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Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

Herzog SA, Low N, Berghold A - BMC Infect. Dis. (2015)

Bottom Line: We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence.The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model.The RR and the sample size needed per group also depend on the natural history parameters of chlamydia.

View Article: PubMed Central - PubMed

Affiliation: Institute for Medical Informatics, Statistics and Documentation, Medical University of Graz, Graz, Austria. herzog.sereina@gmail.com.

ABSTRACT

Background: The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID).

Methods: We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size.

Results: The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia.

Conclusions: Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

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Related in: MedlinePlus

Estimated sample sizes under the two assumptions in the Prevention Of Pelvic (POPI) trial. Plotted curves represent the estimated sample size needed per group while varying power of the study; for the original POPI trial (green lines) and for two types of progression; the one where PID develops at a constant rate throughout infection (dashed-dotted lines), and the one where PID develops at the end of infection (dashed lines). The third type of progression where PID develops immediately after infection is not shown. Panels a and b separate the two different assumptions about the projected follow-up incidence of PID in the original POPI trial: scenario 1 with 2 % per year (Panel a), and scenario 2 with 3 % per year (Panel b). The red circle represents the sample size with 80 % power in the original POPI trial. PID, pelvic inflammatory disease; POPI trial, Prevention Of Pelvic Infection trial
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Fig2: Estimated sample sizes under the two assumptions in the Prevention Of Pelvic (POPI) trial. Plotted curves represent the estimated sample size needed per group while varying power of the study; for the original POPI trial (green lines) and for two types of progression; the one where PID develops at a constant rate throughout infection (dashed-dotted lines), and the one where PID develops at the end of infection (dashed lines). The third type of progression where PID develops immediately after infection is not shown. Panels a and b separate the two different assumptions about the projected follow-up incidence of PID in the original POPI trial: scenario 1 with 2 % per year (Panel a), and scenario 2 with 3 % per year (Panel b). The red circle represents the sample size with 80 % power in the original POPI trial. PID, pelvic inflammatory disease; POPI trial, Prevention Of Pelvic Infection trial

Mentions: Different sets of published assumptions about PID incidence rates and the size of intervention effect lead to different conclusions about the temporal relationship between chlamydia infection and PID (Fig. 2). In scenario 1, the relationship between the power of a trial and the sample size required per group is compatible with the hypothesis that PID can develop throughout the course of infection (Fig. 2a). Assuming a constant progression rate from chlamydia to PID results in a RR of 0.49, which is close to the original RR assumption in the POPI trial (RR = 0.48). If chlamydia progresses to PID only at the end of the infectious period, the model predicts a RR of 0.39. In this scenario, 28.6 % of infected women have to develop PID to achieve the 2 % PID incidence after one year of follow-up.Fig. 2


Sample size considerations using mathematical models: an example with Chlamydia trachomatis infection and its sequelae pelvic inflammatory disease.

Herzog SA, Low N, Berghold A - BMC Infect. Dis. (2015)

Estimated sample sizes under the two assumptions in the Prevention Of Pelvic (POPI) trial. Plotted curves represent the estimated sample size needed per group while varying power of the study; for the original POPI trial (green lines) and for two types of progression; the one where PID develops at a constant rate throughout infection (dashed-dotted lines), and the one where PID develops at the end of infection (dashed lines). The third type of progression where PID develops immediately after infection is not shown. Panels a and b separate the two different assumptions about the projected follow-up incidence of PID in the original POPI trial: scenario 1 with 2 % per year (Panel a), and scenario 2 with 3 % per year (Panel b). The red circle represents the sample size with 80 % power in the original POPI trial. PID, pelvic inflammatory disease; POPI trial, Prevention Of Pelvic Infection trial
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4472252&req=5

Fig2: Estimated sample sizes under the two assumptions in the Prevention Of Pelvic (POPI) trial. Plotted curves represent the estimated sample size needed per group while varying power of the study; for the original POPI trial (green lines) and for two types of progression; the one where PID develops at a constant rate throughout infection (dashed-dotted lines), and the one where PID develops at the end of infection (dashed lines). The third type of progression where PID develops immediately after infection is not shown. Panels a and b separate the two different assumptions about the projected follow-up incidence of PID in the original POPI trial: scenario 1 with 2 % per year (Panel a), and scenario 2 with 3 % per year (Panel b). The red circle represents the sample size with 80 % power in the original POPI trial. PID, pelvic inflammatory disease; POPI trial, Prevention Of Pelvic Infection trial
Mentions: Different sets of published assumptions about PID incidence rates and the size of intervention effect lead to different conclusions about the temporal relationship between chlamydia infection and PID (Fig. 2). In scenario 1, the relationship between the power of a trial and the sample size required per group is compatible with the hypothesis that PID can develop throughout the course of infection (Fig. 2a). Assuming a constant progression rate from chlamydia to PID results in a RR of 0.49, which is close to the original RR assumption in the POPI trial (RR = 0.48). If chlamydia progresses to PID only at the end of the infectious period, the model predicts a RR of 0.39. In this scenario, 28.6 % of infected women have to develop PID to achieve the 2 % PID incidence after one year of follow-up.Fig. 2

Bottom Line: We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence.The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model.The RR and the sample size needed per group also depend on the natural history parameters of chlamydia.

View Article: PubMed Central - PubMed

Affiliation: Institute for Medical Informatics, Statistics and Documentation, Medical University of Graz, Graz, Austria. herzog.sereina@gmail.com.

ABSTRACT

Background: The success of an intervention to prevent the complications of an infection is influenced by the natural history of the infection. Assumptions about the temporal relationship between infection and the development of sequelae can affect the predicted effect size of an intervention and the sample size calculation. This study investigates how a mathematical model can be used to inform sample size calculations for a randomised controlled trial (RCT) using the example of Chlamydia trachomatis infection and pelvic inflammatory disease (PID).

Methods: We used a compartmental model to imitate the structure of a published RCT. We considered three different processes for the timing of PID development, in relation to the initial C. trachomatis infection: immediate, constant throughout, or at the end of the infectious period. For each process we assumed that, of all women infected, the same fraction would develop PID in the absence of an intervention. We examined two sets of assumptions used to calculate the sample size in a published RCT that investigated the effect of chlamydia screening on PID incidence. We also investigated the influence of the natural history parameters of chlamydia on the required sample size.

Results: The assumed event rates and effect sizes used for the sample size calculation implicitly determined the temporal relationship between chlamydia infection and PID in the model. Even small changes in the assumed PID incidence and relative risk (RR) led to considerable differences in the hypothesised mechanism of PID development. The RR and the sample size needed per group also depend on the natural history parameters of chlamydia.

Conclusions: Mathematical modelling helps to understand the temporal relationship between an infection and its sequelae and can show how uncertainties about natural history parameters affect sample size calculations when planning a RCT.

Show MeSH
Related in: MedlinePlus