# Costs and Effects of Chlamydial Screening: Dynamic versus Static Modeling

Objective: The objective of this study was to assess the impact of modeling type on the economic evaluation of screening programs for asymptomatic *Chlamydia trachomatis* infections.

Study: We compared a stochastic network simulation model (dynamic model) with a decision analysis model (static model) for estimating the cost-effectiveness of an opportunistic screening program. The influence of the model type on the required data, the computed results, and the sensitivity of model parameters were investigated.

Results: When compared with static modeling, dynamic modeling yielded different cost-effectiveness ratios and identified other optimal screening strategies as it considers changes in the force of infection caused by screening. However, it is more complex, data- and time-demanding, and more sensitive to some parameters affecting the force of infection than static modeling.

Conclusions: Dynamic models should be applied for the economic evaluation of prevention measures that have the potential to lower the force of infection such as large-scale chlamydial screening programs.

The advantages and disadvantages of dynamic and static modeling in economic evaluation of chlamydial screening programs are presented. We show that dynamic models are necessary to identify optimal screening strategies.

From the * Institute of Health Economics and Health Care Management, GSF-National Research Center for Environment and Health, Neuherberg, Germany; the † Centre for Prevention and Health Services Research, National Institute of Public Health and the Environment, Bilthoven, The Netherlands; ‡ Groningen University Institute for Drug Exploration/Groningen Research Institute for Pharmacy, University of Groningen, The Netherlands; and the § Department of Infectious Diseases Epidemiology, National Institute of Public Health and the Environment, Bilthoven, The Netherlands

Correspondence: Robert Welte, PhD, GSF-National Research Center for Environment and Health, Institute of Health Economics and Health Care Management, Ingolstädter Landstraßae 1, 85764 Neuherberg, Germany. E-mail: robi.welte@web.de, robert.welte@gsf.de. http://www.gsf.de/igm/en/index.html.

Received for publication September 2, 2004, and accepted January 20, 2005.

GENITAL *CHLAMYDIA TRACHOMATIS* (CT) infections are the most prevalent bacterial sexually transmitted diseases (STD) in the industrialized world. They are often asymptomatic and lead to severe sequelae such as pelvic inflammatory disease (PID), ectopic pregnancy, and infertility.^{1} In several regions of Sweden and the United States, screening programs have decreased the CT prevalence by up to 70%.^{2–4} One randomized clinical trial has demonstrated that CT screening reduced the risk for PID in the following year by approximately 50%.^{5} Currently, several countries are discussing the implementation of large-scale screening programs. To support decision-making, many economic evaluations of various CT screening programs have been performed. These evaluations primarily used static decision analysis models.^{6} We have developed a dynamic model and applied it to an opportunistic screening program in The Netherlands.^{7–9} However, despite the availability of this dynamic approach, most scientists are still using static models.^{10–16}

In this study, we compare our dynamic model (a stochastic network simulation model) with the commonly used static model and discuss the advantages and disadvantages of each model.

## Materials and Methods

We investigated static and dynamic modeling for the economic evaluation of chlamydial screening programs. As a case study, we evaluated the cost-effectiveness of an opportunistic general practitioner (GP)-based screening program for the first 10 years in The Netherlands from a healthcare payer perspective. In the baseline analysis, we limited the target group of the screening program to sexually active women aged 15 to 24 years. An extended age range, women aged 25 to 29 years or 25 to 34 years, was investigated in the scenario analysis. The data needs of the models as well as the impact of the model type on the results and on the sensitivity of model parameters were examined. The time horizon of the analysis was 42 years, based on the screening program duration of 10 years and the assumed maximum time between asymptomatic CT infection and treatment of related negative sequelae (32 years for infertility evaluation).^{9} The analysis corresponds to the Dutch guidelines for pharmacoeconomic evaluation^{17} with 1 exception: costs and health effects were discounted at 3% and not at the requested 4% to simplify the comparison of results to international literature^{18} and to our previously published results.^{9}

### Screening Program

Several important parameters of the models are based on a pilot study for an opportunistic screening program, which was conducted in Amsterdam among 22 GPs in 1996 and 1997. All GP visitors aged 15 to 39 years were offered a ligase chain reaction (LCR) test on urine for CT infection once a year if the visit was not related to a sexually transmitted disease and if the patient indicated heterosexual activity. Positively tested visitors were asked to revisit the GP for treatment and partner referral. Three different partner evaluation or treatment strategies were applied: 22% received test-based treatment (test and, if necessary, 1 azithromycin prescription), 37% received epidemiologic treatment 1 (GP visit plus 1 azithromycin prescription), and 41% received epidemiologic treatment 2 (azithromycin prescription only).^{9}

### Costs and Health Effects

All costs are shown in US dollars, price level of 1997, to make all results fully comparable with the ones of the first publication of our model (see Appendix, “Cost Estimation”).^{9}

As main health outcomes, we used major outcomes averted (MOAs), which were defined as all cases of chronic pelvic pain, ectopic pregnancy, infertility, neonatal pneumonia, and symptomatic PID (Appendix, “Progression of Disease”).

### The Dynamic Model

A detailed description of the model can be found elsewhere.^{7–9} The costs, savings, and health outcomes of screening women as well as partner referral are estimated on a population basis, i.e., the impact of screening on the incidence and prevalence of CT in the population is simulated.

The model can be divided into an epidemiologic and an economic model (Fig. 1). The former is a discrete time Markov model describing as stochastic processes the partnership formation and separation and the disease transmission in a heterosexual model population of 10,000 individuals (1:1 sex ratio) between 15 and 64 years with a uniform distribution over the age range. The model differentiates between age (1-year groups), sex, type of CT infection (asymptomatic or symptomatic), low or high sexual activity, steady and casual partnerships, and considers mixing between age groups (Table 1). One time step represents 1 day. The opportunistic screening program was integrated into the model. One hundred Monte Carlo simulations were performed for each scenario. Averages of the yearly incidence and prevalence as well as the number of infected and subsequently successfully treated persons were taken. These outcomes differ for each year as the model takes into account the screening program's impact on the force of infection (per susceptible rate of infection).^{19} The force of infection depends on the number of infectious individuals at that time and decreases with each additional year of screening. The derived yearly incidence is higher than the yearly prevalence as individuals who are infected and get cured or recover and get infected again are counted twice. The model rendered a prescreening prevalence of 4.3% in women and 4.1% in men in the total model population.^{8}

The economic model is a decision analysis model. It was fed with data by sex and 5-year age group from the epidemiologic model to calculate the number of averted infections and averted complications of CT infected persons (see Fig. 1 and Appendix, “Progression of Disease”) and the number of screened and treated persons per year (see Fig. 1). Monetary valuation of the resource use caused by these outcomes yielded the savings and the intervention costs.

### The Static Model

The static model is purely a decision analysis model (Fig. 2). The costs and benefits of screening 1 woman as well as partner referral are estimated on an individual basis. For each strategy (screening vs. no screening), the expected costs and MOAs per screened asymptomatic woman are derived by rolling back and averaging out the decision tree (Fig. 2). Unlike the dynamic model, it uses CT prevalence to estimate the number of (averted) infections per year, which has to be fed into the model. It assumes that this prevalence is stable and does not change as a result of the screening program, i.e., it assumes a constant force of infection during the years of screening. The model works with an average woman who is a statistical composite of a “core/noncore group” woman. The number of current and future partners of core group and noncore group women required by this model was derived through the dynamic model and used to assess the impact of partner referral and reinfection resulting from untreated infected partners (Table 1).^{7,8} Current partners that are CT-infected might infect the successfully treated woman and develop epididymitis, whereas future partners might become infected and thus need medical assistance for urethritis or epididymitis. We assumed that, on average, asymptomatically infected women were found by screening 6 months after they got infected and thus they were assumed to be infectious for another 6 months. One year represents 1 time step.

To make the results of the static model more comparable to the dynamic model, we applied it to the same model population (heterosexual population with 10,000 individuals between 15 and 64 years of age and a uniform distribution of sex and age). We calculated the number of tested women per year identical to the dynamic model (i.e., the number of women * the age-dependent probability of visiting a GP per year * the probability of being sexual active * test acceptance = 510)^{9} and simulated the derived cohort through the decision-analysis model (Fig. 2). To derive the cumulative costs and health effects of screening for 10 years, we added the yearly net costs and MOAs (which are constant because the CT prevalence is assumed to stay constant) correcting for discounting.

### Prevalence

Based on its input parameters, the dynamic model computed an estimate for the CT prevalence in The Netherlands before screening. Although this prevalence estimate corresponded well with the 1 from the pilot study in Amsterdam,^{8} they were not identical. To make the results yielded by the dynamic and static model comparable, we used the prevalence estimate from the dynamic model for the static model (Table 1).

### Sensitivity Analysis

We performed a sensitivity analysis to compare the robustness of the static and the dynamic model for the baseline scenario. The impact of varying the rate of partner referral, the number of partners (see Appendix, “Variation of Partner Number”), the test sensitivity, the duration of the screening program, decreasing the risk of PID caused by CT, and changing the discount rate was investigated.

## Results

### Data Needs

The 2 models strongly differ about the key variable of prevalence. Although the static model requires the CT prevalence as an input variable, the dynamic model simulates the prevalence based on the sexual behavior, disease characteristics, and the screening program; thus, it demands the results of prevalence studies only for assessing the model's validity. In addition, the static model uses a fixed prevalence estimate that does not change during the screening program duration. In contrast, the dynamic model calculates the yearly prevalence and incidence based on the transmission dynamics of CT and the implemented screening program. It uses the prevalence for the calculation of the positive predictive value of the test while it applies the incidence to estimate the number of (averted) infections.

The dynamic model requires much more detailed data about the sexual behavior and the infectious disease than the static model such as duration of partnerships, frequency of sexual intercourse in partnerships, and transmission probability per sexual contact (Table 1). As time step, the dynamic model uses 1-day increments, whereas the static model uses 1 year. Hence, the time units in which the probabilities are expressed must be adjusted respectively. For example, for asymptomatically infected women, the dynamic model uses the daily recovery rate of 0.0027 (calculated as 1 divided by the infectious period in days), whereas the static model uses a rate of 1 per year.

### Impact of Model Structure on Results

The results gained with the dynamic and static model strongly diverge about the analyzed baseline scenario, i.e., GP-based screening of sexually active women aged 15 to 24 years and 65% partner referral for 10 years. Table 2 shows that the static model estimates a cost-effectiveness ratio of approximately US $700 per MOA, whereas the dynamic model renders net savings. Additionally, the static model yields only approximately half of the MOAs computed by the dynamic model.

The 2 models also yield very different results for extending the screening program to older women. For including women aged 25 to 29 years or 29 to 34 years, the static model estimates incremental costs of approximately US $1800 or US $2520 per additionally gained MOA, respectively, whereas the dynamic model calculates net savings. In the dynamic model, screening women aged 15 to 29 or 15 to 34 even strictly dominates screening women aged 15 to 24 years, i.e., both strategies result in more health effects and more savings than baseline. Screening women aged 15 to 29 years renders the highest net savings, whereas screening women aged 15 to 34 years yields the most MOAs (Table 2). By extending the screening program to women aged 25 to 29 years, more additional savings (as a result of prevented CT infections and averted sequelae of CT) than additional intervention costs (as a result of additional screening tests and treatments) are achieved. This is caused by a much stronger decrease of the CT incidence, thus increasing the effectiveness of the screening program on the population basis substantially. The additional inclusion of women aged 29 to 34 years results in an even lower CT incidence and thus more MOAs. However, each additional MOA costs US $59 and thus the total net savings decrease compared with screening women aged 15 to 29 years only.

The diverging outcomes of the static and the dynamic model are mainly caused by the transmission chains considered in the models and assumptions about the screening program's influence on the CT prevalence and force of infection. The dynamic model includes the prevention of the transmission from the cured woman to her male partners and the prevention of transmission from her male partners to other female partners and so on, and considers this in the computation of the yearly incidence and prevalence. Thereby, it accounts for both the direct effects on the cured persons and the indirect protection effects on other persons. The indirect protection of susceptible persons in the population is caused by screening and treating the (future) partners of susceptible persons and thus decreasing the risk of getting infected by a (future) partner. Indirect protection effects lead to a decreased force of infection, which can strongly influence the cost-effectiveness of prevention programs. This effect has been frequently described, defined, and assessed for vaccination programs^{19,21} but rarely for STD screening programs.^{9,22}

In our static model, only the transmission of CT from the current partner to the cured woman (reinfection risk) as well as from the infected woman to future male partners is considered. Thus, the transmission risk from male partners to other female partners and from them to other male partners, and so on, is excluded. As a consequence, it includes only 2 links of possible future transmission chains and therefore a very small part of the indirect protection effect. It also assumes that the screening program has no impact on the force of infection and the resulting CT prevalence per year. As result, the static model overestimates the cost-effectiveness ratio of an effective screening program that impacts the CT prevalence.

Figure 3 shows that the considered indirect protection effects also impact the distribution of savings by disease category. Although the dynamic model computes considerable savings as a result of the indirect prevention of symptomatic CT infections (cervicitis, urethritis), the static model mainly focuses on the savings resulting from prevented sequelae in the screened woman. If we ignore the possible infection of future male partners by the infected woman in the static model, no savings would be computed for averted cases of urethritis. On the other hand, if we extend the static model to include 1 further link of possible future transmission chains, the distribution of savings would change again. This shows the arbitrariness associated with where and when to “stop” the transmission chain in static models, a decision that influences the results.

### Sensitivity of Model Parameters

The sensitivity analysis (Fig. 4) demonstrates that the impact of parameter changes on the results of the dynamic and static model may greatly differ for parameters that affect the force of infection such as partner referral and screening duration. No partner referral is the only investigated scenario for which the dynamic model computes net costs instead of net savings. The influence of screening duration on the program's cost-effectiveness ratio strongly depends on the model used. Figure 5 presents this; the slopes of the lines of the cumulative net costs or MOAs of the static model are approximately constant. There is only a very slight decrease caused by discounting, which has no influence on the cost-effectiveness ratio. On the contrary, the slope of the line of the cumulative net costs derived by the dynamic model substantially decreases after the first year of screening with time. Additionally, the slope of line of the cumulative MOAs of the dynamic model considerably increases with screening time. As a result, the screening program becomes with each year more cost-effective. The slopes of the lines of the dynamic model mainly reflect the decreasing force of infection; the screening program decreases the CT incidence each year to a lower level, and thus the difference in CT incidence and associated complications between screening and no screening increases each year. Clearly, if the prevention program runs long enough, the model will reach a new equilibrium incidence and prevalence and the cost-effectiveness ratio will attain a plateau.^{23}

In the dynamic model, increasing the number of partners leads to a significantly higher CT prevalence and incidence, whereas decreasing the number of partners decreases these measures. On the contrary, changing the number of partners does not affect the prevalence in the static model. As a result, the qualitative effect of a higher or lower number of partners on the net costs and MOAs is predictable in the static model, whereas this effect has to be simulated for each number of partners in the dynamic model. In the latter, fewer partners do not necessarily mean a lower cost-effectiveness ratio as a result of the complex interaction of the various model parameters. Still, both partner number scenarios rendered cost-savings in the dynamic model.

When we change the number of partners as well as the prevalence of the static model so that the latter is identical to the respective prescreening prevalences of the dynamic model, the net costs decrease by 74% or increase by 41%, whereas the number of MOAs increases by 68% or decreases by 28%, respectively (not shown in Fig. 4). These results of the static model diverge not only quantitatively, but also qualitatively from the results gained when changing only the number of partners of the static model (Fig. 4).

Obviously, a higher test sensitivity will result in a more cost-effective screening program. This improvement is stronger in the static than in the dynamic model. The static model assumes the same high CT prevalence for each year and thus the same high number of tested individuals. On the other hand, the dynamic model takes into account the decreasing CT prevalence in response to the successful screening program, and thus fewer infected persons are detected by screening.

Parameter changes that do not affect the force of infection in the dynamic model have a similar level of influence on some outcomes of the 2 models. Decreasing the PID risk resulting from untreated CT infections by 50% leads to an identical decrease (48%) in the number of MOAs in both models. The MOA decrease is less than 50% because the risk for PID does not affect the risk of neonatal pneumonia, a CT complication also considered an MOA. However, the lower PID risk leads to different net costs increases in the 2 models. This is caused by a difference in the percent of averted costs attributable to prevented cases of PID or its sequelae under the dynamic (approximately 70%) or static model (95%) (Fig. 3). Using a different discount rate influences the results of the dynamic model more than those of the static model because the dynamic model estimates more net savings and MOAs in the later years of the screening program than in the starting years. Increasing the discount rate to 4% (as requested by the Dutch pharmacoeconomic guidelines)^{17} has a very limited effect on the results of both models (Fig. 4).

## Discussion

We have shown that our dynamic model leads to very different results than our static model for the investigated GP-based opportunistic screening program for women. As expected, the static model estimated the prevention of fewer negative health outcomes and associated averted costs resulting from screening. Moreover, it identified the incorrect optimal age group. The screening program limited to women aged 15 to 24 years is the most cost-effective option according to the static model. However, in the dynamic model, this screening option is dominated by those including women aged 15 to 29 years and women aged 15 to 34 years. Thus, the assumption that neglecting the influence of an effective screening program on the force of infection may only lead to conservative results is wrong; it may also result in screening the wrong target group. In addition, although the static model indicates that the duration of the screening program has no impact on the cost-effectiveness ratio, the dynamic model shows exactly the opposite. As a result, dynamic and not static models seem appropriate for the economic evaluation of CT screening programs that might affect the force of infection. However, static models have frequently been applied in the past, although many of them have not included the risk of reinfection resulting from failed partner referral.^{6}

Table 3 summarizes the advantages and disadvantages of the 2 models. In general, the dynamic model should be first choice because it treats CT as an infectious and transmittable disease, whereas the static model accounts for this only in a very limited and not appropriate way. The only reasons speaking against using our dynamic stochastic network simulation model are its higher complexity, data demand, time and monetary costs, and need of mathematical modeling expertise. On the other hand, static models might be the preferred option for estimating the cost-effectiveness of screening programs that have no impact on the force of infection. An example of such programs might be screening in developed countries that is limited to pregnant women. Such a program 1) targets only a small group within a population, and 2) the selected group is not likely to consist of a higher-than-average number of core group women.

The problem of (partially) neglecting the infectious character of infectious diseases in economic evaluation is not limited to STDs. When assessing the cost-effectiveness of prevention measures against infectious diseases, researchers often ignore the fact that finding and treating an infected person or the active vaccination of a healthy person might decrease the force of infection and thus result in indirect protection effects. For estimation of the pathogen spread and the impact of intervention, mathematical models of the transmission of infectious pathogens are valuable tools because they enable the integration of biologic, medical, and epidemiologic data. Dynamic models of the SIR-type (susceptible, infected [and infectious], or removed [immune or dead])^{19,24,25} have been frequently used for the economic evaluation of vaccination programs against many infectious pathogens. In these models, the population consists of individuals who are susceptible, infected, or removed and the model describes the transition between these states. The model assumes that the population mixes homogenously (analogously to the law of mass action) and thus that the probability of a contact between any 2 members of the population is always the same. However, it is possible to relax the condition of the SIR model about the population mixing by dividing the population further into subgroups such as persons with high or low sexual activity. SIR models also assume that contacts between individuals take no time. These assumptions seem reasonable for highly infectious diseases such as measles, but not for STDs like CT because partnerships often persist for a long time. To account for partnership duration, pair formation models have been developed. Their main disadvantage is the assumption that individuals can have at most 1 partner at a time. Relaxing this condition leads to unmanageable models. Recently, Eames and Keeling have presented a monogamous network model, which combines features of pair formation and network models. Each person is constrained to, at most, 1 sexually active relationship. After the partnership breaks up, a new partnership may subsequently form within a fixed set of potential partnerships, which are represented by a mixing network.^{26} Stochastic individual-based network models such as the dynamic model presented are capable of considering partnership duration and concurrent partnerships.^{27}

As already mentioned, the concept of indirect protection is well known in the vaccination field, and most definitions only refer to the fact that in a population, a high percentage of immune persons decreases the infectious risk for susceptible persons.^{19,21,28} However, the results of our dynamic model demonstrate that indirect protection effects also occur for STD screening programs; cured persons cannot infect their partners any more, who in turn will not infect their partner, and so on. Nevertheless, cured persons can get reinfected and thus are not immune to the STD. As a result, considering the transmission dynamics is even more important for screening programs of STDs like CT and *Neisseria gonorrhoeae* than for most vaccination programs because a cured person remains—unlike a vaccinated person—still susceptible.

We would like to emphasize that the presented results, about the cost-effectiveness of screening different age classes of women, cannot be simply transferred to other settings and countries. It is necessary to perform a detailed transferability check after which the required adjustments of the results are identified and made.^{29} For example, populations with different sexual behavior would require parameter changes of the dynamic model. In addition to population characteristics, also healthcare system and methodologic characteristics might need to be corrected. Our dynamic model has recently been adjusted for Denmark, where it has been successfully used for the economic evaluation of a systematic home-based screening program.^{30} The evaluation rendered a prescreening CT prevalence that corresponds well with the results of Danish screening studies supporting the validity of our model. At this time, 2 research groups in the United Kingdom and in The Netherlands are creating new dynamic models for simulating the cost-effectiveness of CT screening programs. Members of the *Chlamydia trachomatis* Screening Studies (CLASS) have recently proposed that “all future economic evaluations of chlamydia screening should use a dynamic modeling approach.”^{31} Thus, it seems that the transmittable character of CT is increasingly being recognized in economic evaluations. However, one should keep in mind that there is no perfect model and that dynamic models also have their drawbacks and limitations.

Large-scale screening programs have the potential to decrease the chlamydial incidence and prevent severe sequelae as demonstrated with our dynamic model and observed in some countries. Such programs will also shorten the average duration of infection, which in turn might decrease the development of infection-induced immunity,^{32} resulting in a higher population susceptibility. Another potential danger is the development of antibiotic resistance,^{33} because even a successful screening program will lead to an increase of antibiotic use.

### Appendix

### Progression of Disease

Figure 6 shows the progression of disease. We distinguished between symptomatically and asymptomatically infected persons. Symptomatically infected women and men were defined as all infected persons that visit a healthcare provider for treatment of their disease. We assumed that all of them got effectively treated without serious side effects and that no progression of disease took place. We also assumed that the treatment of asymptomatic persons with azithromycin led to no serious side effects requiring the use of medical resources.

We assumed that PID, epididymitis, and complications in newborns take place in the year of CT infection and that chronic pelvic pain occurs within 5 years of PID onset. The age-specific probabilities of giving birth were used for calculating the age-specific vertical transmission probabilities. The probability of an ectopic pregnancy or infertility assessment depends on the age-specific active interest of having a child. Diagnosis and treatment of infertility was assumed to occur 2 years after the first unsuccessful attempt to conceive.

### Cost Estimation

Table 4 presents the used unit costs. Only direct medical costs were considered. The resource utilization and valuation of the different CT-associated complications have been described in detail in a previous article.^{9} They correspond to the latest STD treatment guidelines of the Centers for Disease Control and Prevention.^{34} Costs were converted from Dutch guilders to US dollars by using gross domestic product purchasing-power parities from the OECD.^{35}

### Variation of Partner Number

For altering the partner number in the sensitivity analysis, we changed the parameters ρ and f in the dynamic model.^{7} The parameter ρ determines the rate of formation of new partnerships, i.e., it determines the number of new partnerships formed per time unit, whereas the parameter f denotes the probability that a partnership is steady (i.e., not casual). For increasing the number of partners, we changed ρ from 0.006 to 0.1 and f from 0.2 to 0.1. For decreasing the partner number, we used 0.005 instead of 0.006 for ρ. The derived higher/lower number of partners was also used in the static model to get comparable results. Cited Here...

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