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

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

The Role of Reinfection and Partner Notification in the Efficacy of Chlamydia Screening Programs

Repeated Chlamydia trachomatis infections after treatment are common. One reason is reinfection from untreated partners in ongoing sexual partnerships. Mathematical models that are used to predict the impact of screening on reducing chlamydia prevalence often do not incorporate reinfection and might overestimate the expected impact. We describe a pair compartmental model that explicitly incorporates sexual partnership duration and reinfection. The pair model predicts a weaker impact of screening when compared directly with a model that does not accommodate partnerships. Effective management of sex partners to prevent reinfection might need to be strengthened in chlamydia control program

Effectiveness and cost-effectiveness of traditional and new partner notification technologies for curable sexually transmitted infections: observational study, systematic reviews and mathematical modelling.

BACKGROUND: Partner notification is essential to the comprehensive case management of sexually transmitted infections. Systematic reviews and mathematical modelling can be used to synthesise information about the effects of new interventions to enhance the outcomes of partner notification. OBJECTIVE: To study the effectiveness and cost-effectiveness of traditional and new partner notification technologies for curable sexually transmitted infections (STIs). DESIGN: Secondary data analysis of clinical audit data; systematic reviews of randomised controlled trials (MEDLINE, EMBASE and Cochrane Central Register of Controlled Trials) published from 1 January 1966 to 31 August 2012 and of studies of health-related quality of life (HRQL) [MEDLINE, EMBASE, ISI Web of Knowledge, NHS Economic Evaluation Database (NHS EED), Database of Abstracts of Reviews of Effects (DARE) and Health Technology Assessment (HTA)] published from 1 January 1980 to 31 December 2011; static models of clinical effectiveness and cost-effectiveness; and dynamic modelling studies to improve parameter estimation and examine effectiveness. SETTING: General population and genitourinary medicine clinic attenders. PARTICIPANTS: Heterosexual women and men. INTERVENTIONS: Traditional partner notification by patient or provider referral, and new partner notification by expedited partner therapy (EPT) or its UK equivalent, accelerated partner therapy (APT). MAIN OUTCOME MEASURES: Population prevalence; index case reinfection; and partners treated per index case. RESULTS: Enhanced partner therapy reduced reinfection in index cases with curable STIs more than simple patient referral [risk ratio (RR) 0.71; 95% confidence interval (CI) 0.56 to 0.89]. There are no randomised trials of APT. The median number of partners treated for chlamydia per index case in UK clinics was 0.60. The number of partners needed to treat to interrupt transmission of chlamydia was lower for casual than for regular partners. In dynamic model simulations, >10% of partners are chlamydia positive with look-back periods of up to 18 months. In the presence of a chlamydia screening programme that reduces population prevalence, treatment of current partners achieves most of the additional reduction in prevalence attributable to partner notification. Dynamic model simulations show that cotesting and treatment for chlamydia and gonorrhoea reduce the prevalence of both STIs. APT has a limited additional effect on prevalence but reduces the rate of index case reinfection. Published quality-adjusted life-year (QALY) weights were of insufficient quality to be used in a cost-effectiveness study of partner notification in this project. Using an intermediate outcome of cost per infection diagnosed, doubling the efficacy of partner notification from 0.4 to 0.8 partners treated per index case was more cost-effective than increasing chlamydia screening coverage. CONCLUSIONS: There is evidence to support the improved clinical effectiveness of EPT in reducing index case reinfection. In a general heterosexual population, partner notification identifies new infected cases but the impact on chlamydia prevalence is limited. Partner notification to notify casual partners might have a greater impact than for regular partners in genitourinary clinic populations. Recommendations for future research are (1) to conduct randomised controlled trials using biological outcomes of the effectiveness of APT and of methods to increase testing for human immunodeficiency virus (HIV) and STIs after APT; (2) collection of HRQL data should be a priority to determine QALYs associated with the sequelae of curable STIs; and (3) standardised parameter sets for curable STIs should be developed for mathematical models of STI transmission that are used for policy-making. FUNDING: The National Institute for Health Research Health Technology Assessment programme

Sex-specific evaluation and redevelopment of the GRACE score in non-ST-segment elevation acute coronary syndromes in populations from the UK and Switzerland: a multinational analysis with external cohort validation.

BACKGROUND The Global Registry of Acute Coronary Events (GRACE) 2.0 score was developed and validated in predominantly male patient populations. We aimed to assess its sex-specific performance in non-ST-segment elevation acute coronary syndromes (NSTE-ACS) and to develop an improved score (GRACE 3.0) that accounts for sex differences in disease characteristics. METHODS We evaluated the GRACE 2.0 score in 420 781 consecutive patients with NSTE-ACS in contemporary nationwide cohorts from the UK and Switzerland. Machine learning models to predict in-hospital mortality were informed by the GRACE variables and developed in sex-disaggregated data from 386 591 patients from England, Wales, and Northern Ireland (split into a training cohort of 309 083 [80·0%] patients and a validation cohort of 77 508 [20·0%] patients). External validation of the GRACE 3.0 score was done in 20 727 patients from Switzerland. FINDINGS Between Jan 1, 2005, and Aug 27, 2020, 400 054 patients with NSTE-ACS in the UK and 20 727 patients with NSTE-ACS in Switzerland were included in the study. Discrimination of in-hospital death by the GRACE 2.0 score was good in male patients (area under the receiver operating characteristic curve [AUC] 0·86, 95% CI 0·86-0·86) and notably lower in female patients (0·82, 95% CI 0·81-0·82; p<0·0001). The GRACE 2.0 score underestimated in-hospital mortality risk in female patients, favouring their incorrect stratification to the low-to-intermediate risk group, for which the score does not indicate early invasive treatment. Accounting for sex differences, GRACE 3.0 showed superior discrimination and good calibration with an AUC of 0·91 (95% CI 0·89-0·92) in male patients and 0·87 (95% CI 0·84-0·89) in female patients in an external cohort validation. GRACE 3·0 led to a clinically relevant reclassification of female patients to the high-risk group. INTERPRETATION The GRACE 2.0 score has limited discriminatory performance and underestimates in-hospital mortality in female patients with NSTE-ACS. The GRACE 3.0 score performs better in men and women and reduces sex inequalities in risk stratification. FUNDING Swiss National Science Foundation, Swiss Heart Foundation, Lindenhof Foundation, Foundation for Cardiovascular Research, and Theodor-Ida-Herzog-Egli Foundation

How nasopharyngeal pneumococcal carriage evolved during and after a PCV13-to-PCV10 vaccination programme switch in Belgium, 2016 to 2018

Background: The current carriage study was set up to reinforce surveillance during/after the PCV13-to-PCVC10 switch in Belgium. Aim: This observational study monitored carriage of Streptococcus pneumoniae (Sp) serotypes, particularly those no longer covered (3, 6A, 19A), as well as Haemophilus influenzae (Hi), because PCV10 contains the non-typeable Hi protein D. Methods: A total of 2,615 nasopharyngeal swabs from children (6-30 months old) attending day care were collected in three periods over 2016-2018. Children's demographic and clinical characteristics and vaccination status were obtained through a questionnaire. Sp and Hi were identified by culture and PCR. Pneumococcal strains were tested for antimicrobial (non-)susceptibility by disc diffusion and serotyped by Quellung-reaction (Quellung-reaction and PCR for serotypes 3, 6A, 19A). Results: The carriage prevalence of Sp (> 75%) remained stable over the successive periods but that of Hi increased (87.4%, 664 Hi-carriers/760 in 2016 vs 93.9%, 895/953 in 2017-2018). The proportion of non-PCV13 vaccine serotypes decreased (94.6%, 438 isolates/463 in 2016 vs 89.7%, 599/668 in 2017-2018) while that of PCV13-non-PCV10 vaccine serotypes (3 + 6A + 19A) increased (0.9%, 4 isolates/463 in 2016 vs 7.8%, 52/668 in 2017-2018), with serotype 19A most frequently identified (87.9%, 58/66 isolates). Non-susceptibility of pneumococci against any of the tested antibiotics was stable over the study period (> 44%). Conclusions: During and after the PCV13-to-PCV10 vaccine switch, the proportion of non-PCV13 serotypes decreased, mainly due to a serotype 19A carriage prevalence increase. These results complement invasive pneumococcal disease surveillance data, providing further basis for pneumococcal vaccination programme policy making

Clinical, serological and epidemiological features of hepatitis A in León, Nicaragua.

Background and Objectives To monitor and document the endemicity and disease burden of acute hepatitis A in the area of an ongoing vaccine effectiveness study in León, Nicaragua. Methods At community health centres in León, all children, adolescents and young adults presenting with jaundice and/or other clinical signs of hepatitis were offered free serologic screening (hepatitis A, B and C) and blood tests for liver enzymes and bilirubin. Clinical and socioeconomic data were collected with a structured questionnaire. Diagnosis of acute hepatitis A was confirmed by anti-HAV IgM testing. Using logistic regression we compared the characteristics and living conditions of acute hepatitis A cases with those of non-cases. Results Of 557 eligible subjects enrolled between May 2006 and March 2010, 315 (56.6%) were diagnosed with hepatitis A, 80.6% of them ≤10 years and five >18 years of age. No severe cases were encountered. Apart from jaundice (95.6%) and other signs of hepatitis A (fever, pale stool, dark urine, nausea, vomiting, anorexia), two thirds of patients had moderately raised liver enzymes. Cases occurred throughout the year, with highest incidences from August to March. Poor sanitary conditions and crowding were the main risk factors. Conclusions In the study area, hepatitis A is still highly endemic in young and school age children living in low socioeconomic conditions. There are, however, first indications that the endemicity level is shifting from high to high-intermediate

Variation in partner notification outcomes for chlamydia in UK genitourinary medicine clinics: multilevel study

Objectives To compare different ways of measuring partner notification (PN) outcomes with published audit standards, examine variability between clinics and examine factors contributing to variation in PN outcomes in genitourinary medicine (GUM) clinics in the UK. Methods Reanalysis of the 2007 BASHH national chlamydia audit. The primary outcome was the number of partners per index case tested for chlamydia, as verified by a healthcare worker or, if missing, reported by the patient. Control charts were used to examine variation between clinics considering missing values as zero or excluding missing values. Hierarchical logistic regression was used to investigate factors contributing to variation in outcomes. Results Data from 4616 individuals in 169 genitourinary medicine clinics were analysed. There was no information about the primary outcome in 41% of records. The mean number of partners tested for chlamydia ranged from 0 to 1.5 per index case per clinic. The median across all clinics was 0.47 when missing values were assumed to be zero and 0.92 per index case when missing values were excluded. Men who have sex with men were less likely than heterosexual men and patients with symptoms (4-week look-back period) were less likely than asymptomatic patients (6-month look-back) to report having one or more partners tested for chlamydia. There was no association between the primary outcome and the type of the health professional giving the PN advice. Conclusions The completeness of PN outcomes recorded in clinical notes needs to improve. Further research is needed to identify auditable measures that are associated with successful PN that prevents repeated chlamydia in index cases

Describing the progression from Chlamydia trachomatis and Neisseria gonorrhoeae to pelvic inflammatory disease: systematic review of mathematical modeling studies

Chlamydia screening is recommended to prevent pelvic inflammatory disease (PID). A systematic review was conducted to determine how the natural history of Chlamydia trachomatis or Neisseria gonorrhoeae infection and progression to PID have been described in mathematical modeling studies

Sample size calculation for estimating key epidemiological parameters using serological data and mathematical modelling

Abstract Background Our work was motivated by the need to, given serum availability and/or financial resources, decide on which samples to test in a serum bank for different pathogens. Simulation-based sample size calculations were performed to determine the age-based sampling structures and optimal allocation of a given number of samples for testing across various age groups best suited to estimate key epidemiological parameters (e.g., seroprevalence or force of infection) with acceptable precision levels in a cross-sectional seroprevalence survey. Methods Statistical and mathematical models and three age-based sampling structures (survey-based structure, population-based structure, uniform structure) were used. Our calculations are based on Belgian serological survey data collected in 2001–2003 where testing was done, amongst others, for the presence of Immunoglobulin G antibodies against measles, mumps, and rubella, for which a national mass immunisation programme was introduced in 1985 in Belgium, and against varicella-zoster virus and parvovirus B19 for which the endemic equilibrium assumption is tenable in Belgium. Results The optimal age-based sampling structure to use in the sampling of a serological survey as well as the optimal allocation distribution varied depending on the epidemiological parameter of interest for a given infection and between infections. Conclusions When estimating epidemiological parameters with acceptable levels of precision within the context of a single cross-sectional serological survey, attention should be given to the age-based sampling structure. Simulation-based sample size calculations in combination with mathematical modelling can be utilised for choosing the optimal allocation of a given number of samples over various age groups