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Accounting for informative sampling in estimation of associations between sexually transmitted infections and hormonal contraceptive methods

Anu Mishra ORCID logo, Petra Bůžková, Jennifer E. Balkus and Elizabeth R. Brown


The relationship between hormonal contraceptive method use and sexually transmitted infections is not well understood. Studies that implement routine screening for STIs among different contraceptive users, such as the ASPIRE HIV-1 prevention trial, can be useful for identifying potential risk factors of STIs. However, the complex nature of non-random data can lead to challenges in estimation of associations for potential risk factors. In particular, if screening for the disease is not random (i. e. it is driven by symptoms or other clinical indicators), estimates of association can suffer from bias, often referred to as informative sampling bias. Time-varying predictors and potential stratification variables can further contribute to difficulty in obtaining unbiased estimates. In this paper, we estimate the association between time- varying contraceptive use and Sexually transmitted infections acquisition, in the presence of informative sampling, by extending the work Buzkova (2010). We use a two-step procedure to jointly model the non-random screening process and sexually transmitted infection risk. In the first step, inverse intensity rate ratios (IIRR) weights are estimated. In the second step, a weighted proportional rate model is fit to estimate the IIRR weighted hazard ratio. We apply the method to evaluate the relationship between hormonal contraception and risk of sexually transmitted infections among women participating in a biomedical HIV-1 prevention trial. We compare our results using the proposed weighted method to those generated using conventional approaches that do not account for potential informative sampling bias or do not use the full potential of the data. Using the IIRR weighted approach we found depot medroxyprogesterone acetate users have a significantly decreased hazard of Trichomonas vaginalis acquisition compared to IUD users (hazard ratio: 0.44, 95% CI: (0.25, 0.83)), which is consistent with the literature. We did not find significant increased or decreased hazard of other STIs for hormonal contraceptive users compared to non-hormonal IUD users.

Corresponding author: Anu Mishra, University of Washington, Biostatistics, Box 357232, Seattle, WA, 98195, USA, E-mail:

Funding source: National Institute of Allergy and Infectious Diseases

Award Identifier / Grant number: UM1AI068615UM1AI068633UM1AI106707

Funding source: Eunice Kennedy Shriver National Institute of Child Health and Human Development


We thank the study participants for their dedication to the ASPIRE trial. We acknowledge the study staff and investigators from the MTN sites; and appreciate the support of the ASPIRE co-chairs and team, and the MTN leadership. ASPIRE Study Team Leadership: Jared Baeten, University of Washington (Protocol Chair); Thesla Palanee-Phillips, Wits Reproductive Health and HIV Institute (Protocol Co-chair); Elizabeth Brown, Fred Hutchinson Cancer Research Center (Protocol Statistician); Lydia Soto-Torres, US National Institute of Allergy and Infectious Diseases (Medical Officer); Katie Schwartz, FHI 360 (Clinical Research Manager). Study sites and site Investigators of Record: Malawi, Blantyre site (Johns Hopkins University, Queen Elizabeth Hospital): Bonus Makanani; Malawi, Lilongwe site (University of North Carolina, Chapel Hill): Francis Martinson and Lameck Chinula; South Africa, Cape Town site (University of Cape Town): Linda-Gail Bekker; South Africa, Durban – Botha’s Hill, Chatsworth, Isipingo, Tongaat, Umkomaas, Verulam sites (South African Medical Research Council): Vaneshree Govender, Samantha Siva, Zakir Gaffoor, Logashvari Naidoo, Arendevi Pather, Bomkazi Tutshana, Jayajothi Moodley, Kubashini Woeber, and Nitesha Jeenarain; South Africa, Durban, eThekwini site (Center for the AIDS Programme for Research in South Africa): Gonasagrie Nair and Leila Mansoor; South Africa, Johannesburg site (Wits Reproductive Health and HIV Institute, University of the Witwatersrand ): Thesla Palanee-Phillips; Uganda, Kampala site (John Hopkins University, Makerere University): Flavia Matovu Kiweewa and Clemensia Nakabiito; Zimbabwe, Chitungwiza, Seke South and Zengeza sites (University of Zimbabwe College of Health Sciences Clinical Trials Research Centre): Nyaradzo Mgodi, Zimbabwe, Harare, Spilhaus site (University of Zimbabwe College of Health Sciences Clinical Trials Research Centre): Felix Mhlanga, Data management was provided by the Statistical Center for HIV/AIDS Research & Prevention (Fred Hutchinson Cancer Research Center, Seattle, WA) and site laboratory oversight was provided by the Microbicide Trials Network Laboratory Center (Pittsburgh, PA).

  1. Fund source: National Institute of Allergy and Infectious Diseases.

  2. Grant numbers: UM1AI068633, UM1AI068615, UM1AI106707, UM1AI148684.

  3. Research funding: This work was supported by the National Institute of Allergy and Infectious Diseases (UM1AI068633, UM1AI068615, UM1AI106707), with co-funding from the Eunice Kennedy Shriver National Institute of Child Health and Human Development and the National Institute of Mental Health, all components of the U.S. National Institutes of Health (NIH).

  4. Author contributions: All authors have accepted responsibility for the entire content of this manuscript and approved its submission.

  5. Competing interests: Authors state no conflict of interest.

  6. Ethical statements are mandatory for original research that involved human or animal subjects.

Appendix A: Derivation of estimating equation

For individual i at time t define Xi(t) define to be the time-varying predictor of interest. Suppose there is a population of size n with i = 1, … n. Let Ni(t) and dNi(t) be the cumulative event process and indicator of event as defined above. Let N~i(t) and dN~i(t) be the cumulative screening process and indicator of screening as defined above. Let Yi(t) be a censoring indicator, such that Yi(t) = 1 when the ith person remains in the risk set at time t. For convenience, we will use the subscript k to denote membership to the kth stratum, with k having levels i = 1,2, … ,K. Let subjects i = 1, … ,nk be in the subjects belonging to the kth stratum.

The zero-mean process used to estimate β, the p-length vector of associations between the repeated outcome and exposure Xi,k(t), is


where K is the total number of stratum, nk is the sample size for stratum k, and subscript k denotes membership to stratum k. This zero-mean process is the same as in Buzkova (2010), with the change that exposure of interest now depends on time t. The corresponding score function is

(7)U(β|γ,δ)=k=1Ki=1nk0τ1ρi,k(t|γ,δ)[Yi,k(t)Xi,k(t)j=1nkYj,k(t)Xj,k(t)e(β+δ)TXj,k(t)l=1nkYl,k(t)e(β+δ)TXl,k(t)]dNi,k(t)dN~i,k(t) .

Since STI diagnosis (i. e. dNi,k = 1) can only occur at visits where the participant was observed (i. e. dN~i,k(t)=1) there is only contribution to the estimating equation when both dN~i,k(t)=1. Therefore Eq. (7) simplifies to

(8)U(β|γ,δ)=k=1Ki=1nk0τ1ρi,k(t|γ,δ)[Yi,k(t)Xi,k(t)j=1nkYj,k(t)Xj,ke(β+δ)TXj,k(t)l=1nkYl,k(t)e(β+δ)TXl,k(t)]dNi,k(t) .

Equation (8) is the proposed estimating equation that provides the IIRR weighted estimator for β, when time-varying covariates and stratification covariates are included in the model.

Appendix B: Example R code

Code for implementing IIRR weighted method is publicly available on

The The R code for obtaining inverse intensity rate ratio-weights is as follows:

gamma.hat < - coxph(Surv(start.time, stop.time, visit) Z, data = dat)$coef delta.hat < - coxph(Surv(start.time, stop.time, visit) X, data = dat)$coef iirr < - exp(Z %*% gamma.hat)/exp(X %*% delta.hat)

The R code for obtaining inverse intensity rate ratio-weighted estimate of association is as follows:

mod < - informSampHaz(outcome exposure, weight = iirr, id = ptid, time = time, strata = strat, data = dat)

iirr.hazRatio < - exp(mod$beta.hat)

Appendix C: Description of weights

Table 5:

Predictors Included in Weight Model and Corresponding Coefficient Estimates (log-scale). Lagged variables indicates indicate any history of covariate prior to visit for which weight is calculated.

>1 Sex Partner at Baseline−0.19−0.17
Reported Condom-less Sex at Baseline−0.02−0.04
Abnormal Pelvic Findings at Baseline0.20
Abnormal Vaginal Discharge at Baseline−0.10
>1 Sex Partner During Follow-up (Lagged)0.11
Reported Condom-less Sex During Follow-up (Lagged)0.07
Change in Primary Sex Partner During Follow-up (Lagged)−0.70
Abnormal Pelvic Findings During Follow-up (Lagged)0.34
Abnormal Vaginal Discharge During Follow-up (Lagged)0.28
Observed Uterine or Adnexal tenderness During Follow-up (Lagged)−0.09
C. trachomatis Diagnoses During Follow-up (Lagged)0.15
N. gonorrhoeae Diagnoses During Follow-up (Lagged)−0.10
T. vaginalis Diagnoses During Follow-up (Lagged)0.17
Baseline STI0.02
Active Drug Study Arm0.05


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Received: 2019-03-06
Accepted: 2020-05-27
Published Online: 2020-07-05

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