Maximizing the effectiveness of 1.5 mg levonorgestrel for emergency contraception: The case for precoital use.

Objectives: U.S. and World Health Organization Selected Practice Recommendations for Contraceptive Use state people may have an advanced supply of emergency contraception (EC) to minimize treatment delays. We sought to characterize the potential improvement in effectiveness of 1.5 mg levonorgestrel (LNG-EC) if it were taken up to a few hours before unprotected sex. Study design: We expanded on an existing mathematical model for the maximum attainable effectiveness of LNG-EC, assuming it exclusively works to disrupt ovulation, and compared results with point estimates from nine studies when it was taken up to 72 hours after sex. We then modelled how effectiveness might have improved if subjects had taken LNG-EC up to 3 hours before sex. Results: Taking LNG-EC immediately after sex could potentially reduce the risk of unintended pregnancy by 91%. However, population-average maximum attainable effectiveness levels ranged from just 49% to 67% when accounting for the distributions of postcoital treatment delays in the example studies. If half the subjects had taken it 3 hours before sex, then maximum effectiveness levels would have ranged from 70% to 81%. Conclusions: At the individual level, taking LNG-EC a few hours before sex is a logical extension of Selected Practice Recommendations regarding an advanced supply of EC and, based on our modeling, should be advocated for people who can reasonably anticipate an unprotected sex act. In the absence of more clinical data, however, people should not routinely rely on precoital use of LNG-EC to prevent pregnancy unless modern, effective contraceptives are inaccessible to them. Implications: Based on mathematical modeling, individuals who anticipate needing to take LNG-EC for an impending unprotected act of sex could further reduce their chance of an undesired pregnancy by taking it a few hours in advance.

An adaptive design to bridge the gap between Phase 2b/3 microbicide effectiveness trials and evidence required for licensure.

BACKGROUND: Vaginally and rectally applied microbicides are being developed to help prevent sexual acquisition of HIV. Due to the lack of surrogate outcomes, the path toward licensure typically moves directly from expanded safety studies to expensive Phase 2b/3 trials with rare incident infection outcomes. The need to confirm an initial trial's significant finding can lead to serious delays in implementing essential programs to reduce the spread of HIV. PURPOSE: To propose an adaptive design where a Phase 2b/3 study powered to detect a clinically meaningful effect with evidence of one trial (observing one-sided p < 0.025) is allowed to expand by a prespecified, feasible amount if interim data suggest the chance of further achieving a more robust evidence threshold (p < 0.001, potentially sufficient for licensure from a single trial) is promising. METHODS: As an example, prespecified conditional power criteria are used to determine whether a 90-event trial with 90% power to detect a 50% reduction in risk should be expanded to 130 events. Asymptotic results and simulations are used to assess false-positive error rates and other operating characteristics of the design. RESULTS: False-positive error rates can be controlled at the desired 0.025 and 0.001 levels with appropriate choice of critical values or expansion criteria. The chance of achieving robust evidence can approach that of a 130-event trial with traditional stopping boundaries (controlling a = 0.001) but with substantially lower expected size for plausible effectiveness levels. LIMITATIONS: Conditional power calculations assume the interim estimate of effect is an unbiased estimate for the remainder of the trial, an assumption which may not hold if product adherence varies over time. Observing a measure of effect with p < 0.001 may not be sufficient for licensure. A decision to expand the trial would be informative to investigators regarding the interim effect size. CONCLUSIONS: A moderate increase in trial size can make the difference between a study with good power to detect a clinically meaningful effect and one which may reasonably obtain the robust evidence required for regulatory bodies and public health programs to consider making a new microbicide available to persons at risk of HIV infection. The proposed design allows for this possibility while not requiring investigators to make an up-front commitment to a prohibitively large trial.

Ovulation suppression following subcutaneous administration of depot medroxyprogesterone acetate.

Objectives: To characterize the relationship between serum medroxyprogesterone acetate (MPA) concentrations and ovulation suppression, and to estimate the risk of ovulation for investigational subcutaneous regimens of Depo-Provera CI (Depo-Provera) and Depo-subQ Provera 104 (Depo-subQ). Study Design: We performed a secondary analysis of 2 studies that assessed the pharmacokinetics and pharmacodynamics of MPA when Depo-Provera is administered subcutaneously rather than by the labeled intramuscular route. Each woman received a single 45 mg to 300 mg subcutaneous injection of Depo-Provera, a single 104 mg subcutaneous injection of Depo-subQ, or 2 injections of Depo-subQ at 3-month intervals. We used an elevation of serum progesterone ≥4.7 ng/mL as a surrogate for ovulation and non-parametric statistical methods to assess pharmacokinetic and pharmacodynamic relationships. Results: This analysis included 101 women with body mass index (BMI) 18 to 34 kg/m2. Return of ovulation occurred at a median MPA concentration of 0.07 ng/mL (95% CI: 0.06-0.08) and the 90th percentile was 0.10 ng/mL (95% CI: 0.09-0.14). Neither age, race, nor BMI significantly influenced this relationship. The estimated probabilities of ovulation within 4 months of a 104 mg subcutaneous injection and within 7 months of a 150 mg subcutaneous injection (6 plus a 1-month grace) were each below 2.2%. Conclusions: The typical MPA concentration associated with loss of ovulation suppression is substantially less than the commonly cited threshold of 0.2 ng/mL. Based on our results, MPA levels would rarely be low enough to permit ovulation if the Depo-subQ reinjection interval were extended to four months or if 150 mg Depo-Provera were injected subcutaneously every 6 months. Implications: Extending the three-month Depo-subQ reinjection interval by one month would result in a 25% reduction in yearly MPA exposure, with little risk of pregnancy. Off-label subcutaneous administration of 150 mg Depo-Provera every 6 months would be a highly effective repurposing of an excellent product, with a similar reduction in cumulative exposure.

Return to ovulation after Sayana Press is injected every 4 months for one year: Empirical and pharmacokinetic/pharmacodynamic modeling results.

Objective: To characterize return to ovulation after injecting Sayana Press (104 mg/0.65 mL medroxyprogesterone acetate [MPA] in the Uniject device) every 4 months for 1 year of treatment. Study design: We followed a subset of women for return to ovulation in a trial that demonstrated Sayana Press remains highly effective when the subcutaneous reinjection interval is extended from 3 to 4 months. We measured serum progesterone in weeks 38 to 42 and 46 to 50 after a final (third) injection and used a concentration ≥4.7 ng/mL as a surrogate for ovulation. We also performed pharmacokinetic and pharmacodynamic modeling to predict differences in MPA accumulation and return to ovulation had - contrary to fact - injections been given every 3 months. Results: Ten of 19 women (53%; 95% confidence interval: 29-76) ovulated within 50 weeks of their last injection. We predicted that typical 12-month trough MPA concentrations are 34% lower (0.46 vs 0.69 ng/mL) and the median time from last dose to ovulation is 1.1 months shorter (13.1 vs 14.2 months) when injections are given every four months for 1 year. Conclusion: Extending the Sayana Press reinjection interval from 3 to 4 months leads to less drug accumulation, without a noticeable loss in efficacy. Although the Sayana Press patient leaflet specifies that over 80% of women desiring pregnancy will conceive within a year of stopping the method (independent of treatment duration), our empirical and modeling results indicate women should anticipate waiting a year or more for fertility to return after repeat dosing, with a somewhat shorter delay were the reinjection interval extended to four months. Implications: Providers should counsel women regarding the distinct possibility that return to fertility will take a year or longer following repeat use of Sayana Press. Extending the dosing interval from 3 to 4 months would result in approximately a 1-month shorter delay, without any appreciable reduction in contraceptive efficacy.

Notes on the frequency of routinely collected and self-reported behavioral data in HIV prevention trials.

HIV prevention trials typically randomize thousands of participants to active or control intervention arms, with regular (e.g. monthly) clinic visits over one or more years of follow-up. Because HIV infection rates are often lower than 3 per 100 person-years even in high prevalence settings, tens of thousands of clinic visits may take place before the number of infections required to achieve adequate study power has been observed. In addition to clinical outcomes, the multitude of study visits provides an opportunity to assess adherence and related participant behaviors in great detail. These data may be used to refine counseling messages, gain insight into patterns of behavior, and perform supporting analyses in an attempt to obtain more precise estimates of treatment efficacy. Exploratory analyses were performed to assess how our understanding of participant behaviors and their relationships to biological outcomes in two recent prevention trials might have been impacted had the frequency of routine behavioral data collection been reduced from monthly to just months 1, 3, 6, 9, and 12. Results were comparably informative in the reduced case, suggesting that unnecessarily extensive amounts of routine behavioral data may be collected in these trials.

Heterosexual anal intercourse has the potential to cause a significant loss of power in vaginal microbicide effectiveness studies.

BACKGROUND: Vaginal microbicides are topical products being studied for their potential to reduce the risk of penile-vaginal human immunodeficiency virus (HIV) transmission. Because the sexual acts that lead to infection in effectiveness trials are unobserved, identification of an effective vaginal product may be unwittingly circumvented if adherence to product is poor or if participants acquire infection through nonvaginal routes of exposure. PURPOSE: To model the impact of receptive anal intercourse (RAI) on the measured effectiveness of vaginal microbicides and the power of clinical trials. METHODS: A mathematical model is proposed for assessing effectiveness and power as a function of microbicide efficacy, the probability that the microbicide is used for vaginal acts of intercourse with exposure to HIV, the probability that an act of intercourse with exposure to HIV is rectal, and the ratio of transmission probabilities for rectal versus vaginal intercourse. RESULTS: The model demonstrated that a moderate frequency of RAI among vaginal microbicide trial participants is expected to substantially reduce study power; if 1 in 50 acts are rectal, and if the rectal transmission probability is 20-fold greater than that of vaginal intercourse, then power to detect an otherwise 40% effective product with a 160 endpoint trial is reduced from 90% to 56%. If 1 in 25 acts are rectal then power is only 34%. LIMITATIONS: Accurate reports of adherence and rates of RAI are difficult to obtain, and precise HIV transmission probabilities are unknown. Hence the true impact of unprotected RAI on vaginal microbicide trials cannot be quantified with certainty. CONCLUSIONS: Counseling against RAI should be provided to all vaginal microbicide trial participants irrespective of sexual history. Collection of accurate behavioral data on RAI during trials is essential to understand whether failure to demonstrate an effect might be attributed to RAI.

A single-arm study to evaluate the efficacy, safety and acceptability of pericoital oral contraception with levonorgestrel.

BACKGROUND: An oral dose of 0.75 mg levonorgestrel (LNG) taken shortly after sex was marketed as a routine, nonemergency contraceptive method until the 1990s. Because a hormonal method used only at the time of intercourse may be desirable for women who have infrequent sex, we conducted a study to reevaluate the potential of pericoital LNG as a primary means of contraception. METHODS: We enrolled women aged 18-45 years in Brazil and the USA who expected to have sex 1-4 days per month for 6.5 months. Participants were instructed to take one tablet 0.75 mg LNG within 24 h before or after sex, with no more than one dose in any 24-h period. The primary efficacy measure was the Pearl Index among women aged 18-35 years. RESULTS: The study was stopped after 72 of the planned 300 participants were enrolled due to slow recruitment and related feasibility considerations. In the primary analysis, three pregnancies occurred during 13.4 woman-years of follow-up, resulting in a Pearl Index of 22.4 (95% confidence interval, 4.6-65.4). No serious adverse events were reported, and vaginal bleeding patterns were generally acceptable. CONCLUSIONS: Our estimated Pearl Index was noticeably higher than expected from previous research of LNG for pericoital contraception. Although the regimen was safe and generally acceptable, the study was challenged by slow enrollment and curtailed person-years of follow-up, resulting in poor precision for the estimated treatment effect. Future research may inform whether our results are symptomatic of the regimen, study design or characteristics of the populations from which we recruited. IMPLICATIONS: Our study failed to confirm prior data suggesting that 0.75 mg LNG for pericoital contraception could be more effective than typical use of barrier methods among women having infrequent sex. Characterizing populations most likely to adhere to, and benefit from, pericoital regimens is essential to future research on these methods.

Statistical tests with accurate size and power for balanced linear mixed models.

The convenience of linear mixed models for Gaussian data has led to their widespread use. Unfortunately, standard mixed model tests often have greatly inflated test size in small samples. Many applications with correlated outcomes in medical imaging and other fields have simple properties which do not require the generality of a mixed model. Alternately, stating the special cases as a general linear multivariate model allows analysing them with either the univariate or multivariate approach to repeated measures (UNIREP, MULTIREP). Even in small samples, an appropriate UNIREP or MULTIREP test always controls test size and has a good power approximation, in sharp contrast to mixed model tests. Hence, mixed model tests should never be used when one of the UNIREP tests (uncorrected, Huynh-Feldt, Geisser-Greenhouse, Box conservative) or MULTIREP tests (Wilks, Hotelling-Lawley, Roy's, Pillai-Bartlett) apply. Convenient methods give exact power for the uncorrected and Box conservative tests. Simulations demonstrate that new power approximations for all four UNIREP tests eliminate most inaccuracy in existing methods. In turn, free software implements the approximations to give a better choice of sample size. Two repeated measures power analyses illustrate the methods. The examples highlight the advantages of examining the entire response surface of power as a function of sample size, mean differences, and variability.

Analytic, Computational, and Approximate Forms for Ratios of Noncentral and Central Gaussian Quadratic Forms.

Many useful statistics equal the ratio of a possibly noncentral chi-square to a quadratic form in Gaussian variables with all positive weights. Expressing the density and distribution function as positively weighted sums of corresponding F functions has many advantages. The mixture forms have analytic value when embedded within a more complex problem. The mixture forms also have computational value. The expansions work well with quadratic forms having few components and small degrees of freedom. A more general algorithm from earlier literature can take longer or fail to converge in the same setting. Many approximations have been suggested for the problem. a positively weighted noncentral quadratic form can always have two moments matched to a noncentral chi-square. For a single quadratic form, the noncentral form performs neither uniformly more or less accurately than older approximations. The approach also gives a noncentral F approximation for any ratio of a positively weighted noncentral form to a positively weighted central quadratic form. The method provides better accuracy for noncentral ratios than approximations based on a single chi-square. The accuracy suffices for many practical applications, such as power analysis, even with few degrees of freedom. Naturally the approximation proves much faster and simpler to compute than any exact method. Embedding the approximation in analytic expressions provides simple forms which correctly guarantee only positive values have nonzero probabilities, and also automatically reduce to partially or fully exact results when either quadratic form has only one term.

BIAS IN LINEAR MODEL POWER AND SAMPLE SIZE CALCULATION DUE TO ESTIMATING NONCENTRALITY.

Data analysts frequently calculate power and sample size for a planned study using mean and variance estimates from an initial trial. Hence power, or the sample size needed to achieve a fixed power, varies randomly. Such calculations can be very inaccurate in the General Linear Univariate Model (GLUM). Biased noncentrality estimators and censored power calculations create inaccuracy. Censoring occurs if only certain outcomes of an initial trial lead to a power calculation. For example, a confirmatory study may be planned (and a sample size estimated) only following a significant result in the initial trial. Computing accurate point estimates or confidence bounds of GLUM noncentrality, power, or sample size in the presence of censoring involves truncated noncentral F distributions. We recommend confidence bounds, whether or not censoring occurs. A power analysis of data from humans exposed to carbon monoxide demonstrates the substantial impact on sample size that may occur. The results highlight potential biases and should aid study planning and interpretation.

Computing Confidence Bounds for Power and Sample Size of the General Linear Univariate Model.

The power of a test, the probability of rejecting the null hypothesis in favor of an alternative, may be computed using estimates of one or more distributional parameters. Statisticians frequently fix mean values and calculate power or sample size using a variance estimate from an existing study. Hence computed power becomes a random variable for a fixed sample size. Likewise, the sample size necessary to achieve a fixed power varies randomly. Standard statistical practice requires reporting uncertainty associated with such point estimates. Previous authors studied an asymptotically unbiased method of obtaining confidence intervals for noncentrality and power of the general linear univariate model in this setting. We provide exact confidence intervals for noncentrality, power, and sample size. Such confidence intervals, particularly one-sided intervals, help in planning a future study and in evaluating existing studies.

Evaluating factors associated with STD infection in a study with interval-censored event times and an unknown proportion of participants not at risk for disease.

Sexually transmitted diseases (STD) are a major cause of morbidity and mortality world-wide. Because of their association with an increased risk of infection with human immunodeficiency virus, the prevention and control of STD are particularly important. Studies designed to evaluate factors associated with the transmission of STD can pose a number of statistical challenges, however. Two such concerns are the interval-censored event times that result from spacing between follow-up test visits, and an unknown proportion of study participants who are not at risk for infection. Researchers in various fields of study have used parametric mixture models to account for individuals not at risk. Owing to non-identifiability concerns within the mixture model framework, however, it is not always possible to distinguish between effects of explanatory variables on the distribution of event times for at-risk individuals and their effects on the probability of being at risk. We address these issues using data from a clinical trial designed to investigate the effectiveness of an intravaginal microbicide in preventing male-to-female transmission of STD. Factors associated with time to infection among at-risk women are initially identified by fitting right-truncated models to the interval-censored event times of participants who tested positive for STD, and hence are known to have been at risk. Subsequently, factors associated with the probability of being at risk are evaluated using mixture models that incorporate information contributed by the right-censored event-free times of uninfected study participants.

Estimating and comparing correct-use failure probabilities in clinical studies of condom functionality.

In a clinical study comparing the failure probabilities of two condom types, the sample of all reported acts of intercourse in which a study condom was used by a randomized participant is typically defined to be the primary analysis sample. However, it may also be desirable to make comparisons among only those acts in which the participants correctly followed all condom use instructions before, during, and after the act of intercourse (i.e., the "correct-use" subset). The timing associated with the definition of correct use creates a dilemma in that an act cannot be classified as a "correct-use act" until after the completion of both intercourse and withdrawal; if a condom fails (e.g., breaks or slips completely off of the penis) during intercourse then the couple has no chance at correct use during withdrawal. As a result of the implicitly conditional nature of this problem, it is not a simple matter to specify a correct-use subset of the primary analysis sample. With this in mind, we develop estimators for the correct-use failure probabilities, the corresponding standard errors, and test statistics for comparing the correct-use failure probabilities between condom groups. We demonstrate the utility of the proposed methods by applying them to data from a clinical study of condom contraceptive effectiveness, and we use simulated data to investigate the finite sample properties of the proposed methods. The simulation results indicate that one of our proposed estimators is at least approximately unbiased, even in small samples. Furthermore, one-sided noninferiority tests performed using this estimator tend to have sizes that are only marginally larger than the nominal test size in moderate to large samples.

Improved approximate confidence intervals for the mean of a log-normal random variable.

Data analysts often compute approximate 100 (1-alpha) per cent confidence intervals for the mean of a log-normal random variable due to the computational effort required for exact intervals. We evaluate two simple approximations and demonstrate that the probabilities with which the intervals fail to capture the population mean (that is, the coverage error) can range from well above the desired level, alpha, to very near zero in small to moderate sample sizes (n < or = 100). The performance of a more sophisticated approximation, implemented via numerical integration or bootstrap sampling, is noticeably improved, but also suffers from coverage errors that are too large when n < or = 25. A new procedure is developed which outperforms existing approximations. Computing these improved intervals requires the integration of standard distribution functions. The calculations are straightforward, however, and lead to satisfactory coverage errors for n as small as 5. A related method that avoids the integration step generally outperforms existing simple approximations for n < or = 100, while maintaining the coverage error at or below alpha. Programs to implement the new procedures are provided in an Appendix.