Pelvic inflammatory disease (PID) is the most common direct complication of sexually transmitted *Chlamydia trachomatis* (chlamydia) and *Neisseria gonorrhoeae* (gonorrhea) infections in women.^{1} PID occurs when microorganisms ascend from the vagina and/or endocervix to the upper genital tract, including endometrium, fallopian tubes, and contiguous structures.^{2} Inflammation and scarring in the fallopian tubes is a strong risk factor for subsequent ectopic pregnancy and tubal infertility.^{3} The link between “latent gonorrhea,” pelvic inflammation, and infertility was first suggested in the late 19th century,^{4} and gonorrhea was the subject of the first mathematical modeling studies examining the impact of sexually transmitted infections on fertility.^{5} Screening to detect and treat asymptomatic chlamydia, which is now the most common notifiable sexually transmitted infection in the United States,^{2} is recommended to prevent PID.^{6},^{7}

It is important to know when during the course of endocervical infection ascension to the upper genital tract occurs, especially because the infectious period for asymptomatic *C. trachomatis* is more than 1 year, on average.^{8} There must be a time window during which screening, followed by treatment of infection, can interrupt this process to be able to observe a beneficial effect in an individual woman.^{9} It has been suggested, however, that there might be a limit to the effectiveness of chlamydia screening interventions to prevent PID because tubal damage might already have occurred by the time of screening and treatment.^{10} Randomized controlled trials provide evidence at the individual level that a once-off offer of a screening test for chlamydia and treatment of positive cases can prevent up to half of PID due to all causes^{11}^{–}^{13} but do not elucidate the causal pathway or the impact when chlamydia screening is part of routine practice.

Mathematical modeling is a useful tool for investigating processes and mechanisms that are difficult to observe in practice.^{14} Ideas about possible processes can be described formally using mathematical equations or rules, and the effects of uncertainty and changing assumptions about processes or parameter values can be analyzed.^{14} The construction of a mathematical model requires the disease process to be described.^{14},^{15} The objective of this study was to conduct a systematic review to determine how progression from chlamydia or gonorrhea to PID has been described in mathematical modeling studies.

#### MATERIALS AND METHODS

We used a protocol to describe the methods and procedures for our systematic review (Supplemental Digital Content 1, online only, available at: http://links.lww.com/OLQ/A39).

##### Eligibility Criteria

Eligible publications studied the progression from chlamydia or gonorrhea infection to PID either using a decision tree or incorporating PID in a mathematical model. We included gonorrhea because it is a curable bacterial sexually transmitted infection that causes PID, in case there were examples of gonorrhea models that might be able to be adapted to chlamydia. We excluded publications if only a male population was incorporated without considering complications in women; no progression to PID was considered, for example, cost of illness studies; animal studies; or where PID was investigated as a complication of surgical instrumentation, such as intrauterine device insertion.

##### Information Sources

We searched Ovid Medline, Embase, Popline, and The Cochrane Library from the earliest date of the database to October 2009 without language restrictions. The reference lists of included articles were searched to identify additional relevant articles. There is no single Medical Subject Heading (MeSH) for mathematical modeling studies; therefore, we combined the following existing MeSH terms: “models, biologic”; “models, theoretical”; “computer, simulation”; “Markov chains”; “decision support”; “decision tools”; “decision making”; or the free text term “model*,” with the MeSH heading “pelvic inflammatory disease” and excluded “animal.”

##### Study Selection

Two reviewers screened titles and abstracts of retrieved articles. Any study selected as being potentially eligible by either reviewer was retained for review of the full text. Discrepancies were resolved by discussion. We included each model only once, even if it was used in more than one publication. A model was considered to be unique in this review if either the structure describing progression from chlamydia or gonorrhea to PID differed or if the model structure was duplicated, but different values for the parameter describing progression to PID were used. If there were multiple publications using the same model, the earliest publication was considered to be the original.

##### Outcomes

The primary outcome was the description of how timing of progression from lower genital tract *C. trachomatis* or *N. gonorrhoeae* infection to PID was modeled. Secondary outcomes were as follows: descriptions of the natural history of chlamydial and gonococcal infection, the rate or probability of progression to PID, or duration of a PID episode.

##### Definitions

The progression from lower genital tract chlamydia or gonorrhea infection to PID could be modeled using dynamic or static methods. In this study, a dynamic model was defined as one in which the incidence of PID was dependent on time and on changes in the number of women infected with chlamydia or gonorrhea. This definition was not affected by the way in which the supply of infected chlamydia or gonorrhea cases was modeled. Thus, progression to PID could be defined as static even if cases of infection were derived from a dynamic transmission model.

##### Dynamic Model Structures.

Markov model (also known as a state-transition model): assumes that a person is always in one of a finite number of health states and that the transition to the next health state is only dependent on the current state. The time line is split into equal intervals (cycles), and after each cycle, the system of health states is updated using the transition probabilities.^{16}

Compartmental model (also known as population-based model): persons within a population are categorized into different stages (states or compartments) of the natural history of a disease. The rate of flow from one stage to the other has to be defined on a continuous time scale.^{17}^{–}^{19}

Individual-based models (also known as agent-based models): each individual in the population is represented separately so the state of each individual is known. Mathematical rules determine interactions between individuals. The model can keep track of the disease history of each individual.^{18},^{19}

##### Static Model Structure.

Static decision tree models describe the probabilities with which a person moves from one health state to another but do not specify when an event occurs, for example, progression to PID. A decision tree consists of 3 types of nodes (decision nodes, chance nodes, and end nodes).^{16}

##### Data Collection

A form was developed using EpiData 3.1 (www.epidata.dk) and piloted to extract information about descriptions of the natural history of infection and details of model structure and parameter values (questionnaire available on request). We assessed the completeness of reporting of selected items required in dynamic modeling studies by adapting guidance from the *American Journal of Epidemiology*.^{20} Key items, with specific criteria in brackets, were as follows: an appropriate description of the natural history of infectiousness and of disease (explicit descriptions in text); a clear description of the model structure (including a diagram); key assumptions presented (values used for the percentage or rate of progression to PID in all models, duration of PID for dynamic models); all parameters and variables clearly defined (with parameter ranges justified by citations or confidence intervals); appropriate sensitivity; and/or uncertainty analysis. Two pairs of reviewers independently extracted data. Discrepancies were resolved by discussion or by consultation with a third reviewer.

##### Data Analysis

For all publications, we documented explicit statements describing the natural history of chlamydia or gonorrhea infection in women and the timing of progression to PID. For studies using dynamic models, we also described how progression to PID was incorporated into the model.^{15} Values used for the percentage or rate of progression from chlamydia or gonorrhea to PID were summarized separately for dynamic and static models because of the differences in model structure. For dynamic models, the duration of PID was also documented, if stated.

#### RESULTS

Our literature searches identified 253 unique publications; 61 full-text publications were screened and 45 eligible publications were included.^{9},^{21}^{–}^{64} Reasons for exclusion are summarized in Figure 1. Of these 45 publications, 40 were considered to be a unique model (Table 1). There were 4 models that are linked to 2 or more publications using the same model structure and parameter values, that is, identified by the first author of the main publication: Buhaug^{25},^{26}; Hu^{38},^{39}; Low^{41},^{56}; and Postma.^{53}^{–}^{55} In 2 further cases, a linked publication using the same model structure was considered a unique model because the parameter value describing progression to PID differed.^{23},^{27}

Figure 1 Image Tools |
Table 1 Image Tools |

Of the 40 unique models, 34 considered progression from chlamydia only to PID, 5 examined both gonorrhea and chlamydia,^{9},^{30},^{40},^{43},^{62} and 1 looked at gonorrhea only.^{22} All models that included both chlamydia and gonorrhea assumed the same values for progression from each infection to PID. In 39 models, the purpose of the model was to examine the cost-effectiveness of interventions for the diagnosis and management of chlamydia or gonorrhea; 1 model examined the effects of a chlamydia vaccine.^{34} Nine models incorporated progression from chlamydia or gonorrhea to PID dynamically.^{9},^{22},^{25},^{31},^{34},^{38},^{41},^{57},^{60} Of these, we categorized 4 as Markov models,^{9},^{22},^{38},^{60} 3 as compartmental models,^{25},^{31},^{57} and 2 as individual-based network models.^{34},^{41} There were 28 static decision trees.^{21},^{23},^{24},^{27}^{–}^{30},^{32},^{35}^{–}^{37},^{40},^{42}^{–}^{44},^{47}^{–}^{53},^{58},^{59},^{61}^{–}^{64} This group includes 4 models that considered the transmission of chlamydia infection dynamically^{21},^{23},^{27},^{63} but used static decision trees for the progression to PID. In 3 publications, it was not possible to determine whether progression to PID was incorporated statically or dynamically.^{33},^{45},^{46} Further descriptive analyses were therefore restricted to the remaining 37 models.

##### Descriptions of Chlamydia or Gonorrhea Natural History and Progression to PID in Dynamic Models

For 4 of 9 dynamic models, explicit statements about the timing of progression from chlamydia or gonorrhea infection to PID were found with descriptions about how this was implemented in the model (Table 2); 2 of 4 Markov models,^{9},^{38},^{39} 1 of 3 compartmental models,^{57} and 1 of 2 individual-based models.^{34} For Smith et al, the influence of the timing of progression on the cost-effectiveness of different screening intervals was the main research question.^{9} In their Markov model with a 1-month cycle time, the interval from initial infection to PID development time was varied between 1 and 12 months, with an assumption that PID development time was the same for chlamydial and gonococcal infections. Results showed that screening prevented more cases of PID when the PID development time was 12 months than 1 month. The authors did not reach a conclusion about the most likely interval for PID development because this was not a required outcome for the economic analysis. In another Markov model with a 6-month cycle, Hu et al stated explicit assumptions that 30% of women would develop PID within 6 months of initial chlamydia infection, and that the risk of PID continued as long as chlamydia infection persisted; the average duration of chlamydia infection was assumed to be 0.93 years.^{38}

Among the compartmental models, Townshend and Turner made an explicit assumption that tubal damage occurs in the second half of chlamydia infection.^{57} Their compartmental model included different chlamydia infection stages: stage 1 “allows individuals to be screened very early … before any damage is done”; in stage 2, a proportion of women develop PID. The mean time to reaching the second stage was assumed to be half the mean natural duration of the infection.^{57} In an individual-based model, Gray et al stated their assumption that PID can occur uniformly during the infectious period.^{34}

In the remaining dynamic models, the timing of progression to PID was not stated explicitly but could be inferred from the model structure. Buhaug et al published the first compartmental model on progression from chlamydia to PID in 1989.^{25} This model included a separate compartment to incorporate progression (with a probability of 20%) from chlamydia to a PID episode, which lasted 3 weeks, and after this period, a woman became susceptible. Gift et al also published a model with a separate compartment for PID to investigate the effects of chlamydia screening in men on prevention of sequelae in women as an outcome.^{31} Low et al used an individual-based model with a daily progression rate to PID calibrated to PID incidence rates from empirical estimates.^{41},^{65} Aledort et al and Walleser et al used Markov models with cycle times of 6 and 12 months, respectively.^{22},^{60} Walleser et al stated that there was no conclusive information about the timing or rate of progression from chlamydia to PID (Table 2).

##### Descriptions of Chlamydia or Gonorrhea Natural History in Static Models

In one study, it was explicitly stated that the timing of progression was unknown^{61} (Table 2). There were also some statements in introduction or discussion sections that implicitly assumed that that progression to PID does not happen immediately, for example: “Early diagnosis of [chlamydia] is important, not only to minimize disease spread, but also to prevent untreated infections from progressing to pelvic inflammatory disease …”^{24} Values in the decision trees for the percentage of women with chlamydia infection who progress to PID are shown in Figure 2. The average of the main value was 22.4% (range, 10%–35%, n = 25). For 16 of 28 models references to published articles were given for the stated ranges.

##### Reporting Quality of Dynamic Models

Reported characteristics of the 9 dynamic models are summarized in Table 3. A picture of the model structure was shown in 5 of 9 models, and only 2 provided mathematical details. In the 3 models that stated a value, the duration of PID ranged from 1 day to 2 months. Only Buhaug et al^{25} explicitly considered that the risk of developing PID might change over time, with a decreasing fraction of chlamydia-infected women developing PID with increasing age.

#### DISCUSSION

This systematic review found 40 unique mathematical models that considered the progression from chlamydia or gonorrhea infection to PID. Among these, 4 distinct possibilities for the timing of the development of PID were identified in studies that modeled the progression to PID dynamically. In most included studies, there was no explicit statement about progression or natural history. In static models, the average fraction of cases of chlamydia assumed to develop PID was 22%.

The strength of this study is the collation of publications for more than 20 years, which allowed an overview of conceptual frameworks in mathematical modeling studies about the natural history of chlamydia and gonorrhea infections and of the quality of reporting of dynamic models. This review expands the scope of a previous systematic review, which was limited to studies about *C. trachomatis* transmission to examine the cost-effectiveness of chlamydia screening.^{66} Among the modeling studies that incorporated both chlamydia and gonorrhea, all assumed the same characteristics for both infections. Although there might be differences, these probably did not affect study outcomes because chlamydia accounts for a much higher proportion of PID cases than gonorrhea. A weakness of the present review is that the literature search might have missed some relevant studies because there is no single MeSH term for mathematical modeling studies. We tried to overcome this by building a search string combining MeSH headings for relevant study designs and by searching for additional studies in the reference lists of included publications.

This review has identified 4 potential ways in which the timing of progression of chlamydia or gonorrhea infections to PID has been conceptualized by authors of mathematical modeling studies: uniformly throughout the duration of infection^{34}; in the first half of the infectious period^{38}; in the second half of the infectious period^{57}; or that there is a most likely interval from the initial infection for the development, which varies between 1 to 12 months.^{9} These possibilities span the whole duration of the lower genital tract infection. It is not possible to compare the results of these studies directly to say which of the potential timings is most plausible because of the many other differences in model structure, parameter values, and presentation of findings. Model structures that incorporate a longer^{9},^{34},^{57} rather than a shorter^{38} interval for PID development would be expected to predict a strong impact of a chlamydia screening interventions, consistent with that observed in randomized controlled trials.^{12},^{13} This is not consistent with studies in mice, however, in which salpingitis was documented 24 hours after vaginal inoculation with a *C. trachomatis* mouse pneumonitis biovar.^{67} Empirical studies in humans cannot provide the information needed because it is not possible to measure the timings of the start of a chlamydia infection and the onset of upper genital tract infection accurately.

The common feature of all the dynamic modeling studies in this review^{9},^{22},^{25},^{31},^{34},^{38},^{41},^{57},^{60} was that the chlamydia screening intervention had a direct effect of removing women from the infected state before PID occurs. This direct effect is observed in trials of chlamydia screening that are randomized at the individual level.^{11},^{13} There are several pathologic mechanisms for such an effect at the individual level. Of the studies that described possible mechanisms, all mentioned that early chlamydia detection and treatment could prevent ascending infection. Additional possibilities are that screening and treatment limit damage from an infection that has already ascended^{68} or prevent tubal damage from repeat infections,^{9} probably through immunologically mediated mechanisms. In the models that incorporate both *C. trachomatis* transmission and progression to PID dynamically,^{25},^{31},^{34},^{41},^{57} the intervention also has an indirect effect; reducing chlamydia prevalence over time reduces exposure to the causative agent.^{10} In the cluster-randomized trial of Ostergaard et al, it is possible that indirect effects within sexual networks of the students participating in the trial contributed to the reduction in PID.^{12} In models that include *C. trachomatis* transmission dynamic and progression to PID statically,^{21},^{63} the predicted preventive effect of the screening intervention results entirely from the indirect effect of reduced chlamydia prevalence on exposure to initial infection.

Assumptions about the probability of progression from chlamydia or gonorrhea infection to PID are known to have a strong influence on the predicted effectiveness of chlamydia screening.^{21},^{39} The average value used for the percentage of women developing chlamydia-associated PID in decision tree analyses was around 20%. This is higher than the probability of around 10% within 12 months estimated by Oakeshott et al in the control arm of their randomized controlled trial.^{13},^{69} Adams et al also compared the prediction from their model with empirical data about cases of PID diagnosed in primary care in England and concluded that “an estimate of around 10% progression to PID is the most likely.”^{21}

Understanding the natural history of disease and the mechanisms of action of interventions are important components of the program science that is needed to understand the effects of prevention programs whose primary aim is to reduce morbidity.^{70} The main unanswered question identified by this review is that of PID development time. Smith et al suggest that further research is worthwhile from a cost-effectiveness standpoint in populations that are not at high risk of developing PID,^{9} which includes the young female populations targeted by current chlamydia screening recommendations.^{6},^{7} This review allows recommendations for future research and reporting practice. First, models that use a dynamic structure for the progression from lower genital tract infection to PID are needed to investigate uncertainty about mechanisms of PID development. Second, a single dynamic mathematical model that can incorporate the different possible mechanisms identified in this review would allow direct comparison of the incidence of PID predicted by each mechanism as well as comparison with the observed results from randomized controlled trials of chlamydia screening interventions, such as that done by Oakeshott et al.^{13} Third, reports of mathematical modeling studies should describe how the natural history of chlamydia infection is conceptualized and implemented in the model.^{14},^{15} The results of this review offer the opportunity to advance our understanding about the how chlamydia screening interventions work to prevent PID.