2015 at 12:11