Limits...
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.

Show MeSH

Related in: MedlinePlus

Relative risk and sample size per group varying duration of infection and fraction developing PID. The contour plots present the estimated relative risk (RR) and the corresponding sample size needed per group for the constant progression (Panel a and c) and for the progression at the end (Panel b and d) while varying infection duration and fraction of women developing PID. The contour lines show for which combinations the RR and the sample size remain the same. For all other model parameters the baseline values were used (Table 1, Generic sample size calculation). Note that the RR and sample size needed per group cannot be estimated if the fraction of women who develop PID equals the prevalence and progression to PID is constant because this results in a division by zero in the RR formula (indicated by the grey area in (a) and (c))
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Fig4: Relative risk and sample size per group varying duration of infection and fraction developing PID. The contour plots present the estimated relative risk (RR) and the corresponding sample size needed per group for the constant progression (Panel a and c) and for the progression at the end (Panel b and d) while varying infection duration and fraction of women developing PID. The contour lines show for which combinations the RR and the sample size remain the same. For all other model parameters the baseline values were used (Table 1, Generic sample size calculation). Note that the RR and sample size needed per group cannot be estimated if the fraction of women who develop PID equals the prevalence and progression to PID is constant because this results in a division by zero in the RR formula (indicated by the grey area in (a) and (c))

Mentions: Varying the duration of infection from 290 to 440 days and the fraction of women who develop PID from seven to 13 % results in a median PID incidence of 0.007 per year (range 0.0041–0.0115, Fig. 3). The incidence of PID decreases with increasing duration of infection because fewer women in the control group become newly infected during the follow-up period. PID incidence increases with an increasing fraction of women who develop PID. Figure 4 shows the resulting RR and the sample size needed per group for constant progression and progression at the end. Although the RR decreases with increasing duration of infection (Fig. 4a and 4b), the sample size needed per group is almost unaffected by the change in duration of infection (Fig. 4c and 4d) or by changing chlamydia prevalence (not shown).Fig. 3


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)

Relative risk and sample size per group varying duration of infection and fraction developing PID. The contour plots present the estimated relative risk (RR) and the corresponding sample size needed per group for the constant progression (Panel a and c) and for the progression at the end (Panel b and d) while varying infection duration and fraction of women developing PID. The contour lines show for which combinations the RR and the sample size remain the same. For all other model parameters the baseline values were used (Table 1, Generic sample size calculation). Note that the RR and sample size needed per group cannot be estimated if the fraction of women who develop PID equals the prevalence and progression to PID is constant because this results in a division by zero in the RR formula (indicated by the grey area in (a) and (c))
© Copyright Policy - open-access
Related In: Results  -  Collection

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

Fig4: Relative risk and sample size per group varying duration of infection and fraction developing PID. The contour plots present the estimated relative risk (RR) and the corresponding sample size needed per group for the constant progression (Panel a and c) and for the progression at the end (Panel b and d) while varying infection duration and fraction of women developing PID. The contour lines show for which combinations the RR and the sample size remain the same. For all other model parameters the baseline values were used (Table 1, Generic sample size calculation). Note that the RR and sample size needed per group cannot be estimated if the fraction of women who develop PID equals the prevalence and progression to PID is constant because this results in a division by zero in the RR formula (indicated by the grey area in (a) and (c))
Mentions: Varying the duration of infection from 290 to 440 days and the fraction of women who develop PID from seven to 13 % results in a median PID incidence of 0.007 per year (range 0.0041–0.0115, Fig. 3). The incidence of PID decreases with increasing duration of infection because fewer women in the control group become newly infected during the follow-up period. PID incidence increases with an increasing fraction of women who develop PID. Figure 4 shows the resulting RR and the sample size needed per group for constant progression and progression at the end. Although the RR decreases with increasing duration of infection (Fig. 4a and 4b), the sample size needed per group is almost unaffected by the change in duration of infection (Fig. 4c and 4d) or by changing chlamydia prevalence (not shown).Fig. 3

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