Extending mixed effects models for longitudinal data before and after treatment

For the analysis of longitudinal biomedical data in which the timing of observations in each patient is irregular and in which there is substantial loss to follow-up, it is important that statistical models adequately describe both the patterns of variation within the data and any relationships between the variable of interest and time, clinical characteristics and response to treatment. We develop novel statistical models motivated by the analysis of pre- and post-treatment CD4 cell counts from HIV-infected patients, using the UK Register of Seroconverters and CASCADE datasets. The addition of stochastic process components, specifically Brownian motion, to standard linear mixed effects models has previously been shown to improve model fit for pre-treatment CD4 cell counts. We review and further develop computational techniques for such models, and also propose the use of a more general ‘fractional Brownian motion’ process in this setting. Residual diagnostic plots for such models, based on a marginal multivariate normal distribution, show very heavy tails, and we address this issue by further extending the model to allow between-patient differences in variability over time. It is known from the literature that response to treatment in HIV-patients is dependent on their baseline CD4 level at initiation. In order to further investigate the factors that determine the characteristics of recovery in CD4 counts, we develop a framework for the combined modelling of pre- and post-treatment CD4 cell counts in which key features of the response to treatment for each patient are dependent on a latent variable representing the unobserved ‘true’ baseline value, conditioned on all pre-treatment data for each patient. We further develop the model structure to account for uncertainty in the exact time of seroconversion for each patient, by integration of the log-likelihood function over all possible dates

Combined models for pre- and post-treatment longitudinal biomarker data: an application to CD4 counts in HIV-patients.

BACKGROUND: There has been some debate in the literature as to whether baseline values of a measurement of interest at treatment initiation should be treated as an outcome variable as part of a model for longitudinal change or instead used as a predictive variable with respect to the response to treatment. We develop a new approach that involves a combined statistical model for all pre- and post-treatment observations of the biomarker of interest, in which the characteristics of response to treatment are treated as a function of the 'true' value of the biomarker at treatment initiation. METHODS: The modelling strategy developed is applied to a dataset of CD4 counts from patients in the UK Register of HIV Seroconverters (UKR) cohort who initiated highly active antiretroviral therapy (HAART). The post-HAART recovery in CD4 counts for each individual is modelled as following an asymptotic curve in which the speed of response to treatment and long-term maximum are functions of the 'true' underlying CD4 count at initiation of HAART and the time elapsed since seroconversion. Following previous research in this field, the models developed incorporate non-stationary stochastic process components, and the possibility of between-patient differences in variability over time was also considered. RESULTS: A variety of novel models were successfully fitted to the UKR dataset. These provide reinforcing evidence for findings that have previously been reported in the literature, in particular that there is a strong positive relationship between CD4 count at initiation of HAART and the long-term maximum in each patient, but also reveal potentially important features of the data that would not have been easily identified by other methods of analysis. CONCLUSION: Our proposed methodology provides a unified framework for the analysis of pre- and post-treatment longitudinal biomarker data that will be useful for epidemiological investigations and simulations in this context. The approach developed allows use of all relevant data from observational cohorts in which many patients are missing pre-treatment measurements and in which the timing and number of observations vary widely between patients

A Bayesian averted infection framework for PrEP trials with low numbers of HIV infections: application to the results of the DISCOVER trial

Trials of candidate agents for HIV pre-exposure prophylaxis (PrEP) might randomly assign participants to be given a new PrEP agent or oral coformulated tenofovir disoproxil fumarate plus emtricitabine. This design presents unique challenges in interpretation. First, with two active arms, HIV incidence might be low. Second, the effectiveness of tenofovir disoproxil fumarate plus emtricitabine varies across populations; thus, similar HIV incidence between groups could be consistent with a wide range of effectiveness for the new PrEP. We propose a two-part approach to trial results. First, we use Bayesian methods to incorporate assumptions about the background incidence of HIV in the trial in the absence of PrEP, possibly augmented by external data. On the basis of the estimated background incidence, we estimate and compare the number of averted (or prevented) HIV infections in each of the two trial groups, calculating the averted infections ratio. We apply these methods to a completed trial of tenofovir alafenamide plus emtricitabine for PrEP. Our framework shows that leveraging external information to estimate averted infections and the averted infections ratio enhances the efficiency and interpretation of active-controlled PrEP trials

Confidence limits for the averted infections ratio estimated via the counterfactual placebo incidence rate

Objectives The averted infections ratio (AIR) is a novel measure for quantifying the preservation-of-effect in active-control non-inferiority clinical trials with a time-to-event outcome. In the main formulation, the AIR requires an estimate of the counterfactual placebo incidence rate. We describe two approaches for calculating confidence limits for the AIR given a point estimate of this parameter, a closed-form solution based on a Taylor series expansion (delta method) and an iterative method based on the profile-likelihood. Methods For each approach, exact coverage probabilities for the lower and upper confidence limits were computed over a grid of values of (1) the true value of the AIR (2) the expected number of counterfactual events (3) the effectiveness of the active-control treatment. Results Focussing on the lower confidence limit, which determines whether non-inferiority can be declared, the coverage achieved by the delta method is either less than or greater than the nominal coverage, depending on the true value of the AIR. In contrast, the coverage achieved by the profile-likelihood method is consistently accurate. Conclusions The profile-likelihood method is preferred because of better coverage properties, but the simpler delta method is valid when the experimental treatment is no less effective than the control treatment. A complementary Bayesian approach, which can be applied when the counterfactual incidence rate can be represented as a prior distribution, is also outlined

Fractional Brownian motion and multivariate-t models for longitudinal biomedical data, with application to CD4 counts in HIV-patients

Longitudinal data are widely analysed using linear mixed models, with 'random slopes' models particularly common. However, when modelling, for example, longitudinal pre-treatment CD4 cell counts in HIV-positive patients, the incorporation of non-stationary stochastic processes such as Brownian motion has been shown to lead to a more biologically plausible model and a substantial improvement in model fit. In this article, we propose two further extensions. Firstly, we propose the addition of a fractional Brownian motion component, and secondly, we generalise the model to follow a multivariate-t distribution. These extensions are biologically plausible, and each demonstrated substantially improved fit on application to example data from the Concerted Action on SeroConversion to AIDS and Death in Europe study. We also propose novel procedures for residual diagnostic plots that allow such models to be assessed. Cohorts of patients were simulated from the previously reported and newly developed models in order to evaluate differences in predictions made for the timing of treatment initiation under different clinical management strategies. A further simulation study was performed to demonstrate the substantial biases in parameter estimates of the mean slope of CD4 decline with time that can occur when random slopes models are applied in the presence of censoring because of treatment initiation, with the degree of bias found to depend strongly on the treatment initiation rule applied. Our findings indicate that researchers should consider more complex and flexible models for the analysis of longitudinal biomarker data, particularly when there are substantial missing data, and that the parameter estimates from random slopes models must be interpreted with caution. © 2015 The Authors. Statistics in Medicine Published by John Wiley & Sons Ltd

Patterns of Second- and Third-Trimester Growth and Discordance in Twin Pregnancy: Analysis of the Southwest Thames Obstetric Research Collaborative (STORK) Multiple Pregnancy Cohort.

INTRODUCTION: This study investigates patterns of intertwin size discordance in dichorionic diamniotic (DCDA) and monochorionic diamniotic (MCDA) twin pregnancies. MATERIAL AND METHODS: Ultrasound measurements of twin pregnancies, from 14 weeks to term, were collected by 9 hospitals over a 10-year period. This analysis considers the modelled and observed levels of discordance in abdominal circumference (AC) and estimated fetal weight (EFW) in relation to gestational age. Fitted models were analysed to produce charts displaying the expected range of intertwin discordance in AC and EFW at any given examination. RESULTS: The dataset for analysis included a total of 9,866 ultrasound examinations in 1,802 DCDA and 323 MCDA twin pregnancies. The 95th percentile of intertwin discordance in EFW increased from 18.3% (95% CI, 17.8-18.7%) at 20 weeks to 21.9% (95% CI, 21.3-22.4%) at 30 weeks for DCDA pregnancies. The 95th percentile for intertwin discordance in AC was stable at 10-11% for this period. Slightly higher levels of discordance were observed for MCDA than for DCDA pregnancies. DISCUSSION: The expected range of intertwin discordance in EFW and AC shows differences with gestational age and between DCDA and MCDA pregnancies

The averted infections ratio: a novel measure of effectiveness of experimental HIV pre-exposure prophylaxis agents

Tenofovir disoproxil fumarate combined with emtricitabine is a highly effective oral pre-exposure prophylaxis (PrEP) agent for preventing the acquisition of HIV. This effectiveness has consequences for the design and analysis of trials assessing experimental PrEP regimens, which now generally include an active-control tenofovir disoproxil fumarate plus emtricitabine group, rather than a placebo group, as a comparator. Herein, we describe major problems in the interpretation of the primary measure of effectiveness proposed for these trials, namely the ratio of HIV incidence in the experimental agent group to that in the active-control group. We argue that valid interpretation requires an assumption about one of two parameters: either the incidence among trial participants had they not received PrEP or the effectiveness of tenofovir disoproxil fumarate plus emtricitabine within the trial. However, neither parameter is directly observed because of the absence of a no-treatment group, thus requiring the use of external evidence or subjective judgment. We propose an alternative measure of effectiveness based on the concept of averted infections, which incorporates one of these parameters. The measure is simple to interpret, has clinical and public health relevance, and is a natural preservation-of-effect criterion for assessing statistical non-inferiority. Its adoption could also allow the use of smaller sample sizes, currently a major barrier to the assessment of experimental PrEP regimen

No overall change in the rate of weight gain after switching to an integrase-inhibitor in virologically suppressed adults with HIV

OBJECTIVE: Excessive weight gain has been reported with integrase strand transfer inhibitors (INSTIs). We evaluated weight changes in virologically-suppressed adults with HIV who switched from non-INSTI regimens to raltegravir- or dolutegravir-containing antiretroviral therapy. DESIGN: Retrospective single-centre cohort. METHODS: Adults who switched to raltegravir or dolutegravir before or between January-2015 and October-2017 were identified. Virologically-suppressed, treatment-experienced (≥2 years) individuals, ≥6 months on INSTI, with weight measurements ≤2years pre- and post-switch were included. Our analysis used a random effects model with linear slope pre- and post-INSTI with adjustment for age, gender, ethnicity, pre-switch-regimen (protease inhibitor vs. non-protease inhibitor), and raltegravir vs. dolutegravir use. RESULTS: 378 individuals, 81.2% male, 70.1% white ethnicity, median age of 49 years, median of four weight measurements per participant, and median weight and body mass index (BMI) at switch, of 76.6 kg, and 25.3 kg/m respectively were included. Weight increased by an average of 0.63 kg/year (95% CI 0.17-1.09) pre-switch with no overall change in rate of weight gain post-switch [+0.05 kg/year (-0.61-0.71, p = 0.88)]. In our adjusted model, a transition from minimal weight change to weight gain post-switch was isolated to older individuals though this lacked statistical significance [e.g. +1.59 kg/year (-0.26-3.45) if aged 65 years]. Our findings did not differ by gender, ethnicity, pre-switch regimen, or raltegravir vs. dolutegravir. Similar results were seen for BMI and after adjusting for fixed nucleoside/nucleotide reverse transcriptase inhibitor backbone. CONCLUSION: We found no clear evidence of an overall increase in rate of weight gain following switch to INSTI in virologically-suppressed individuals

Associations between baseline characteristics, CD4 cell count response and virological failure on first-line efavirenz + tenofovir + emtricitabine for HIV

Objectives: The aim of this study was to investigate associations between baseline characteristics and CD4 cell count response on first-line antiretroviral therapy and risk of virological failure (VF) with or without drug resistance. Methods: We conducted an analysis of UK Collaborative HIV Cohort data linked to the UK HIV Drug Resistance Database. Inclusion criteria were viral sequence showing no resistance prior to initiation of first-line efavirenz + tenofovir disoproxil fumarate + emtricitabine and virological suppression within 6 months. Outcomes of VF (≥200 copies/mL) with or without drug resistance were assessed using a competing risks approach fitted jointly with a model for CD4 cell count recovery. Hazard ratios for each VF outcome were estimated for baseline CD4 cell count and viral load and characteristics of CD4 cell count response using latent variables on a standard normal scale. Results: A total of 3640 people were included with 338 VF events; corresponding viral sequences were available in 134 with ≥1 resistance mutation in 36. VF with resistance was associated with lower baseline CD4 (0.30, 0.09-0.62), lower CD4 recovery (0.04, 0.00-0.17) and higher CD4 variability (4.40, 1.22-12.68). A different pattern of associations was observed for VF without resistance, but the strength of these results was less consistent across sensitivity analyses. Cumulative incidence of VF with resistance was estimated to be <2% at 3 years for baseline CD4 ≥350 cells/μL. Conclusion: Lower baseline CD4 cell count and suboptimal CD4 recovery are associated with VF with drug resistance. People with low CD4 cell count before ART or with suboptimal CD4 recovery on treatment should be a priority for regimens with high genetic barrier to resistance

Risk factors and outcomes for the Q151M and T69 insertion HIV-1 resistance mutations in historic UK data

BACKGROUND: The prevalence of HIV-1 resistance to antiretroviral therapies (ART) has declined in high-income countries over recent years, but drug resistance remains a substantial concern in many low and middle-income countries. The Q151M and T69 insertion (T69i) resistance mutations in the viral reverse transcriptase gene can reduce susceptibility to all nucleoside/tide analogue reverse transcriptase inhibitors, motivating the present study to investigate the risk factors and outcomes associated with these mutations. METHODS: We considered all data in the UK HIV Drug Resistance Database for blood samples obtained in the period 1997-2014. Where available, treatment history and patient outcomes were obtained through linkage to the UK Collaborative HIV Cohort study. A matched case-control approach was used to assess risk factors associated with the appearance of each of the mutations in ART-experienced patients, and survival analysis was used to investigate factors associated with viral suppression. A further analysis using matched controls was performed to investigate the impact of each mutation on survival. RESULTS: A total of 180 patients with Q151M mutation and 85 with T69i mutation were identified, almost entirely from before 2006. Occurrence of both the Q151M and T69i mutations was strongly associated with cumulative period of virological failure while on ART, and for Q151M there was a particular positive association with use of stavudine and negative association with use of boosted-protease inhibitors. Subsequent viral suppression was negatively associated with viral load at sequencing for both mutations, and for Q151M we found a negative association with didanosine use but a positive association with boosted-protease inhibitor use. The results obtained in these analyses were also consistent with potentially large associations with other drugs. Analyses were inconclusive regarding associations between the mutations and mortality, but mortality was high for patients with low CD4 at detection. CONCLUSIONS: The Q151M and T69i resistance mutations are now very rare in the UK. Our results suggest that good outcomes are possible for people with these mutations. However, in this historic sample, viral load and CD4 at detection were important factors in determining prognosis