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

Table 1 Parameter values describing sample size calculation, the natural history of chlamydia infection and PID development

Parameters		Re-examine POPI trial		Generic sample size calculation		Source
		Baseline values	Range	Baseline values	Range
Sample size calculation
inc	PID incidence (per year)	1) 2 % & 2) 3 %^a		calculated^†		POPI trial [14]
RR	Relative risk	1) 0.48 & 2) 0.44^a		calculated^a		POPI trial [14]
t	Follow-up time (in days)	365		365	90–540^‡	POPI trial [14]
α	Significance level	5 %		5 %		POPI trial [14]
1-β	Power	80 %	10–90 %^†	80 %		POPI trial [14]
Infection parameter
λ	Force of infection (per day)	calculated^§		calculated^§
1/r	Duration of infection (in days)	365	365 ± 75	365	365 ± 75	Model [17]^¶
p	Prevalence of infection	7 %	3–10 %^‡	7 %	3–10 %^‡	POPI trial [14]
Progression to PID
f	Fraction of women with chlamydia who progress to PID in absence of testing	calculated^†		10 %	7–13 %	Model [16]^¶
1/γ	Infection progression (in days)	calculated^#		calculated^#

^aFor the three types of progression, PID incidence is used for the control group and RR is calculated per type
^†The fraction f and the PID incidence inc in the control group satisfy the equation: fprt = inc
^‡Range determined by agreement among authors
^§In the absence of the trial, to observe chlamydia prevalence p at steady state: \( \lambda =\frac{pr}{1-p} \)
^¶Results of a mathematical model which used published trial data
^#To achieve the same cumulative PID incidence in all three processes in absence of the trial: \( \gamma =\frac{fr}{1-f} \)
PID, pelvic inflammatory disease; RR, relative risk

ISSN: 1471-2334