 Methodology
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Improved adherence adjustment in the Coronary Drug Project
Trials volume 19, Article number: 158 (2018)
Abstract
Background
The survival difference between adherers and nonadherers to placebo in the Coronary Drug Project has been used to support the thesis that adherence adjustment in randomized trials is not generally possible and, therefore, that only intentiontotreat analyses should be trusted. We previously demonstrated that adherence adjustment can be validly conducted in the Coronary Drug Project using a simplistic approach. Here, we reanalyze the data using an approach that takes full advantage of recent methodological developments.
Methods
We used inverseprobability weighted hazards models to estimate the 5year survival and mortality risk when individuals in the placebo arm of the Coronary Drug Project adhere to at least 80% of the drug continuously or never during the 5year followup period.
Results
Adjustment for postrandomization covariates resulted in 5year mortality risk difference estimates ranging from − 0.7 (95% confidence intervals (CI), − 12.2, 10.7) to 4.5 (95% CI, − 6.3, 15.3) percentage points.
Conclusions
Our analysis confirms that appropriate adjustment for postrandomization predictors of adherence largely removes the association between adherence to placebo and mortality originally described in this trial.
Trial registration
ClinicalTrials.gov, Identifier: NCT00000482. Registered retrospectively on 27 October 1999.
Background
In 1980, an analysis of the Coronary Drug Project (CDP) randomized trial found a greater survival in individuals who adhered to placebo than in those who did not adhere to placebo [1]. Statistical adjustment for multiple prognostic factors could not remove these survival differences. This finding was used to support the thesis that adherence adjustment in randomized trials is not generally possible and, therefore, that only intentiontotreat analyses should be trusted.
In 2016, we reported a reanalysis of the CDP placebo arm that incorporated statistical advances not available in 1980. Our reanalysis showed that most of the survival differences between placebo adherers and nonadherers were actually removed after adjustment for pre and postrandomization prognostic factors [2]. Specifically, we modified the definition of adherence at missed visits, updated the method of adjustment for baseline predictors of adherence, and added adjustment for postrandomization predictors of adherence via inverseprobability (IP) weighting.
With these changes, the 5year survival difference between placebo adherers and nonadherers decreased from 10.9 percentage points (95% confidence interval, 7.5, 14.4) to 2.5 percentage points (95% confidence interval, − 2.1, 7.0).
However, our reanalysis did not take full advantage of the recent methodological advances. In an attempt to conduct a reanalysis as comparable as possible to the original 1980 analysis, we used a cumulative incidence model that did not account for the exact time of death during the 5year period, and a somewhat unintuitive measure of adherence – a binary indicator for cumulative adherence greater than 80% during the entire 5year period. Although modeling the data this way was useful to demonstrate that methods developed since 1980 can address previously intractable sources of bias, the analytic approach we used is not the recommended one. Here, we demonstrate a better approach which uses a more natural definition of adherence and a survival analysis approach to incorporate time of death.
A brief introduction to the Coronary Drug Project
The CDP was a sixarm double blind, placebocontrolled randomized trial of 8341 men with a history of myocardial infarction (MI) enrolled between 1966 and 1969 [3]. Eligibility criteria for participation in the trial included men aged 30–64 years at entry, with an electrocardiogramdocumented MI at least 3 months prior to enrollment, a New York Heart Association functional class of I (no limitation in physical activity) or II (slight limitations only), no prior surgery for coronary artery disease, no anticoagulant therapy or lipidinfluencing therapy use at entry, and no other chronic medical conditions which could affect trial participation. In addition, potential participants were required to complete a 2month control period during which all individuals were given placebo and only those who adhered to at least 80% were eligible for randomization. Participants were then randomized within study center and by risk group (low risk if one prior MI with no complications; high risk if more than one MI or complications).
Study medications were prescribed as three pills daily at randomization, and dosage was increased to nine pills daily, based on tolerance, over the following 2 months. Adherence was assessed by study clinicians at each visit based on a visual inspection of pill bottles, and recorded as a sixlevel categorical variable (≥ 80%, 60–79%, 40–59%, 20–39%, 1–19%, none) which was then adjusted for expected dose at that visit [1, 2].
Three of the five active treatment arms were discontinued early because of adverse events (low and highdose equine estrogen, and dextrothyroxine) [4,5,6], and the other two treatments (clofibrate and niacin) were not found to be effective in reducing mortality [7]. The 5year cumulative incidence of mortality was 20.9% in the placebo arm, 20.0% in the clofibrate arm, and 21.2% in the niacin arm [7].
Methods
We restricted our analyses to the 2787 men in the placebo arm. Let t be an index for visit, where t = 0 is the baseline visit and t = 14 is the last visit at year 5, with 4month intervals between each visit. Let A_{ t } be an indicator for adherence ≥ 80% to the protocolspecified placebo dose between t and t + 1, Y_{ t } an indicator of death between t and t + 1, C_{t + 1} an indicator for loss to followup defined as three consecutive missed study visits at t + 1, V a set of 39 variables measured at the time of randomization, and L_{ t } a set of postrandomization variables measured at each t. The baseline covariates V were adherence during the runin period, demographics (age, race), lifestyle characteristics (cigarette smoking, physical activity), medical history (risk group, weight, New York Heart Association class, comorbidities, blood pressure), use of nonstudy medications, laboratory findings, and electrocardiogram findings. All of these variables (except age, race, weight, risk group) were also postrandomization variables L_{ t } at each visit t. When an individual missed a study visit, the most recent covariate and adherence values were carried over from the most recent available data, up to three consecutive missed visits. Participants were censored at the expected date of their third consecutive missed study visit.
The choice of 80% as a cutpoint for adherence was based on standard practice, as reflected by the use of a runin period requiring 80% adherence to placebo among all trial participants. Note that, since adherence was assessed as a categorical variable, with the highest category ≥ 80% of prescribed pills taken, higher thresholds were not possible for the binary adherence indicator.
In our primary analysis, we artificially censored individuals when they reported an adherence level that differed from their baseline adherence level, that is, when A_{ t }≠ A_{0} [8, 9]. We then fit the IPweighted pooled logistic model for the discretetime hazards at each time [10]:
where θ_{0,t} is a timevarying intercept modeled as a restricted cubic spline of time (knots at 0, 5, 10, 15 visits), and θ_{2} is a vector parameter. The timevarying stabilized weights [11] were defined as:
where M_{ t } is an indicator for measurement of adherence at visit t (1 if measured, 0 otherwise), and overbars indicate history of the variable. The weight models were fit in the full population before artificial censoring; in a sensitivity analysis, we restricted the fit of the weight models to personvisits with A_{ k }= A_{0} for 0 < k ≤ t.
To estimate the denominator of the weights, we fit the model logit(Pr[M_{ t } = 1\( {A}_0,{\bar{A}}_{t1},V,{\overline{L}}_t,{C}_t=0 \)]) = α_{0t} + α_{1}A_{0} + α_{2}A_{t − 1} + α_{3}V + α_{4}L_{t − 1} to all personvisits, and the model logit(Pr[A_{ t } = 0\( {A}_0,{\bar{A}}_{t1},V,{\overline{L}}_t,{C}_t=0 \),M_{ t } = 1]) = β_{0t} + β_{1}A_{0} + β_{2}A_{t − 1} + β_{3}V + β_{4}L_{ t } to the personvisits with measured adherence. When adherence was not measured at a visit (M_{ t } = 0) but the individual was not yet defined to be lost to followup (that is, at the first or second consecutive missed visit), adherence was carried forward from the previous visit and the factor in the denominator of the adherence weight was 1 for that visit.
Similar models that did not include the timevarying covariates were fit to estimate the numerators of the weights. The final weight for each individual at each time was the product of the measurement and adherence weights for that individual up to that time point. As in previous studies, we truncated the estimated IP weights at the 99th percentile to avoid undue influence of outliers. The truncated weight estimates had a mean of 1.00 (SD = 0.29) and a range of 0.02 to 2.55.
We used the parameter estimates from the weighted outcome logistic model to estimate the 5year survival as previously described [2]. We compared the survival for always vs. never at least 80% adherent, that is, A_{0} = 0 vs. A_{0} = 1.
We conducted a second analysis where, rather than censor individuals who reported a change in adherence, we specified a doseresponse function for the effect of adherence on mortality. To do so, we summarized the adherence history Ā_{ t } between baseline and visit t by the cumulative average cum(Ā_{ t }) = \( \frac{1}{t+1}\sum \limits_{k=0}^t{A}_k \) (i.e., the proportion of visits during which an individual was adherent to at least 80% of the placebo dose), and then fit the pooled logistic model
where f[·] is a doseresponse function and θ_{1} is a vector parameter.
In separate analyses, we specified more flexible doseresponse functions. Specifically, we considered both a quadratic doseresponse function θ_{1}f[cum(Ā_{ t })] = θ_{1,1}cum(Ā_{ t }) + θ_{1,2}[cum(Ā_{ t })]^{2}, and a function that allowed for a separate effect of recent adherence θ_{1,0}A_{ t } + θ_{1,1}cum(Ā_{t  1}) + θ_{1,2}[cum(Ā_{t  1})]^{2}. We also considered functions that included product terms with the time parameters.
To compute 95% confidence intervals, we used nonparametric bootstrapping with 500 samples.
SAS 9.4 was used for all analyses and code is provided in the supplementary online materials (see Additional file 1).
Results
Using our primary hazards models with artificial censoring, the estimated 5year mortality risk difference between adherers and nonadherers in the placebo arm was 0.01 percentage points (95% confidence interval, 12.2, 13.2) after adjusting for postrandomization covariates (Table 1). Estimates based on doseresponse hazards models without artificial censoring gave consistent estimates ranging from less than 1 percentage point to approximately 5 percentage points. Using an oversimplified doseresponse model (a linear term only for cumulative adherence) resulted in implausible risk estimates (data not shown). The results were robust to other modeling choices, such as the number or placement of knots for the spline of time. As a sensitivity analysis, we also assessed censoring individuals for loss to followup at the second missed visit. Results were similar with an estimated 5year mortality risk difference of 8.8 percentage points (95% CI, − 1.7, 20.7) in the unadjusted analysis and 0.6 percentage points (95% CI, − 8.1, 10.5) after adjusting for postrandomization covariates. When we restricted the fit of the weight models to personvisits with A_{ k }= A_{0} for 0 < k ≤ t, the 5year mortality risk difference adjusted for postrandomization covariates increased slightly to 3.1 percentage points (95% CI, − 3.1, 9.4).
Discussion
Our analysis confirms that the survival differences between adherers and nonadherers to placebo can be largely adjusted away in the Coronary Drug Project. Adjustment for postrandomization predictors of adherence results in estimated 5year mortality risk differences comparing adherence and nonadherence to placebo that are approximately null regardless of the analytic approach used. Our previous analysis [2] reached a similar conclusion but, by simply estimating the cumulative mortality at the end of followup, ignored the timing of events. In contrast, the current analyses use a survival analysis approach that allows estimation of adjusted survival curves for adherers and nonadherers throughout the followup.
We used two methods to compare the survival under continuous highaverage adherence vs. low adherence (< 80%). The first method was a relatively inefficient censoring procedure that does not require a doseresponse model for the effect of cumulative adherence on mortality. The second method was a theoretically more efficient method that requires a doseresponse model and, therefore, will result in bias if the doseresponse model is misspecified. We considered a variety of doseresponse functions, which made different assumptions about the relationship between adherence and mortality over time. When sufficient data are available, more flexible doseresponse functions are generally preferable as they impose fewer a priori constraints. For example, a function that models separately current adherence and prior cumulative adherence (using, say, linear and quadratic terms as in our analysis) requires fewer assumptions than a function that models total cumulative adherence. However, the added flexibility comes at the price of less precise estimates. Unlike in other examples [12], our estimates were not very sensitive to the choice of doseresponse model. Further research into doseresponse modeling for adherenceadjusted estimates is warranted.
Obtaining a null estimate when comparing adherers and nonadherers in the placebo arm supports the validity of adherenceadjusted effect estimates in randomized trials. However, this comparison relies on the lack of psychobiological effects of placebo on mortality. For other outcomes, such as pain or symptom severity, this assumption may be less reasonable.
Conclusion
Adherenceadjusted analyses of randomized controlled trials have been viewed with some skepticism with some authors suggesting that adherence is intractably confounded [1]. However, we have demonstrated that adjustment for postrandomization predictors of adherence can create comparability between adherers and nonadherers when rich data on preand postrandomization confounders exist.
Abbreviations
 CDP:

Coronary Drug Project
 CI:

Confidence interval
 IP:

Inverseprobability
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Acknowledgements
We would like to thank Dr. Roger Logan for providing technical assistance.
Funding
This work was supported through a PatientCentered Outcomes Research Institute (PCORI) Award (ME150328119). All statements in this report, including its findings and conclusions, are solely those of the authors and do not necessarily represent the views of the PatientCentered Outcomes Research Institute (PCORI), its Board of Governors or Methodology Committee.
Availability of data and materials
A SAS code for all analyses is available in the supplementary online materials. The full CDP dataset has been submitted to the National Heart, Blood, and Lung Institute.
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EM conducted the analysis. EM and MH designed the analysis, and wrote the manuscript. Both authors read and approved the final manuscript.
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This project was reviewed and exempted by the Harvard T.H. Chan School of Public Health IRB office. No consent was needed from study participants.
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The authors declare that they have no competing interests.
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Additional file
Additional file 1:
SAS 9.4 code for placeboarm adherence analysis. A SAS code for all analyses is provided in this file. If you have any questions, comments, or discover an error, please contact Eleanor Murray at emurray@mail.harvard.edu. For the most updated versions of related SAS programs, please visit www.hsph.harvard.edu/causal/. (PDF 316 kb)
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Murray, E.J., Hernán, M.A. Improved adherence adjustment in the Coronary Drug Project. Trials 19, 158 (2018). https://doi.org/10.1186/s1306301825195
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Keywords
 Perprotocol effect
 Intentiontotreat effect
 Inverseprobability weighting
 Coronary Drug Project
 Adherence