What about theta?
 Revised: 2001-10-28

Question: How do you know the value of theta? Will it always be 1? Please use the sore throat as a model although it may be applied to other diagnoses as well.

(First read the page presenting the formulas used to calculate EPV. That page will define theta.)

To understand this let us use the following situation:

Consider the following example: A conventional throat culture has been obtained during a summer period from 36 children of age 3-15 years having a sore throat possibly caused by group A beta-hemolytic streptococci (GABHS)1. Among those 36 cultures a throat culture indicated presence of the bacterium GABHS in 11 (31%).

However, some of the children might be ill due to a virus as well as carrying GABHS. To investigate this phenomenon we may collect data from healthy children. During the same period of time throat cultures were obtained from 290 healthy children of age 3-15 living in the same geographical area, and showing no signs indicating possible GABHS-caused tonsillopharyngitis1. Among those 290 cultures a throat culture indicated presence of GABHS in 37 (13%).

This situation may be described as:

Relation between test outcome (T+, T-) and presence (D+) or absence (D-) of specified disease  in patients having a sore throat
  A sore throat caused by....
  ....GABHS (D+) ....other than GABHS (D-)
  GABHS present
(M+)		 (GABHS not present)
(M-)		 GABHS present
(M+)		 GABHS not present
(M-)

Positive test (T+)

 True positive ----- False positive* False positive

Negative test (T-)

 False negative ----- True negative** True negative
*The positive test does not represent true disease (D+) and is therefore considered to be false positive. However, it indicates that the patient is a carrier of GABHS.

**Although the patient carry GABHS a negative test will correctly identify the patient as not having the disease, thus being (D-).

To calculate Etiologic predictive value (EPV) we need to estimate the proportion of carriers in patients with a sore throat caused by something else than the marker (in our scenario a sore throat caused by something else than GABHS). This is done by using information from a healthy control population.

The relation between the proportion of positive tests in patients sick from another cause (the proportion of symptomatic carriers) and the proportion of positive tests in healthy individuals (the proportion of asymptomatic carriers) is defined as theta (θ). Since theta is defined by

 

 and since

 

 it can be shown that

 

Sen is the sensitivity of the test.

There are three principal ways to estimate theta:

  1. The first one is to define that theta =1; i.e. the found agent is of etiologic importance in a population as soon as the proportion of positive tests exceeds that of a healthy control population.
     

  2. The second way is to find a gold standard predicting disease caused by the etiologic agent. This gold standard could be used to estimate theta. Unfortunately, there is seldom such a gold standard.
     

  3. The third way is to make a reasonable assumption. Assume that there are 500 healthy individuals and that 50 of these are asymptomatic carriers of a bacterium, for example GABHS. Assume that 20% of these 500 randomly acquire an acute upper respiratory tract disease caused by a virus. By chance, approximately 10 of these 100 viral infected symptomatic individuals will be symptomatic carriers of GABHS. The proportion of symptomatic carriers will initially be the same as the proportion of asymptomatic carriers among healthy individuals. There are several mechanisms that might affect the continuation of events:

  1. Spreading of GABHS from symptomatic or asymptomatic carriers might occur to individuals not harboring GABHS. However, since asymptomatic carriers of GABHS have a low tendency to spread their bacterium2 this will be a slow process. Furthermore, if spreading occurs, it will affect both individuals sick due to a virus as well as healthy individuals. It is unlikely that this mechanism alters theta.
     

  2. A viral infection might alter the carriage in a symptomatic carrier into disease caused by GABHS and thus lower the proportion of symptomatic carriers. A viral infection might alter the properties of mucous membranes in the respiratory tract and as a consequence enhance adhesion or penetration through the mucous membrane. An association between infection with GABHS and influenzae A has been shown in vitro3. An association has also been seen in vivo so that varicella-zoster seems to increase the risk for invasive infection with GABHS4-5. Another study has in vitro showed that a viral infection increases the adhesion of S. pneumoniae to epithelial cells6. However, the clinical importance of these studies remains to be investigated and it is generally considered that asymptomatic carriers do not have an increased risk for developing sickness caused by GABHS7. Theoretically this mechanism might result in a slightly lower theta.
     

  3. Altering the mucous membrane by a viral infection might alter the number of bacteria per surface unit. If the number of bacteria increase it might enhance the test’s ability to discover the bacteria and thus, possibly indirectly increase the proportion of symptomatic carriers. This phenomenon is only likely to occur if the sensitivity of the test is low. Theoretically this mechanism might result in a slightly higher theta.
     

  4. Spreading of GABHS from patients ill by GABHS is more likely to occur than spreading of GABHS from carriers8-9. There is a possibility that a viral-infected individual is more susceptible to this spreading of bacteria than healthy individuals. If this were true it would increase theta. However, there is no clear evidence that this type of spreading is much more likely to occur if the potential recipient has a viral infection compared to healthy individuals. Furthermore, if spreading occurs it will still affect both individuals sick by a virus as well as healthy individuals. Theoretically, this mechanism might result in a slightly higher theta. However, this remains to be proven.

As seen, initially theta=1. It might later deviate slightly from one. The initial phase would probably last a couple of weeks by which time the viral infection will be gone. Thus, it is reasonable to assume that in case of a sore throat caused by GABHS, theta approximates the value of one, an opinion shared by most authorities7,10-12. In most other situations where the etiologic predictive value would be of clinical value the assumption that theta=1 would apply.

One may find it frustrating that the estimation of theta introduces some uncertainty to the etiologic predictive value. However, it can be shown this uncertainty is rather small. The possible error caused by estimating theta is far less than the error caused by assuming that predicting presence of the etiologic agent is similar to predicting presence of the specified disease.

In other scenarios than the sore throat it would be appropriate to start by assuming that theta is one. Then try to reason and find arguments supporting or contradicting the hypothesis that theta is one (in a similar way as with the sore throat).

Other WebPages of interest

Other pages with subjects that might be of interest is:

(You can click on these links to quickly see the pages)

References

  1. Gunnarsson, R.K., Holm, S.E. and Söderström, M. `The prevalence of beta-haemolytic streptococci in throat specimens from healthy children and adults. Implications for the clinical value of throat cultures' , Scand J Prim Health Care, 15, 149-155 (1997).
     
  2. Kaplan EL, Gastanaduy AS, Huwe BB. The Streptococcal carrier: an axplanation for treatment failures with antibiotics. In Basic Concepts of Streptococci and Streptococcal Diseases. Holm SE, Christensen P. Chertsey, Surrey: Reedbooks 1982, pp165-6.
     
  3. Sanford BA, Davison VE, Ramsay MA. Fibrinogen-mediated adherence of group A Streptococcus to influenza A virus-infected cell cultures. Infect Immun 1982;38(2):513-20.
     
  4. Laupland KB, Davies HD, Low DE, Schwartz B, Green K, McGeer A. Invasive group A streptococcal disease in children and association with varicella-zoster virus infection. Ontario Group A Streptococcal Study Group. Pediatrics 2000;105(5):E60.
     
  5. Doctor A, Harper MB, Fleisher GR. Group A beta-hemolytic streptococcal bacteremia: historical overview, changing incidence, and recent association with varicella. Pediatrics 1995;96(3 Pt 1):428-33.
     
  6. Håkansson A, Kidd A, Wadell G, Sabharwal H, Svanborg C. Adenovirus infection enhances in vitro adherence of Streptococcus pneumoniae. Infect Immun 1994;62:2707-14.
     
  7. Gerber MA, Randolph MF, Mayo DR. The group A streptococcal carrier state. A reexamination. Am J Dis Child 1988;142:562-5.
     
  8. Breese BB, Breese HC, Le C. Carriers. In Beta Hemolytic streptococcal diseases. Breese BB, Breese HC. Boston: Houghton Mifflin Professional Publishers 1978, pp143-53.
     
  9. Falck G, Holm SE, Kjellander J, Norgren M, Schwan A. The role of household contacts in the transmission of group A streptococci. Scand J Infect Dis 1997;29(3):239-44.
     
  10. Begovac J, Bobinac E, Benic B, Desnica B, Maretic T, Basnec A et al. Asymptomatic pharyngeal carriage of beta-haemolytic streptococci and streptococcal pharyngitis among patients at an urban hospital in Croatia. Eur J Epidemiol 1993;9:405-10.
     
  11. Hoffmann S. The throat carrier rate of group A and other beta hemolytic streptococci among patients in general practice. Acta Pathol Microbiol Immunol Scand [B] 1985;93:347-51.
     
  12. Centor RM, Meier FA, Dalton HP. Throat cultures and rapid tests for diagnosis of group A streptococcal pharyngitis. Ann Intern Med 1986;105:892-9.

Ronny Gunnarsson MD PhD
Department of Primary Health Care
Göteborg University
SWEDEN

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