Skip to main content
Browse Subject Areas

Click through the PLOS taxonomy to find articles in your field.

For more information about PLOS Subject Areas, click here.

  • Loading metrics

CalPen (Calculator of Penetrance), a web-based tool to estimate penetrance in complex genetic disorders


25 Jun 2020: Addepalli A, Kalyani S, Singh M, Bandyopadhyay D, Naga Mohan K (2020) Correction: CalPen (Calculator of Penetrance), a web-based tool to estimate penetrance in complex genetic disorders. PLOS ONE 15(6): e0235547. View correction


Mutations conferring susceptibility to complex disorders also occur in healthy individuals but at significantly lower frequencies than in patients, indicating that these mutations are not completely penetrant. Therefore, it is important to estimate the penetrance or the likelihood of developing a disease in presence of a mutation. Recently, a method to calculate penetrance and its credible intervals was developed on the basis of the Bayesian method and since been used in literature. However, in the present form, this approach demands programming skills for its utility. Here, we developed ‘CalPen’, a web-based tool for straightforward calculation of penetrance and its credible intervals by entering the number of mutations identified in controls and patients, and the number of patients and controls studied. For validation purposes, we show that CalPen-derived penetrance values are in good agreement with the published values. As further demonstration of its utility, we used schizophrenia as an example of complex disorder and estimated penetrance values for 15 different copy number variants (CNVs) reported in 39,059 patients and 55,084 controls, and 145 SNPs reported in 45,405 patients and 122,761 controls. CNVs showed an average penetrance of 7% with 22q11.21 CNVs having highest value (~20%) and 15q11.2 deletions with lowest value (~1.4%). Most SNPs, on the other hand showed a penetrance of 0.7% with rs1801028 having the highest penetrance (1.6%). In summary, CalPen is an accurate and user-friendly web-based tool useful in human genetic research to ascertain the ability of the mutation/ variant to cause a complex genetic disorder.


In contrast to the simple Mendelian disorders where mutation of a gene is always associated with the disease, in case of complex disorders, mutations in multiple genes are not always associated with the disease but contribute as risk factors. Therefore, the risk-conferring mutations are also found in normal controls. In this context, geneticists use statistics to determine first whether the mutation occurs at a significantly higher frequency in patients than in controls to establish an association. Once such significant association is established, it becomes important to determine penetrance (likelihood of causing the disease) of the mutation. Accordingly, a mutation can be either completely (100%) penetrant in which the presence of mutation definitively causes the disease or highly penetrant (there is more than 50% chance that the presence of mutation causes the disease) or low penetrant (there is less than 50% likelihood that the mutation causes the disease) [1]. However, in complex genetic disorders, the identified mutations are often incompletely (<100%) penetrant [2]. In order to calculate penetrance for a mutation conferring risk for a complex disease, Vassos et al [3] developed a Bayesian method, which is currently being used worldwide. According to this method, five types of data are needed: (i) the number of mutations identified in a patient sample, (ii) the number of patients studied, (iii) the number of mutations identified in the control sample, (iv) the number of controls studied and, (v) the general incidence of the disease under investigation in the population from which patients and controls are sampled (lifetime morbidity risk or baseline risk). This method involved simulation using the R statistical package to make prior distributions based on the observed frequencies in controls and patients. From these curves, 2.5th, 50th and 97.5th percentiles are extracted to obtain the median penetrance and its ~95% credible intervals. However, these calculations require programming skills which are generally not familiar to geneticists. Given these difficulties, a user-friendly web-based tool is desirable for direct determination of penetrance and its credible intervals without going through the need for programming skills. If such tool is available, then it would enable calculation of penetrance for mutations reported in a number of studies for common disorders and may eventually result in a database that will be useful in prenatal genetic screening and genetic counselling.

Here, we used python interface to develop ‘CalPen’, a free web-based tool, that enables calculation of penetrance and its ~95% credible intervals. We show that the values obtained using CalPen were in good agreement with the reported values. Using published data, we also estimated penetrance and credible intervals for the 15 most replicated copy number variants reported in schizophrenia patients from multiple studies. We also show a wider utility of CalPen by estimating penetrance using information on 145 SNPs significantly associated with schizophrenia.

Materials and methods

Description of the code

The python script developed is deposited in GitHub software development platform ( and in the supporting files (S1 and S2 Files). Briefly, penetrance is calculated using population-based probabilistic method using the published dataset of the copy number variations (CNVs) at different locations in the genomes of schizophrenia patients and controls, wherein the data selection criteria were identical as described by Vassos et al. [3]. Based on the number of mutations identified in a given sample of controls and patients, median penetrance values were calculated from the formula:

Wherein P(D|G)] is the penetrance or the probability of developing the disease (D) for patients with genotype (G) carrying the CNV. P(G|D) is the frequency of the CNV in patients, P(D) is the lifetime morbid risk (baseline risk) for the disease, is the frequency of the CNV in controls and is the probability that an individual is normal (1 –P(D)).

For determination of the credible intervals, we first derived binomial prior distributions for controls and patients for each mutation by Wilson’s method [4] using Python ver. 3.5 and SciPy package ver. 1.2. These prior distributions were generated using the respective frequencies of mutations as the mean values for both cases and controls. For each prior distribution, the value corresponding to Mean + 2 σ gave the 97.5th percentile value whereas Mean—2σ gave the 2.5th percentile value (σ represents standard deviation). From the 2.5th and 97.5th percentiles of controls and patients, the upper bound and lower bounds of the credible intervals were calculated for each mutation by Bayesian method as follows

Wherein f97.5 and f2.5 correspond to the frequencies (proportions) at 97.5th and 2.5th percentiles respectively.

Development of the web-based tool

The web application was created using Python Flask (a web application framework written in Python to develop websites; and PythonAnywhere (; an online integrated development environment and web-hosting service based on the Python programming at HTML was used to allow the user to use a graphical user interface (GUI). Features were added so that this web-based HTML application alerts the user if any of the five valid inputs are not provided.

Validation of CalPen

We used Pearson correlation coefficient as a means of validating the CalPen-derived penetrance values against those obtained in two published reports [3, 5]; (Table 1)]. For this purpose, the lifetime morbidity risk (baseline risk), the number of mutations and the sample sizes used were obtained from the reports and the values were entered in the dialog boxes of CalPen to obtain penetrance values and their credible intervals. Correlation coefficient for median penetrance was calculated and scatter plots were made using Microsoft excel 2016 [6]. In case of credible intervals, coefficient of range was calculated using the formula using values from CalPen and published reports

The individual values of the coefficients were then used to calculate the correlation coefficient and obtain scatter plots.

Table 1. Details of schizophrenia-associated copy number variants (CNVs) identified in different case-control studies.

The reported penetrance values were used for comparison with the values obtained using CalPen. Credible intervals are shown in brackets. Data for CNVs numbered 1–8 were taken from Vassos et al. (2009; ref. 3) whereas from 9–21 were taken from Rosenfeld et al. (2011; ref. 5. del: deletion, dup: duplication.

Tests of significance

We used two methods to determine whether there is a significant difference in penetrance values reported and those obtained by CalPen. First, we used an online tool ( and calculated the P value for obtaining the correlation coefficient (r) against n-2 degrees of freedom. As an independent approach, we also performed a χ2 test of association using the reported penetrance values as expected and Calpen values as observed values ( A P value < 0.05 is taken as significant.

Determination of penetrance values for CNVs and SNPs associated with schizophrenia

In order to obtain a more comprehensive estimates of penetrance for different CNVs found to be associated with schizophrenia (SZ), we identified a report suggesting 15 different CNVs that seem to have a better probability of getting replicated in future studies [7]; (Table 2). We then performed a thorough literature search and extracted the frequencies of these 15 CNVs from different case-control studies [814]. In addition, we also obtained frequencies from a different set of case-control studies that identified 145 SNPs associated with schizophrenia [1529]; (Table 3). Of these, 128 were identified by the Psychiatric Genetics Consortium [29]. Using the sample sizes, the frequencies of these CNVs from these reports and the lifetime morbidity risk (baseline risk) of 0.7% [30], we calculated penetrance and the credible intervals.

Table 2. Published data on Schizophrenia–associated CNVs used for calculation of penetrance using CalPen.

Del: Deletion; Dup: Duplication. Filled boxes indicate the identified CNV.

Table 3. Published data on Schizophrenia–associated SNPs used for calculation of penetrance using CalPen.

Results and discussion

In order to develop a web-based tool for calculation of penetrance (CalPen), we used the same parameters as described by Vassos et al. [3] and Python script in the SciPy package (see Materials and Methods). A schematic of the workflow resulting in computation of median penetrance and credible intervals is shown in Fig 1A. An example of steps involved in using CalPen is shown in Fig 1B wherein the user needs to enter the appropriate number against the dialog boxes given. For example, the data in Fig 1B indicates that there are 10 mutations in 1000 patients but five among 1000 controls. After entering the baseline risk (lifetime morbidity risk), the user needs to click the dialog box named ‘Calculate Penetrance’ and, the software gets forwarded to the next webpage showing the values of penetrance and credible intervals at the bottom. The user does not need to go to the previous webpage to start with another mutation but can continue from the same page by entering a new set of relevant numbers.

Fig 1. Development of CalPen, a web-based tool and its evaluation in calculating penetrance for copy number variants associated with schizophrenia.

(A) Schematic drawing of the pipeline used to determine the median penetrance and the critical intervals. (B) Screen shots showing the process of calculation of penetrance and credible intervals for a mutation (CNV). The numbers in the dialog boxes are indicative.

In order to validate the performance of CalPen, we used the published data from Vassos et al [3] and Rosenfeld et al [5]. In both cases, we used baseline risks as given by the authors. Data from CalPen and the two published reports is shown in Table 1. A comparison of the median penetrance values obtained using CalPen with the reported values gave a coefficient of correlation (r) of 0.992 (Fig 2A), with a P value < 0.001 indicating a significant degree of association between reported and CalPen-derived penetrance data. As an independent measure we used χ2 test with Yate’s correction, which gave a value of 0.04, corresponding to a P value of 1.0, indicating a high-degree of agreement in the two sets of values. In case of credible intervals, we first calculated the coefficient of range of these intervals and then used for calculation of correlation coefficient. The data shown in Fig 2B gave a r value of ~0.95, again indicating that there is a significant similarity between the published and CalPen-calculated credible intervals (P <0.001). As in case of penetrance values, a χ2 test with Yates correction gave a P value of 1.0 indicating that the published credible intervals were very similar to those calculated using CalPen. Taken together, these results suggest that CalPen software gives reliable values of both penetrance and credible intervals.

Fig 2. CalPen-mediated determination of penetrance values and credible intervals for different CNVs.

(A) Validation of penetrance values obtained using CalPen by correlation with those obtained from published reports using the same data sets. (B) Correlation of credible intervals for the data shown in (Fig 2A). (C) Estimates of penetrance values for different CNVs found to be associated with schizophrenia from multiple studies. For each CNV on the X-axis, values from multiple studies are plotted on the Y axis. Average value is shown as a larger red circle. (D) Penetrance value distribution among 145 SNPs associated with schizophrenia.

To demonstrate the wider utility of CalPen, we chose schizophrenia (SZ) as an example of complex disorder in which two categories of variants viz., Copy Number Variants (CNVs) and Single nucleotide polymorphisms (SNPs) are widely studied. CNVs are sub-microscopic deletions and duplications ranging in size from few kilobases to a few megabases, affecting one to many genes, constituting about 5–10% of human variation [31]. Among the different CNVs identified in SZ, meta-analysis resulted in identification of a specific set of 15 CNVs that are more likely to be replicated in a diverse set of populations [7]. Data on these 15 CNVs was obtained from different published reports [814]; (Table 2) and penetrance values were calculated using CalPen (Fig 2C). The data suggests that for a given CNV, there was a range of penetrance values from different reports. For example, 3q29 deletions showed penetrance values ranging from 1.8% to 15.3%. Overall the average penetrance of the 15 CNVs is ~7%, meaning that among 100 individuals with a CNV, there is a likelihood of seven individuals being abnormal. CNVs of 22q11.21 appear to have the highest average penetrance (~20%) whereas 15q11.2 deletions, which also represent variants of uncertain significance, have the lowest average penetrance (~ 1.4%). We also estimated the penetrance values of 128 SNPs using a large set of data reported by the psychiatric Genetics Consortium [29] and other reports that identified 17 SNPs among schizophrenia patients [1528]; (Table 3). In contrast to CNVs, the odds ratios of the SNPs are always lower, rarely approach a ratio of 1.5 [32] and therefore are likely to have lesser penetrance than CNVs. In agreement with this expectation, 117 out of 145 SNPs studied showed a penetrance of 0.7%. Eleven SNPs showed lowest (0.6%) and rs1801028 showed the highest (1.6%) penetrance values (Fig 2D; S1 Table).


In conclusion, CalPen is a straight forward tool for accurate determination of penetrance and credible intervals of mutations/variants associated with complex disorders and circumvents the bottleneck of the requirement of programming skills. At this juncture, this tool can calculate penetrance for one variant at a time and does not allow a set of variants identified in case-control studies to be analyzed together. Also, it is not possible to perform complex calculations resulting in estimations of combined penetrance in patients with more than one variant. With these improvements, CalPen in future may enable in better understanding of the phenotypic outcomes in complex disease genetics. For routine penetrance calculations, this web-based tool can be accessed from

Supporting information

S1 Table. Penetrance value distribution of 145 SNPs associated with schizophrenia.



KNM lab is supported by OPERA award from BITS Pilani and by the Centre for Human Disease Research.


  1. 1. Lobo I. Same genetic mutation, different genetic disease phenotype. Nat. Edu. 2008; 1: 64.
  2. 2. Strachan T, Read A. Human Molecular Genetics, 4th ed. Garland Science Press; 2011.
  3. 3. Vassos E, Collier DA, Holden S, Patch C, Rujescu D, St Clair D, et al. Penetrance for copy number variants associated with schizophrenia. Hum Mol Genet. 2010; 19(17): 3477–3481. pmid:20587603
  4. 4. Wilson EB. Probable Inference, the Law of Succession, and Statistical Inference. J Amer Stat Assoc 1927; 22(158): 209–212.
  5. 5. Rosenfeld JA, Coe BP, Eichler EE, Cuckle H, Shaffer LG. Estimates of penetrance for recurrent pathogenic copy-number variations. Genet Med. 2013; 15(6): 478–481. pmid:23258348
  6. 6. Schmuller J. Statistical Analysis with Excel® for dummies. 4th ed. John Wiley & Sons press; 2016.
  7. 7. Rees E, Walters JT, Georgieva L, Isles AR, Chambert KD, Richards AL, et al. Analysis of copy number variations at 15 schizophrenia-associated loci. Br J Psychiatry. 2014; 204(2): 108–114. pmid:24311552
  8. 8. Marshall CR, Howrigan DP, Merico D, Thiruvahindrapuram B, Wu W, Greer DS, et al. Contribution of copy number variants to schizophrenia from a genome-wide study of 41,321 subjects. Nat Genet. 2017; 49(1): 27–35. pmid:27869829
  9. 9. Li Z, Chen J, Xu Y, Yi Q, Ji W, Wang P, et al. Genome-wide Analysis of the Role of Copy Number Variation in Schizophrenia Risk in Chinese. Biol Psych. 2016; 80(4): 331–337.
  10. 10. Glessner JT, Reilly MP, Kim CE, Takahashi N, Albano AA, Hou C, et al. Strong synaptic transmission impact by copy number variations in schizophrenia. Proc Natl Acad Sci. (USA) 2010; 107(23): 10584–10589.
  11. 11. Szatkiewicz JP, O'Dushlaine C, Chen G, Chambert K, Moran JL, Neale BM, et al. Copy number variation in schizophrenia in Sweden. Mol Psych. 2014; 19(7): 762–773.
  12. 12. Chen J, Calhoun VD, Perrone-Bizzazero NI, Pearlson GD, Sui J, Du Y, et al. A pilot study on commonality and specificity of copy number variants in schizophrenia and bipolar disorder. Transl Psych. 2016; 6(5): e824.
  13. 13. Kushima I, Aleksic B, Nakatochi M, Shimamura T, Okada T, Uno Y, et al. Comparative analysis of copy-number variation in autism spectrum disorder and schizophrenia reveal etiological overlap and biological insights. Cell Reports. 2018; 24(11): 2838–2856. pmid:30208311
  14. 14. Warland A, Kendall KM, Rees E, Kirov G, Caseras X. Schizophrenia-associated genomic copy number variants and subcortical brain volumes in the UK Biobank. Mol Psych. 2019:1.
  15. 15. Hori H, Yamamoto N, Fujii T, Teraishi T, Sasayama D, Matsuo J, et al. Effects of the CACNA1C risk allele on neurocognition in patients with schizophrenia and healthy individuals. Sci Rep. 2012; 2: 634. pmid:22957138
  16. 16. Chowdari KV, Northup A, Pless L, Wood J, Joo YH, Mirnics K, Lewis DA, et al. DNA pooling: a comprehensive, multi-stage association analysis of ACSL6 and SIRT5 polymorphisms in schizophrenia. Genes Brain Behav. 2007; 6(3): 229–239. pmid:16827919
  17. 17. Buttenschøn HN, Flint TJ, Foldager L, Qin P, Christoffersen S, Hansen NF, et al. An association study of suicide and candidate genes in the serotonergic system. J Affect Disord. 2013; 148(2–3): 291–298. pmid:23313272
  18. 18. Faul T, Gawlik M, Bauer M, Jung S, Pfuhlmann B, Jabs B, et al. ZDHHC8 as a candidate gene for schizophrenia: analysis of a putative functional intronic marker in case-control and family-based association studies. BMC Psychiatry. 2005; 5(1): 35.
  19. 19. Kim HJ, Park HJ, Jung KH, Ban JY, Ra J, Kim JW, et al. Association study of polymorphisms between DISC1 and schizophrenia in a Korean population. Neurosci Lett. 2008; 430(1): 60–63. pmid:17997036
  20. 20. Nunokawa A, Watanabe Y, Muratake T, Kaneko N, Koizumi M, Someya T. No associations exist between five functional polymorphisms in the catechol-O-methyltransferase gene and schizophrenia in a Japanese population. Neurosci Res. 2007; 58(3): 291–296. pmid:17482701
  21. 21. Zhang J, Che R, Li X, Tang W, Zhao Q, Tang R, et al. No association between the FXYD6 gene and schizophrenia in the Chinese Han population. J Psychiatr Res. 2010; 44(6):409–412. pmid:20149392
  22. 22. Shin HD, Park BL, Kim EM, Lee SO, Cheong HS, Lee CH, et al. Association analysis of G72/G30 polymorphisms with schizophrenia in the Korean population. Schizophr Res.2007; 96(1–3): 119–124. pmid:17651942
  23. 23. Richards M, Iijima Y, Kondo H, Shizuno T, Hori H, Arima K, et al. Association study of the vesicular monoamine transporter 1 (VMAT1) gene with schizophrenia in a Japanese population. Behav Brain Funct. 2006; 2(1): 39.
  24. 24. Khan RA, Chen J, Shen J, Li Z, Wang M, Wen Z, et al. Common variants in QPCT gene confer risk of schizophrenia in the Han Chinese population. Am J Med Genet B Neuropsychiatr Genet. 2016; 171B(2): 237–242. pmid:26492838
  25. 25. Fan H, Zhang F, Xu Y, Huang X, Sun G, Song Y, et al. An association study of DRD2 gene polymorphisms with schizophrenia in a Chinese Han population. Neurosci Lett. 2010; 477(2): 53–56. pmid:19913597
  26. 26. Wang T, Zeng Z, Hu Z, Zheng L, Li T, Li Y, et al. FGFR2 is associated with bipolar disorder: a large-scale case-control study of three psychiatric disorders in the Chinese Han population. World J Biol Psychiatry. 2012; 13(8): 599–604. pmid:22404656
  27. 27. Sun S, Wang F, Wei J, Cao LY, Wu GY, Lu L, et al. Association between interleukin-3 receptor alpha polymorphism and schizophrenia in the Chinese population. Neurosci Lett. 2008; 440(1): 35–37. pmid:18547720
  28. 28. Zhang F, Fan H, Xu Y, Zhang K, Huang X, Zhu Y, et al. Converging evidence implicates the dopamine D3 receptor gene in vulnerability to schizophrenia. Am J Med Genet B Neuropsychiatr Genet. 2011; 156B(5): 613–619. pmid:21595009
  29. 29. Schizophrenia Working Group of the Psychiatric Genomics Consortium. Biological insights from 108 schizophrenia-associated genetic loci. Nature 2014; 511(7510): 421–427. pmid:25056061
  30. 30. McGrath J, Saha S, Chant D, Welham J. Schizophrenia: a concise overview of incidence, prevalence, and mortality. Epidemiol Rev. 2008; 30(1): 67–76.
  31. 31. Zarrei M, MacDonald JR, Merico D, Scherer SW. A copy number variation map of the human genome. Nat Rev Genet. 2015; 16(3):172–83. pmid:25645873
  32. 32. Hodge SE, Greenberg DA. How can we explain very low odds ratios in GWAS? I. Polygenic Models. Hum Hered. 2016; 81(4): 173–180. pmid:28171865