Some Reference Texts on Nomograms & Nomography




There is a considerable amount of literature on Nomograms and Nomography, much of it dating from the 1940's and 1950's. This was a time when the engineering disciplines were starting to undergo rapid change but with fairly limited calculational tools, that is, adding machines and slide rules. The demand for more rapid calculating power led to the design of custom nomograms. The books listed below seem to have been written by applied mathematicians and mechanical draftsmen. All emphasize methodologies for designing nomograms for highly specialized technical computing. The thing to notice about the design of nomograms is that issues such as (I) the ranges of the variables and (II) the choice of practical units for these variables are taken into consideration from the outset in the design process. It is regrettable that the same attention to these vital matters is not evident in the incredibly powerful, computer-based software of today. An excellent SURVEY of different types of nomograms has been compiled into a powerpoint presentation by Charles Pheatt at Emporia State U. in Kansas. If you use any of his materials, courtesy demands that you properly acknowledge the source.

H.J. Allcock and J.R. Jones, The Nomogram, 3rd ed., (London: Sir Isaac Pitman & Sons, Ltd.) 1946.

D.S. Davis, Nomography and Empirical Equations, (New York: Reinhold Publishing Corp.) 1955.
first half of book concerns empirical equations and correlations, geometric approach to charts.

D.S. Davis, Empirical Equations and Nomography, (New York: McGraw-Hill Book Co.) 1943.

R.D. Douglass and D.P. Adams, Elements of Nomography, (New York: McGraw-Hill Book Co.) 1947.
graphical approach, very methodical, avoids matrices and determinants.

M. Kraitchik, Alignment Charts: Construction and Use, (New York: D. Van Nostrand Co.) 1944.
nice basic treatment of mathematics of nomograms, uses determinant matrices throughout for generality.

L.E. Johnson, Nomography and Empirical Equations, (New York: John Wiley & Sons) 1952.
organized by equation type, scales are nicely explained, nice geometrical approach.



There are a number of papers in the medical fields that research using nomograms. Compiled below is a list of papers in the fields of Oncology, Vision, Fetal Development and Physical Therapy.

Oncology Papers:

Chen, John J; Pugach, Jeff; Patel, Manoj; Luisiri, Atchawee; Steinhardt, George F, The renal length nomogram: multivariable approach, The Journal of Urology, Volume 168, Issue 5, November 2002, Pages 2149-2152.

D'Amico, A V; Whittington, R; Malkowicz, S B; Fondurulia, J; Chen, M H; Kaplan, I; Beard, C J; Tomaszewski, J E; Renshaw, A A; Wein et al., Pretreatment nomogram for prostate-specific antigen recurrence after radical prostatectomy or external-beam radiation therapy for clinically localized prostate cancer, Journal of Clinical Oncology: Official Journal of the American Society of Clinical Oncology, Volume 17, Issue 1, January 1999, Pages 168-172.

Eastham, James A; Kattan, Michael W; Scardino, Peter T, Nomograms as predictive models, Seminars in Urologic Oncology, Volume 20, Issue 2, May 2002, Pages 108-115.

Eastham, James A.; May, Robert; Robertson, John L.; Sartor, Oliver; Kattan, Michael W. Development of a nomogram that predicts the probability of a positive prostate biopsy in men with an abnormal Digital Rectal Examination and a Prostate-Specific Antigen between 0 and 4 ng/mL. Urology, Volume 54, Issue 4, Pages 709-713.

Graefen, M.; Karakiewicz, P.; Cagiannos, I.; Hammerer, P.; Haese, A.; Palisaar, J.; Fernandez, S.; Noldus, J.; Erbersdobler, A.; Huland, H.; Scardino, P.; Kattan, M. A validation of two preoperative nomograms predicting recurrence following radical prostatectomy in a cohort of European men. Urologic Oncology, Volume 7, Pages 141-146.

Kattan, M W; Wheeler, T M; Scardino, P T, Postoperative nomogram for disease recurrence after radical prostatectomy for prostate cancer, Journal of Clinical Oncology: Official Journal of the American Society of Clinical Oncology, Volume 17, Issue 5, May 1999, Pages 1499-1507.

Kattan, Michael W.; Zelefsky, Michael J.; Kupelian, Patrick A.; Scardino, Peter T.; Fuks, Zvi; Leibel, Steven A. Pretreatment nomogram for predicting the outcome of three-dimensional conformal radiotherapy in prostate cancer. Journal of Clinical Oncology, Volume 18, Issue 19, Pages 3352-3359.

Kattan, Michael W.; Potters, Louis; Blasko, John C.; Beyer, David C.; Fearn, Paul; Cavanagh, William; Leibel, Steven; Scardino, Peter T. Pretreatment nomogram for predicting freedom from recurrence after permanent prostate brachytherapy in prostate cancer. Urology, Volume 58, Issue 3, Pages 393-399.

Kattan, Michael W.; Reuter, Victor; Motzer, Robert J.; Katz, Jared; Russo, Paul. A postoperative prognostic nomogram for renal cell carcinoma. The Journal of Urology, Volume 66,July 2001, Pages 63-67.

Khoury, Joseph M.; Marson, Lesley ; Carson, Culley C. III. A comparative study of the Abrams Griffith nomogram and the linear passive urethral relation to determine bladder outlet obstruction. The Journal of Urology, Volume 159, Issue 3, Pages 758760.

Massacesi, C.; Norman, A.; Price, T.; Hill, M.; Ross, D.; Cunningham, D. A clinical nomogram for predicting long-term survival in advanced colorectal cancer. European Journal of Urology, Volume 36, Pages 2044- 2052.

Polascik, T J; Pearson, J D; Partin, A W, Multivariate models as predictors of pathological stage using Gleason score, clinical stage, and serum prostate-specific antigen, Seminars in Urologic Oncology, Volume 16, Issue 3, August 1998, Pages 160-171.

Rabbani, Farhang; Bastar, Andrew; Fair, William. Site specific predictors of positive margins at radical prostatectomy: An argument for risk based modification of technique, The Journal of Urology, Volume 160, Issue 5, Pages 1727-1733.

Smaletz O.; Scher H.I.; Small E.J.; Verbel D.A.; McMillan A.; Regan K.; Kelly W.K.; Kattan M.W., Nomogram for overall survival of patients with progressive metastatic prostate cancer after castration, Journal of Clinical Oncology, Volume 20, Issue 19, October 2002, Pages 3972-3982.

Vision Papers:

Balazsi, G; Mullie, M; Lasswell, L; Lee, P A; Duh, Y J, Laser in situ keratomileusis with a scanning excimer laser for the correction of low to moderate myopia with and without astigmatism, Journal of Cataract and Refractive Surgery, Volume 27, Issue 12, December 2001, Pages 1942-1951.

Bashour, Mounir, Risk factors for epithelial erosions in laser in situ keratomileusis, Journal of Cataract and Refractive Surgery, Volume 28, Issue 10, October 2002, Page 1780.

Budak, K; Yilmaz, G; Aslan, B S; Duman, S, Limbal relaxing incisions in congenital astigmatism: 6 month follow-up, Journal of Cataract and Refractive Surgery, Volume 27, Issue 5, May 2001, Pages 715-719.

Dartnall, H J A, The interpretation of spectral sensitivity curves, British Medical Bulletin, Volume 9, Issue 1, 1953, Pages 24 30.

James P. Pulaski, Arcuate keratotomy for asymmetrical steep islands after laser in situ keratomileusis and automated lamellar keratoplasty, Journal of Cataract & Refractive Surgery, Volume 28, Issue 8, August 2002, Pages 1424-1432.

MacRae, S M; Peterson, J S; Koch, D D; Rich, L F; Durrie, D S, Photoastigmatic refractive keratectomy in myopes. Nidek US Investigators Group, Journal of Refractive Surgery (Thorofare, N.J.: 1995), Volume 16, Issue 2, March - April 2000, Pages 122-132.

Rao, S K; Cheng, A C; Fan, D S; Leung, A T; Lam, D S, Effect of preoperative keratometry on refractive outcomes after laser in situ keratomileusis, Journal of Cataract and Refractive Surgery, Volume 27, Issue 2, February 2001, Pages 297-302.

Shah, S; Sebai Sarhan, A R; Doyle, S J; Pillai, C T; Dua, H S, The epithelial flap for photorefractive keratectomy, The British Journal of Ophthalmology, Volume 85, Issue 4, April 2001, Pages 393-396.

Sheludchenko, V M; Fadeykina, T, Comparative results between standard and bitoric nomograms for astigmatism correction, Journal of Refractive Surgery (Thorofare, N.J.: 1995), Volume 17, Issue 2, Supplement, March - April 2001, Pages S238-S241.

Tabbara, K F; El-Sheikh, H F; Islam, S M, Laser in situ keratomileusis for the correction of hyperopia from +0.50 to +11.50 diopters with the Keracor 117C laser, Journal of Refractive Surgery (Thorofare, N.J.: 1995), Volume 17, Issue 2, March - April 2001, Pages 123-128.

Neonatal/Fetal Development Papers:

R E Ariano, D S Sitar, M Davi and S A Zelenitsky, Bayesian Pharmacokinetic Analysis of a Gentamicin Nomogram in Neonates: A Retrospective Study, Current Therapeutic Research, Volume 64, Issue 3, March 2003, Pages 178-188.

Bronshtein, M; Zimmer, E Z; Tzidony, D; Hajos, J; Jaeger, M; Blazer, S, Transvaginal sonographic measurement of fetal lingual width in early pregnancy, Prenatal Diagnosis, Volume 18, Issue 6, June 1998, Pages 577-580.

Heling, K S; Tennstedt, C; Chaoui, R; Kalache, K D; Hartung, J; Bollmann, R, Reliability of prenatal sonographic lung biometry in the diagnosis of pulmonary hypoplasia, Prenatal Diagnosis, Volume 21, Issue 8, August 2001, Pages 649-657. Malinger, G; Ginath, S; Lerman-Sagie, T; Watemberg, N; Lev, D; Glezerman, M, The fetal cerebellar vermis: normal development as shown by transvaginal ultrasound, Prenatal Diagnosis, Volume 21, Issue 8, August 2001, Pages 687-692.

Ten Hof, Judith; Nijhuis, Ilse J M; Mulder, Edu J H; Nijhuis, Jan G; Narayan, Harini; Taylor, David J; Westers, Paul; Visser, Gerhard H A, Longitudinal study of fetal body movements: nomograms, intrafetal consistency, and relationship with episodes of heart rate patterns a and B, Pediatric Research, Volume 52, Issue 4, October 2002, Pg 568-575.

Merz, E; Miric-Tesanic, D; Bahlmann, F; Weber, G; Hallermann, C, Prenatal sonographic chest and lung measurements for predicting severe pulmonary hypoplasia, Prenatal Diagnosis, Volume 19, Issue 7, July 1999, Pages 614-619.

Rosati, Paolo; Bartolozzi, Francesco; Guariglia, Lorenzo, Reference values of fetal orbital measurements by transvaginal scan in early pregnancy, Prenatal Diagnosis, Volume 22, Issue 10, October 2002, Pages 851-855.

Ulm, M R; Kratochwil, A; Oberhuemer, U; Ulm, B; Blaicher, W; Bernaschek, G, Ultrasound evaluation of fetal spine length between 14 and 24 weeks of gestation, Prenatal Diagnosis, Volume 19, Issue 7, July 1999, Pages 637-641.

Zalel Y.; Gamzu R.; Mashiach S.; Achiron R., The development of the fetal thymus: An in utero sonographic evaluation, Prenatal Diagnosis, Volume 22, Issue 2, 2002, Pages 114-117.

Zalel, Yaron; Lotan, Danny; Achiron, Reuven; Mashiach, Shlomo; Gamzu, Ronni, The early development of the fetal kidney-an in utero sonographic evaluation between 13 and 22 weeks' gestation, Prenatal Diagnosis, Volume 22, Issue 11, November 2002, Pages 962-965.

Physical Therapy Papers:

Baun, W.B.; Baun, M.R.; and Raven, P.B, A nomogram for the estimate of percent body fat from generalized equations, Research Quarterly for Exercise and Sport, Volume 52, Issue 3, 1981, Pages 380 384.

Buckley, J.; Cannon, E.; Mapp, G., The development of a nomogram for predicting VO2 max from ratings of percieved exertion during submaximal exercise on a cycle ergometer, Journal of Sports Sciences, Volume 16, Issue 1, 1998, Pages 14-15

Cibulka, M.T.; Aslin, K., How to use evidence-based practice to distinguish between three different patients with low back pain, Journal of Orthopaedic & Sports Physical Therapy, Volume 31, Issue 12, 2001, Pages 678-695.

Cohn, Peter F., A symposium: Myocardial Ischemia: Mechanisms, risk reduction, and management, The American Journal of Cardiology, Volume 73, Issue 6, March 1994, Pages 590 596.

Shepard, R.J, A nomogram to calculate the oxygen-cost of running at slow speeds, Journal of Sports Medicine and Physical Fitness, Volume 9, 1969, Pages 10 - 16.


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