# Tunneling Operation Risks Rating Using Linear Assignment Method

# Tunneling Operation Risks Rating Using Linear Assignment Method

**Length:** 2688 words (7.7 double-spaced pages)

**Rating:** Excellent

#### Essay Preview

More ↓Due to the uncertain nature of tunneling projects and the need for optimum disbursement of the resources, risk management of these projects is ¬of great importance, and a key element of the accuracy of this management process is rating of the risks with the aim of identifying the priority of each risk for ¬ proper planning on the part of decision makers in allocating the resources to deal with risks [1].

Tunneling projects are consistently associated with a high percentage of risk due to related uncertainties, and minimizing the probability of risk occurrence or negative impacts of it on implementation of these projects require accurate and timely management of subsequent risks, ¬which are frequently neglected. For example, in a global survey on tunneling projects [2], 30 to 50 percent increase in time and costs has been reported due to faulty management. Based on another survey (among English companies in 1994), 40% of the projects have surpassed the specified time or budget, and in more than 60% of them, the risk management of the organization has been evaluated as poor [3].

In recent years, risk assessment in tunneling projects has become considerably important, and several studies in this field have been reported. In the studies conducted by the International Tunneling Association, the product of the probability of an event has been used to define the concept of risk [4].

### How to Cite this Page

**MLA Citation:**

"Tunneling Operation Risks Rating Using Linear Assignment Method."

__123HelpMe.com__. 22 Aug 2019

<https://www.123helpme.com/view.asp?id=270702>.

## Need Writing Help?

Get feedback on grammar, clarity, concision and logic instantly.

Check your paper »## Essay on Benefits Of Using Linear Model

- Benefits (1) O/C model provides Coos’ the greatest cost savings while incurred smallest cost increases compared with the other four models. Its projected total cost savings are $11,750,000, and total costs increases are only $4,880,000. In other words, for every dollar saving, O/C model would cost $0.4153. For material resource planning model, every dollar saving would create $1.7403 cost increases. We can see that it is not an economic option to adopt this model. Linear model generates $0.8504 cost increases for every dollar saving, 2 times as much as that of O/C model.... [tags: Costs, Cost, Investment, Supply chain]

**Research Papers**

722 words (2.1 pages)

## Essay about Using A Non Linear Mixed Logit ( Ml )

- The model is estimated using a non-linear mixed logit (ML), in which interactions between the subjective risk perceptions and all main effects – except the cost– are controlled for(3). The model of best fit is chosen from a set of tentative models with varying specifications and mixing distributions (results are robust to different specifications). Except for the coefficient on Seawalls which was specified as fixed, coefficients on all other attributes are specified as random with the assumption of no correlation exists among their distributions.... [tags: Standard deviation, Normal distribution]

**Research Papers**

1158 words (3.3 pages)

## Essay The Posivist Approach

- Research Question 2 Philosophy The positivist approach will be used for the second research question. Such an approach is viewed to be a scientific method that aims to gain information with the objective of discovering laws that may be generalised within similar conditions. Since the research is tackling the issue of foreign aid and sustainability, it has used the example of the effect of foreign aid in countries of Africa in order to contrast similarities in Palestine. Because the researcher is independent, and will adopt a traditional and scientific approach, it results in a concrete finding of similarity in the related situations, which would allow a more comprehensive conclusion and prov... [tags: Scientific Method, Gaining Information, Research]

**Research Papers**

1456 words (4.2 pages)

## The Decipherment of Linear A and Linear B Essay

- In 1886 an archeologists named Arthur Evans discovered an ancient stone that was engraved with mysterious writings. Through continuous investigation and research Evans made a connection between the mysterious writing system and the Aegean empire of the ancient Minoans. Later Evans discovered another unique form of writing that was very similar to the first one he discovered. Evans called these forms of writing Linear A and Linear B. Linear A and B is a form of writing systems that were used by ancient Crete.... [tags: form of writing used in ancient Crete]

**Free Essays**

519 words (1.5 pages)

## Essay about Project Data Analysis Techniques For A Linear Fashion

- Project-Data Analysis Techniques Name Institution Introduction In an effort to bring order, structure and meaning to any mass of collected data, data analysis does not flow in a linear fashion. It is often ambiguous, messy and time-consuming as the researcher searches for general statements regarding relationships among data categories. However, according to Hai-Jew (2015), any qualitative researcher has to find ways of managing the data to engage in-depth analysis. The current paper provides an analysis of the core content of the observations of people’s interactions that took place in the stadium hosting the 2016 Junior Olympics.... [tags: Scientific method, Observation, Data analysis]

**Research Papers**

854 words (2.4 pages)

## Linear Quadratic Optimal Control System Design Using Evolutionary Algorithms

- Selecting appropriate weighting matrices for desired Linear Quadratic Regulator (LQR) controller design using evolutionary algorithms is presented in this paper. Obviously, it is not easy to determine the appropriate weighting matrices for an optimal control system and a suitable systematic method is not presented for this goal. In other words, there isn’t direct relationship between weighting matrices and control system characteristics and selecting these matrices is done using by trial and error based on designer’s experience.... [tags: Mathematics]

**Research Papers**

2475 words (7.1 pages)

## Essay on Historical Method Of The Scientific Method

- Sociologists must understand how to collect and analyze data precisely. Sociology utilizes the scientific method to collect and evaluate data accurately. There are multiple ways to gather data including “experiments, surveys, participant observations and using existing data” (Macionis). An important aspect of the scientific method is to produce valid, reliable and unbiased results. Personal bias is the influence of the researches own beliefs that is introduced into the data which could undermine it unintentionally.... [tags: Scientific method, Research]

**Research Papers**

783 words (2.2 pages)

## Linear Programming Essay

- The development of linear programming has been ranked among the most important scientific advances of the mid 20th century. Its impact since the 1950’s has been extraordinary. Today it is a standard tool used by some companies (around 56%) of even moderate size. Linear programming uses a mathematical model to describe the problem of concern. Linear programming involves the planning of activities to obtain an optimal result, i.e., a result that reaches the specified goal best (according to the mathematical model) among all feasible alternatives.... [tags: Computer Programming]

**Free Essays**

1277 words (3.6 pages)

## Linear Programming Essay

- Linear Programming Part A Introduction “Linear programming was developed by George B. Dantzig in 1947 as a technique for planning the diversified activities of the U.S Air Force.” Linear programming is a powerful mathematical technique that can be used to deal with the problem of allocating limited facilities and resources among many alternative uses in order to find out the optimal benefits. The main objective of the linear programming problem in management is to maximize profit or minimize cost.... [tags: Computer Science]

**Research Papers**

1461 words (4.2 pages)

## Essay on Newton's Method

- Finding roots of a function is often a task which faces mathematicians. For simple functions, such as linear ones, the task is simple. When functions become more complex, such as with cubic and quadratic functions, mathematicians call upon more convoluted methods of finding roots. For many functions, there exist formulas which allow us to find roots. The most common such formula is, perhaps, the quadratic formula. When functions reach a degree of five and higher, a convenient, root-finding formula ceases to exist.... [tags: Newton-Raphson Method]

**Free Essays**

827 words (2.4 pages)

In these studies, risk assessment results are not reliable and realistic due to the use of risk 'effect' and 'probability' indices in the form of probability-impact risk rating matrix (I-P Matrix) [11], since by using this matrix and considering the high probability and low impact risks equivalent with low probability and high impact ones may ignore low probability and high impact risks, resulting in systematic error [12]. Therefore, further studies with respect to several risk factor indices have been conducted.

The indices of "organization's ability to respond to risk" [13] and "estimation uncertainty" [14] have been addressed for assessment and rating in some projects. Baccarini & Archer have applied probability and degree of impact on time, cost and quality of the project in risk rating [15]. Waterland et al have used the three criteria of occurrence, severity of impact and tracking for risk assessment [16]. In addition to probability and impact matrices, Haimes used risk management capabilities and risk exposure to prioritize the risks [17]. In some project control software, the two complementary indicators of accessibility and proximity of risk occurrence have been considered [18]. In other sources, socio-economic and environmental impact indicators have been applied [19].

Today, prioritization of multivariate decision-making units based on their relative importance and applying the experiences of individuals ¬with expertise, skills, and scientific perspectives has become important. Group and multivariate decision making techniques (e.g., linear assignment method) are appropriate tools to rate risk and make correct decisions in this field [0]. In these techniques, using the aggregation of several expert opinions instead of a single one involves more details in decision-making analyses [21].

In this study, the main risks in construction operations of Golab water tunnel, which is excavated by TBM, have been identified, assessed and ranked. Risk identification is the first step in risk management process, and risk breakdown structure technique has been used to identify and group the risks in this study. Risk breakdown structure (RBS) is a hierarchical structure of project risks, which can be used for structuring and guiding the risk management process [22]. Given the large number and variety of risks affecting the tunneling projects, efficient and effective risk management is not virtually possible without identification and preparation of RBS. On the other hand, any measure to understand and deal with risks is difficult without a systematic and accurate procedure for the identification and management of risks. ¬ Using RBS can contribute to this, since it presents an effective tool for targeted and classified risk identification [21]. Afterwards, group decision making procedure has been used to gather expert opinions, and average agglomeration method was used to aggregate the expert opinions. In addition, linear assignment has been used as a multi-criteria decision making method to rate the risks.

1.2 Linear assignment method

Multivariate decision ¬making methods are used to select the optimum choice from among m available options, and a distinctive feature of them is presence of a few numerable options in advance. The best option in a multi-criteria model will be the option providing the most preffered value from each available characteristic. Modeling is based on development and formation of contingency tables [23].

Linear assignment is among these important methods. The basis of rating ¬in linear assignment method is the total of assumed options of a problem from each index option, and the final rank of the options is specified by a linear compensation process. In this way, based on the property of simplex solution space, while considering all the arrangements implicitly, optimal solution is extracted within a convex simplex space. Moreover, the compensatory effect of indexes results from exchange between ranks and options, although the index weight vector is obtained based on expert opinion. The main Advantage of this multi-criteria decision making method is taking advantage of both hard and soft (combination) skills. In soft decision making techniques, model expression is based on a contingency table, while in hard decision making techniques, the model is defined based on a system of mathematical equations. Combination decision-making techniques apparently follow the logic of soft techniques, and are defined according to contingency table but take advantage of methematical equations system practically in the solution process; therefore, they have the strengths of both hard and soft techniques [24]. On the one hand, this method causes exchange between indices and lacks complicated calculations using a simple rating for the options, and on the other hand, there is no requirement for measuring scales, and the indices can be of any scale [25].

This method of rating is applied in the following steps [24]: ¬

- Determining the risk rating for each index: formation of a matrix (m × m), in which the row indicates rank and the column shows index.

- Formation of allocation matrix or matrix-gamma (γ): formation of a square matrix (m × m) with line as I showing risk and column as k showing rank. Components of γ matrix ( ) are the total weight of indices whose ith risk has the kth rank.Gamma matrix is an allocation matrix giving the optimal solution using any of the allocation methods (transport, Hungarian method, grid method and linear zero and one programming method). The most common solution method in linear assignment is the linear programming method.

- Rating based on linear programming: Rating is done according to the following models.

2.2 Shannon entropy method

This is an appropriate technique to extract the coefficient of indices in problem solving procedure using linear assignment method, which is done in the following steps [2]:¬

- Converting the value of entry (decision matrix) to :

- Calculation of value of the jth characteristic entropy:

- Calculation of vakue for each characteristic:

- Calculation of weight of kth characteristic:

To apply an importance coefficient for each index ( ), weight is calculated according to the below equation:

3. Risk assessment criteria

In general, validity of the risk assessment results are subject to the comprehensiveness of studied factors, although in most studies for tunnels, a comprehensive set of risk assessment criteria have not been simultaneously introduced and used. Table 1 shows risk assessment criteria in two categories, primary and secondary (complementary) with associated symbols. In this table, the positivity of impact aspect of each criterion indicates higher criticality of that risk and vice versa. Another important point in this table is independence of criteria from each other and lack of logical significant correlation between the indices.

Table 1. Risk assessment criteria along with sign and impact aspect

Definition Impact aspect Symbol criterion

Indicates that the estimator expects the occurrence of risk. Positive C1 Likelihood of risk

Capacity of predicting the risk occurrence and exposure of risk during occurrence Negative C2 Risk discovery rate

Indicative of replication rate and risk exposure during project implementation Positive C3 Exposure to risk

Indicative of the capacity to predict risk occurrence and ability to manage and respond to it Negative C4 Management of risk-taking

Indicative of the uncertainty of analyst from risk assessment values Positive C5 Uncertainty of estimates

Indicative of the negative effect of risk on the timing of project Positive C6 The effect of risk on time

Indicative of the negative effect of risk on project costs Positive C7 The effective of risk on cost

Indicative of the negative effect of risk on quality of project Positive C8 The effect of risk on quality

Indicative of the negative effect of risk on the rang of project activities Positive C9 The effect of risk on the range

4. Risk assessment of water tunnel of Golab

4.1 - Golab water tunnel introduction

Golab water tunnel and access tunnel in continuation of it with a total length of 11 kilometers from the eastern slopes of Zayanderud River under Corun Plain has been designed and implemented to supply water for Kashan County. Geographically, the tunnel is located 110 km to northwest of Isfahan, and is located geologically in part of Sanandaj-Sirjan zone. The main tunnel has been excavated using a full section mechanized TB458/TS model excavation machine with dual (telescopic) shield and prefabricated hexagonal concrete wall coverage towards the junction of the access tunnel [24].

4.2 Identifying the risks of tunnel excavation operations

As noted above, the first step in risk assessment and management is identifying the project risks; therefore, the main risks of Golab water tunnel were classsified using RBS method (Table 2). This table has followed the Work Breakage Structure (WBS), and presents a hierarchical structure of risks associated with excavation operations of Golab water tunnel. The designed structure includes three levels. In the first level, the overall risks of Golab water tunnel in three sets of internal, external-internal and external have been classified. In the second level, the risks have been classified based on RBS method in the form of five subsets, and in the third level in the form of 25 main risks (risk factors). We have attempted to analyze and classify the risks as comprehensive as possible to minimize their interface, and present the risks in an appropriate understandable form compatible with risk and project management.

Table 2: Hierarchical structure of risks of Golab tunnel at 3 levels (including 25 main risks)

Level zero Level 1 Level 2 Level 3

Risks associated with excavation of Golab tunnel using TBM TBM Internal risk Technical risks Alignment of the machine in the wrong path R1

Low rate of machine progress R2

Electrical and mechanical problems in the machine R3

Segment not preventing water entry R4

Crack and breaks in segmen R5

Workforce risks Low experience staff R6

Workforce clash and accident R7

Management risks Defective equipment R8

Delayed equipment and support of the instrument R9

Internal-external risks Operation risks TBM shield arrest R10

Instrument cutter head clog R11

Overexcavation R12

Fire or explosion event R13

Segment ring distortion R14

External risks Environmental risks Unstable walls and ceiling of the tunnel R15

Work front unstability R16

Seepage and groundwater influx R17

Gas leak R18

Excessive wear of cutting tools

R19

Injury or damage caused by mental ¬ orientation R20

Chemical corrosion R21

Realizability crush (Crush)

R22

Swelling of clay rocks

R23

Mixed work front R24

Sticky clay soils and rocks

R25

5.2 Rating steps of tunnel risks

5.2.1 Collection and aggregation of experts' opinions

First, due to the main identified risks of the third level (R1 to R25) and nine assessment criteria (Table 1), a questionnaire was designed, and expert opinions were collecting by taking advantage of group decision making techniques. Table 3 shows the scoring range for each of the studied risk indices.

Table 3: Scoring range and linguistic variables for criteria values for each risk [26]

Very high High The average high Average Average low Low Very low Variable expression

10 9 7 5 3 1 0 Value

Thus, the decision matrix containing 225 entries includes 25 rows (main risks) and 9 columns (assessment indices) was formed, and the entry values were the average of scores collected from experts (Table 4).

2.2.5 Calculation of the weight of indices

At this point, the weight of each of the nine indices (W i) was obtained by combining expert views and Shannon entropy method according to equations 1 to 5, which is shown in Table 5.

Table 5: Calculation of final weight of each index by combining expert opinions and Shannon entropy

5.2.3- Rating the risks

Risk rating (R1 to R25) was done based on nine indicators in three steps using linear assignment method. Firstly, the rank of each risk for any of the available indices was calculated as a matrix (9 × 25), of which the row indicates rank and column indicates the index, and the results are shown in Table 6.

Table 6: Risk rating for each one of the indices

Secondly, the allocation matrix or gamma matrix ( ) was formed as a square 25 × 25 matrix, the row of which showed the i risk and the column shows k rank. The components of this matrix ( ) consisted of the set of index weights, in which the ith risk had the kth rank. The results of this step are presented in Table 7.

In the third step, risk rating was done¬ using linear programming method and the model presented in equations 1-3. In this study, given the high load of computing (625 decision variables), LINGO software was used. Since the decision variables have the value of 0 or 1, the output of this program for values of 1 indicates the rank of the risk under study. For example, h (15, 5) indicates rate 5 for risk No.15, and h (11, 8) indicates rate 8 for risk No.11. Accordingly, the risk rating ¬is presented in Table 8.

As can be seen, R22 and R17 have the lowest rating (first and second, respectively), and are identified as the most critical risks in this study. Therefore, project management must give priority to ¬solving and controlling these risks in its reaction and management measures, and the other risks have a lower rank in terms of criticality.

Finally, to rank the level 2 risks (five risk categories), the rate of each category can be determined by calculating the rate of main risks (Table 9). As can be seen, management risks have the lowest rate.

Table 9: Rating the five main risk categories according to the rank of the main risks

6. Conclusion

Risky construction projects such as tunneling require necessary meaures for risk managament and solution through correct identification and rating of the vital risky factors. In this study, we have dealt with rating the studied risk factors by linear assignment method considering both traditional risk assessment criteria (including probability and risk impact) and complementary indices by identifying the risk factors of Golab water tunnel and aggregating the expert opinions. Higher validity of the results of this method relative to the traditional method is due to additional assessment indices, simultaneous consideration of a few indices, considering different weights for indices, exchange between the indices, flexibility of the method and more analytic results. In this case study, crush ¬realizability (crush), leakage and flow of ground water and overerosion of cutting tools have respectively the lowest and highest criticality of risk, and should be in priority of reactionary and risk management measures.

Works Cited

1. Scalapino KJ, Davis JC, Jr. The treatment of ankylosing spondylitis. Clin Exp Med. [Research Support, Non-U.S. Gov't

Research Support, U.S. Gov't, P.H.S.

Review]. 2003 Feb;2(4):159-65.

2. Lim HJ, Lim HS, Lee MS. Relationship between self-efficacy and exercise duration in patients with ankylosing spondylitis. Clin Rheumatol. [Comparative Study

Letter]. 2005 Aug;24(4):442-3.

3. Braun J, Bollow M, Remlinger G, Eggens U, Rudwaleit M, Distler A, et al. Prevalence of spondylarthropathies in HLA-B27 positive and negative blood donors. Arthritis Rheum. [Research Support, Non-U.S. Gov't]. 1998 Jan;41(1):58-67.

4. Gorman JD, Sack KE, Davis JC, Jr. Treatment of ankylosing spondylitis by inhibition of tumor necrosis factor alpha. N Engl J Med. [Clinical Trial

Randomized Controlled Trial

Research Support, Non-U.S. Gov't

Research Support, U.S. Gov't, P.H.S.]. 2002 May 2;346(18):1349-56.

5. Brandt J, Marzo-Ortega H, Emery P. Ankylosing spondylitis: new treatment modalities. Best Pract Res Clin Rheumatol. [Review]. 2006 Jun;20(3):559-70.

6. Landgren O, Engels EA, Pfeiffer RM, Gridley G, Mellemkjaer L, Olsen JH, et al. Autoimmunity and susceptibility to Hodgkin lymphoma: a population-based case-control study in Scandinavia. J Natl Cancer Inst. [Research Support, N.I.H., Intramural]. 2006 Sep 20;98(18):1321-30.

7. Skinnider BF, Mak TW. The role of cytokines in classical Hodgkin lymphoma. Blood. [Research Support, Non-U.S. Gov't

Review]. 2002 Jun 15;99(12):4283-97.

8. Marshall NA, Christie LE, Munro LR, Culligan DJ, Johnston PW, Barker RN, et al. Immunosuppressive regulatory T cells are abundant in the reactive lymphocytes of Hodgkin lymphoma. Blood. [Research Support, Non-U.S. Gov't]. 2004 Mar 1;103(5):1755-62.

9. Kuppers R. Molecular biology of Hodgkin's lymphoma. Adv Cancer Res. [Research Support, Non-U.S. Gov't

Review]. 2002;84:277-312.

10. Schwering I, Brauninger A, Klein U, Jungnickel B, Tinguely M, Diehl V, et al. Loss of the B-lineage-specific gene expression program in Hodgkin and Reed-Sternberg cells of Hodgkin lymphoma. Blood. [Research Support, Non-U.S. Gov't]. 2003 Feb 15;101(4):1505-12.

11. Ries L, Eisner M, Kosary C, Hankey B, Miller B, Clegg L, et al. SEER Cancer Statistics Review, 1975–2000. Bethesda, MD: National Cancer Institute; 2003. Available on http://seer cancer gov/csr. 2005.

12. Green MR, Monti S, Rodig SJ, Juszczynski P, Currie T, O'Donnell E, et al. Integrative analysis reveals selective 9p24.1 amplification, increased PD-1 ligand expression, and further induction via JAK2 in nodular sclerosing Hodgkin lymphoma and primary mediastinal large B-cell lymphoma. Blood. [Research Support, N.I.H., Extramural

Research Support, Non-U.S. Gov't]. 2010 Oct 28;116(17):3268-77.

13. Askling J, Klareskog L, Blomqvist P, Fored M, Feltelius N. Risk for malignant lymphoma in ankylosing spondylitis: a nationwide Swedish case-control study. Ann Rheum Dis. 2006 Sep;65(9):1184-7.

14. Diak P, Siegel J, La Grenade L, Choi L, Lemery S, McMahon A. Tumor necrosis factor alpha blockers and malignancy in children: forty-eight cases reported to the Food and Drug Administration. Arthritis Rheum. 2010 Aug;62(8):2517-24.

15. Nash PT, Florin TH. Tumour necrosis factor inhibitors. Med J Aust. [Review]. 2005 Aug 15;183(4):205-8.

16. Ward MM. Health‐related quality of life in ankylosing spondylitis: A survey of 175 patients. Arthritis Care & Research. 1999;12(4):247-55.

17. Braun J, Brandt J, Listing J, Zink A, Alten R, Golder W, et al. Treatment of active ankylosing spondylitis with infliximab: a randomised controlled multicentre trial. Lancet. [Clinical Trial

Multicenter Study

Randomized Controlled Trial

Research Support, Non-U.S. Gov't]. 2002 Apr 6;359(9313):1187-93.

18. Nannini C, Cantini F, Niccoli L, Cassara E, Salvarani C, Olivieri I, et al. Single-center series and systematic review of randomized controlled trials of malignancies in patients with rheumatoid arthritis, psoriatic arthritis, and ankylosing spondylitis receiving anti-tumor necrosis factor alpha therapy: is there a need for more comprehensive screening procedures? Arthritis Rheum. [Review]. 2009 Jun 15;61(6):801-12.

19. Zintzaras E, Voulgarelis M, Moutsopoulos HM. The risk of lymphoma development in autoimmune diseases: a meta-analysis. Arch Intern Med. [Meta-Analysis

Review]. 2005 Nov 14;165(20):2337-44.

20. van der Heijde D, Dijkmans B, Geusens P, Sieper J, DeWoody K, Williamson P, et al. Efficacy and safety of infliximab in patients with ankylosing spondylitis: results of a randomized, placebo-controlled trial (ASSERT). Arthritis Rheum. [Clinical Trial

Multicenter Study

Randomized Controlled Trial

Research Support, Non-U.S. Gov't]. 2005 Feb;52(2):582-91.

21. Brandt J, Haibel H, Cornely D, Golder W, Gonzalez J, Reddig J, et al. Successful treatment of active ankylosing spondylitis with the anti-tumor necrosis factor alpha monoclonal antibody infliximab. Arthritis Rheum. [Clinical Trial]. 2000 Jun;43(6):1346-52.

22. Fouache D, Goeb V, Massy-Guillemant N, Avenel G, Bacquet-Deschryver H, Kozyreff-Meurice M, et al. Paradoxical adverse events of anti-tumour necrosis factor therapy for spondyloarthropathies: a retrospective study. Rheumatology (Oxford). 2009 Jul;48(7):761-4.

23. Ekstrom K, Hjalgrim H, Brandt L, Baecklund E, Klareskog L, Ekbom A, et al. Risk of malignant lymphomas in patients with rheumatoid arthritis and in their first-degree relatives. Arthritis Rheum. [Research Support, Non-U.S. Gov't]. 2003 Apr;48(4):963-70.

24. Shibata A, Zhao S, Makuch R, Wentworth C, Veith J, Wallis W, editors. Lymphoma risk in ankylosing spondylitis patients is greater than that observed in the general population. Ann Rheum Dis; 2004: BMJ PUBLISHING GROUP BRITISH MED ASSOC HOUSE, TAVISTOCK SQUARE, LONDON WC1H 9JR, ENGLAND.