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JAIDS Journal of Acquired Immune Deficiency Syndromes:
doi: 10.1097/01.qai.0000186364.27587.0e
Epidemiology and Social Science

Factors Associated With Nonadherence to Highly Active Antiretroviral Therapy: A 5-Year Follow-Up Analysis With Correction for the Bias Induced by Missing Data in the Treatment Maintenance Phase

Carrieri, Maria Patrizia*; Leport, Catherine PhD†; Protopopescu, Camelia PhD*; Cassuto, Jill-Patrice MD‡ ; Bouvet, Elisabeth MD†; Peyramond, Dominique MD§; Raffi, Francois MD∥ ¸; Moatti, Jean-Paul PhD*; Cheê, Geneviéve PhD¶; Spire, Bruno PhD*

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From *INSERM U379, Marseille, France; †Faculté Xavier Bichat, Paris, France; ‡Hôpital Larchet, Nice, France; §Croix-Rousse Hospital, Lyon, France; ∥Hôtel-Dieu, Nantes, France; and ¶INSERM U593, Bordeaux, France

Supported by the French Agency for AIDS research (ANRS), Collège des fcUniversitaires de Maladies Infectieuses et Tropicales (CMIT ex APPIT), Sidaction Ensemble contre le Sida and associated pharmaceutical companies: Abbott, France, Boehringer-Ingelheim, France, Bristol-Myers Squibb, France, Glaxo-SmithKline, France, Merck Sharp and Dohme, France, Roche, France.

Reprints: Bruno Spire, INSERM U379, 23 rue Stanislas Torrents, 13006 Marseille, France (e-mail: spire@marseille.inserm.fr).

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Abstract

Summary: This study aimed to identify factors associated with nonadherence during the maintenance phase of highly active antiretroviral therapy (months 12-60) in the Anti PROtease Cohort (APROCO) cohort after correcting for the bias due to missing outcome data. A Heckman 2-stage approach (generalized estimating equations probit model) was used to compare visits with moderate or poor adherence and visits with high adherence. Between months 12 and 60, at least 1 self-reported adherence measure was available for 970 of the 1110 patients with at least 12 months of follow-up (3889 visits with adherence assessments). Adherence was rated as high at 2466 visits, moderate at 1125, and poor at 298. After adjustment for "missingness," moderate and poor adherence were independently associated with age (younger), perceived treatment side effects, dosing frequency different from twice daily, and a protease inhibitor-based regimen. They were also associated with depression and lack of support from the main partner. High adherence was most likely among patients born outside the European Union. A comparison restricted to poor-adherence and high-adherence visits yielded a similar pattern of predictors. Adjusting for missing outcome data changed the predictor set. Reasons for nonadherence are multifactorial. Psychosocial interventions and the selection of the best-tolerated regimens are needed to improve long-term adherence of HIV-infected patients to their lifelong treatment.

Because of the crucial role of highly active antiretroviral therapy (HAART) in slowing clinical progression and increasing survival in HIV-infected individuals, adherence has become a major issue since HAART introduction.1,2 High levels of adherence to HAART are associated with its virologic3,4 and immunologic success.5 However, adherence behaviors may change considerably over time.6,7 We reported in a previous paper that the level of adherence required for sustained virologic suppression can be lower in the late (after the 1st year of HAART) compared with the early phase (within the first 4 months) of HAART.8 Thus, both high adherence to HAART in the initial phase of treatment and at least moderate adherence in the maintenance phase of treatment independently predicted long-term sustained virologic suppression.

These results suggest that patients starting HAART undergo 2 separate phases: an induction phase for which high adherence is required for long-term immunovirologic success, and a maintenance phase, during which small deviations from high adherence do not harm long-term immunovirologic success. Conversely, poor adherence during the maintenance phase may seriously compromise a patient s long-term virologic response.8 Moreover, the greater the cumulative nonadherence, the greater the compromise may be.2

Several studies have identified treatment-related or psychosocial factors associated with nonadherence during the early phase of treatment9,10 or cross-sectionally11-13 that could put into evidence factors that influence nonadherence during the maintenance phase.14 However, because adherence is often assessed by self-administered questionnaires, missing data may hinder analysis of prospective epidemiologic studies, and most results from cross-sectional studies are not corrected for selection bias. Several methods exist to correct for selection bias,15 but to our knowledge they have never been used for adherence data. This issue may be particularly critical when dealing with longitudinal data subject to a considerable amount of missing data, especially when patients fill out self-administered questionnaires.

The aim of the present study was to identify factors associated with nonadherence during the maintenance phase with 5-year follow-up data from the APROCO cohort6 after correction for the possible bias induced by missing data.

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PATIENTS AND METHODS

Patients

The French APROCO cohort was designed to study the clinical, immunologic, virologic, and sociobehavioral course of disease in HIV-1-positive individuals who started a treatment regimen including protease inhibitors (PI). Subjects were enrolled between May 1997 and June 1999, at their first PI prescription (M0); clinical and laboratory data were collected every 4 months. A self-administered questionnaire collected psychologic and behavioral characteristics at enrollment, at M4, and every 8 months thereafter (through M60). Only patients with at least 12 months of clinical follow-up are included in this analysis.

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Questionnaires
Medical Questionnaire

At each visit, the HIV care provider completed a medical questionnaire that included clinical and laboratory data (plasma HIV RNA, CD4+ cell counts, clinical stage) and the antiretroviral regimen prescribed. The medical questionnaire at enrollment (M0) included retrospective data about the patient s HIV history: transmission category, time since diagnosis, and antiretroviral naiveté at enrollment in the cohort. Other information was recorded, including place of birth.

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Self-Administered Questionnaire

The questionnaire collected social and demographic information about age, gender, parental status, education, main partner, and housing conditions. It also asked for information about adherence to antiretroviral treatment, depression, self-reported symptoms, alcohol consumption, and support from partner (whether principal or not).

Five questions about adherence to HAART were included in all self-administered questionnaires, in accordance with the methodology established by the AIDS Clinical Trial Group.16 Adherence at each assessment was classified in one of 3 categories: high, moderate, or poor.6 Patients were first asked to list each drug included in their HAART regimen and the number of pills they had taken on each of the 4 days before the visit. When patients reported they had taken all of their prescribed doses in the past 4 days, adherence was classified as high for that assessment, unless they also reported in subsequent answers that they had skipped a dose during the past weekend; had "almost totally" followed their HAART regimen; had modified the prescribed scheduling several times; or had taken all their medication at one time each day, in which case adherence was classified as moderate. Adherence at assessments at which patients reported taking 80%-99.9% of their prescribed doses of HAART in the previous 4-day period was also classified as moderate. Adherence was classified as poor if patients reported they had taken <80% of their pills in the previous 4-day period or had followed their HAART prescriptions "partially" or "not at all." The questionnaire also asked about the specific regimen and the daily dosing frequency: daily, twice daily, and 3 times daily (or more) were specifically distinguished.

Depression was measured using the French version ''''''of the Center for Epidemiologic Studies Depression Scale (CES-D),17 which is a 20-item scale commonly used in population-based studies, and particularly in studies involving HIV-infected patients. Although not a diagnostic of clinical depression, a score of ≥16 is considered indicative of significant depressive symptoms.

A 13-item scale collected information about self-reported symptoms. This scale is a French version of the symptom index validated by Justice et al,18 previously used in other investigations.9,19,20 Patients were asked if they had experienced, at least once in the past 4 weeks, each of the following symptoms: diarrhea, nausea, stomach pain, headache, change in taste, skin itching, muscle pain, heartburn, sore mouth, vomiting, fever, kidney stones, or fatigue. A score based on the sum of all self-reported symptoms (excluding lipodystrophy) was constructed for a quantitative assessment of perceived side effects. The patients questionnaire also contained a list of 9 symptoms related to possible manifestations of lipodystrophy.21

Finally, the self-administered questionnaire included 2 questions about alcohol consumption over the past 7 days (frequency and quantity consumed). Patients were considered to consume alcohol daily if the average number of units of alcohol per day was ≥1.22

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Statistical Analysis

We conducted 2 separate analyses to identify factors associated with nonadherence during the maintenance phase (M12-M60) and to assess the impact of missing data on the relation between these factors and adherence. In these analyses, all scheduled visits between M12 and M60 were considered. Visits missed due to death were excluded from all analyses.

Initially, questionnaires reporting moderate/poor adherence were compared with high-adherence assessments. The univariate and the multivariate analyses were based on generalized estimating equations (GEE),23 under the hypothesis of a binomial distribution of the outcome with a probit link function. This approach was used because a preliminary analysis showed that there was no influence of time of follow-up after M12 on the pattern of factors associated with nonadherence. All variables analyzed were considered eligible for the final multivariate model, to prevent the masking of important predictors by the confounding effects present in the data.24-26 The model-building process used the Wald statistic as the criterion for including and removing variables from the model by forward stepwise selection.

Secondly, we adapted the 2-stage Heckman approach,15 as described by Shelton et al,27 to take into account missing adherence data. Heckman has already shown in cross-sectional studies that this approach allows us to properly correct for the bias induced by missing data, and Shelton et al extended this approach to longitudinal data. Adherence data might be missing due to failure either to respond to the self-administered questionnaires or to return for follow-up visits. The hypothesis underlying this approach is that the values are missing not at random (MNAR), following the terminology of Little and Rubin,28 where the probability of nonresponse depends on the unobserved outcome. It is known that in this case the "missingness" process can affect inference about the outcome and that valid results can be obtained only if the nonresponse process is explicitly modeled.29

In the first stage, a GEE probit model was used to identify factors associated with missing data at any visit of the scheduled follow-up. Baseline fixed variables, last available CD4+ cell counts, and viral load were considered to identify the pattern of variables independently associated with outcome. The residuals of this model were used to compute the inverse Mills ratio (IMR), representing the effect of all unobserved variables that can influence the missingness process.

In the second stage, a GEE probit model compared the moderate- and poor-adherence assessments with the high-adherence assessments. At this stage the IMR was added as a covariate to adjust for the bias due to the missing data in both univariate and multivariate analyses. Including the IMR in the second-stage analysis for the outcome serves to eliminate such a bias. The bias correction is to be interpreted as follows: when the IMR coefficient is significant and positive, the selection bias due to missingness has the effect of underestimating the probability of poor/moderate adherence. Conversely, when the IMR coefficient is significant and negative, the selection bias due to missingness has the effect of overestimating the probability of poor/moderate adherence. The effect of unobserved factors that can affect both the missingness process and the outcome is captured by the residuals of the first-stage model. The method based on IMR adjustment is described in more detail in the Appendix. Two models were built: Model I was obtained with a forward approach for entering all possible variables in the model without IMR correction, and model II with a forward approach for entering all possible variables in the model with IMR.

A similar restricted analysis focused solely on poor adherence compared with high adherence assessments, to verify whether the pattern of predictors was similar to that identified in the overall comparison.

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RESULTS

Descriptive Analysis

The cohort included 1110 patients with at least 12 months of clinical follow-up, and 970 had completed at least 1 self-administered questionnaire between M12 and M60 (for 3889 visits with adherence self-assessments). Of the 1110 patients, 22% were women, 17% had been infected through injection drug use (IDU), median age at M12 was 37 years, and the median (interquartile range [IQR]) duration of antiretroviral exposure was 1 year (0-4 years). At M0 the median (IQR) CD4+ cell count was 284 (139-425) and 20% of patients were in AIDS clinical stage. The median (IQR) time since the first HIV-positive test was 3.8 (0.5-8.2) years. Nearly three-quarters of the cohort (792 patients, 71%) were born in the European Union (EU). Of the 318 who were not, 86 (27%) were born in sub-Saharan Africa, 95 patients (30%) outside the EU but not in sub-Saharan Africa, and the remaining 137 (43%) outside the EU but in an unspecified country. Sixty-one percent reported comfortable housing conditions and 46% were unemployed. A minority (29%) never reported having a main partner throughout the study period. Less than half of the patients (40%) either reported receiving poor or no support from their partner or had no partner. From M12 through M60, depression was identified at 36% of all visits, and 56% of patients were depressed at least once; daily alcohol consumption was reported at 16% of all visits, and 23% of patients reported daily consumption at least once. At M12, 88% of patients were being treated with PIs, but this proportion dropped to 41% at M60. At M60, 58% of patients had an undetectable viral load and 90% had CD4+ cell counts >200 CD4+/mm3. At M60 79% reported a twice-daily regimen, 8% reported a daily regimen, and 13% of patients a regimen with a dosing frequency of at least 3 doses daily. During the M12-M60 period, the median number of self-reported side effects varied between 3 and 4. Although only 28% of patients reported at least 1 lipodystrophy-related symptom at M12, this prevalence varied between 65% and 77% for the remaining follow-up. The proportion of patients whose last available viral load was detectable (>500 cp/mL) increased linearly (P < 0.001) with the number of poor-adherence assessments reported from M12 through M60 (34% in patients with no poor-adherence reports, 50% in those with 1, 51% in those with 2, and 67% in individuals with ≥3).

Of the 3889 assessments with complete adherence data (corresponding to 970 patients), adherence was classified as high at 2466 (63%) of these assessments, as moderate at 1125 (29%), and as poor at 298 (8%). The median (IQR) number of'adherence assessments was 4 (1-6) whereas the median (IQR) number of high-adherence visits was 2 (0-4) (Spearman ρ = 0.78, P < 0.001). During the study period, only 92 visits '''''''''''(2.7%) corresponded to 82 patients who were on therapeutic interruption. These patients reported to have been highly adherent before treatment interruption in half of the visits '''''''''''(n = 46). Of the 215 patients who reported poor adherence at least once during the maintenance period, 158 (73%) reported it only once, 40 (19%) twice, and 17 (8%) ≥3 times.

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Analysis of Missingness (first-stage analysis)

If all cohort members had survived through M60, the 1110 individuals would have accounted for 7770 visits from M12 through M60. During this period, however, 23 individuals died, corresponding to 76 missed visits. The 1110 individuals should therefore account for 7694 visits. Adherence response was missing for 3805 visits (49%), either because the clinical visit was missed (38%, n = 1463) or because there was no answer to adherence questions (62%, n = 2342). More precisely, the proportion of clinical visits missed at each scheduled follow-up increased regularly over time (from 5% at M12 to 34% at M60). The proportion of missing data due to missing adherence responses was more stable over time, ranging from 23% to 37% (Figure 1).

Figure 1
Figure 1
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The process of missingness, regardless of the reason, at any visit of the scheduled follow-up was modeled by a GEE probit model that compared the 3805 visits with missing information with the 3889 visits with adherence data (Table 1). This analysis allowed us to compute the IMR that was used in the second-stage analyses and to identify the independent factors associated with missingness. Among the social and demographic factors, age, female gender, transmission through IDU, inadequate housing, and birth outside the European Union were associated with absent adherence data. Of the clinical factors, missing data were more frequent for individuals in whom HIV had been diagnosed >6 months previously at enrollment and who were antiretroviral-naive at treatment initiation. Patients with intermediate immunovirologic status (detectable viral load, CD4+ cell counts >200/mm3, and stage A or B at last available visit) were also more likely to have missing adherence data.

Table 1
Table 1
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Factors Associated With Nonadherence (second-stage analysis)

Table 2 reports the factors associated with moderate/poor adherence. It includes the coefficient and 95% CI estimates based on the GEE probit model, both without and with adjustment for IMR, which was statistically significant in all analyses. This indicates that the parameter estimates for the factors explaining moderate/poor adherence would have been biased without the introduction of IMR in the second stage. Moreover, the positive sign for the IMR value means that the effect of the bias would have been to underestimate the probability of moderate/poor adherence.

Table 2
Table 2
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Model I finally included some social and demographic factors associated with nonadherence, such as age, IDU transmission, and poor housing conditions, but it did not take into account the bias due to missing data (Table 3). When we adjusted for this bias with IMR, the latter 2 variables were no longer significant in the final multivariate model (model II). In contrast, model II showed that individuals born in the EU were at higher risk of nonadherence than immigrants from outside the EU. This factor became significant only after adjustment for age and IMR. Similarly, antiretroviral naivete became an independent factor of nonadherence only after correction for this bias.

Table 3
Table 3
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Model II also confirms that psychosocial characteristics (poor support from the partner and depression) have a negative impact on adherence; in addition, HAART-related characteristics, including more perceived side effects, PI in the treatment regimen, and a non-twice daily-based regimen, also influenced adherence negatively. Moreover, the comparison of model I with model II showed that IDU transmission and adequate housing were no longer significant when the bias due to missing data was taken into account by adjustment with the IMR.

When restricting the analysis to patients who were antiretroviral naive at enrollment in the cohort; the same pattern of factors identified in model II was found except for the variable "born in EU," probably because of a lack of power.

To verify whether the pattern of factors identified in model II was also valid in the comparison restricted to nonadherence vs. high-adherence assessments, we performed new univariate and multivariate analyses, both adjusted for the IMR (data not shown). This analysis confirmed that the pattern of factors was similar to that identified in the general comparison. Only depression was no longer significant, probably due to a loss of power.

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DISCUSSION

This report describes results from the longest follow-up thus far of adherence data in patients enrolled in a cohort study when they began HAART. There are bound to be missing data from so long a follow-up of adherence data collected through self-administered questionnaires in a "real life" situation. This is a major concern as adherence is a dynamic process and intermittent nonadherence episodes, potentially missed or unnoticed, could account for unfavorable long-term outcome on antiretroviral therapy.6,8 This study shows clearly that these missing data, mainly due to patients failing to answer the adherence questions but also to missed clinical visits, induce considerable bias. An important finding is that the pattern of factors associated with adherence during the maintenance phase when we adjust for this bias differs from the pattern obtained without correcting for it. More specifically, factors related to social status (housing conditions and transmission group) were not associated with adherence once the analysis included the adjustment for missingness. This adjustment also made it possible to show in the multivariate analysis that patients born outside the EU were more adherent than those born inside it. In contrast, treatment-related characteristics (number of self-reported side effects, PI-based regimen, daily intake, antiretroviral naivete) and psychosocial factors (depression, lack of support from partner) were associated with nonadherence with and without the adjustment. Finally, the pattern of factors identified did not differ when we restricted the comparison to poorly adherent patients (adherence <80%) rather than moderately and poorly adherent groups. It was important to make this specific limited comparison because moderate adherence, unlike poor adherence, has not been shown to be detrimental for long-term virologic response.8

After controlling for missing data, nonadherence was not associated with IDU transmission or poor housing conditions, both proxies for social status. This finding indicates that highly adherent individuals, with higher social status, are "overrepresented" during follow-up. Similarly, the higher risk for nonadherence of persons born in the EU appeared only after controlling for missingness and age. This may suggest that the nonadherent subjects born in the EU were less likely to have adherence data, whereas nonadherence was not related to missingness among patients born outside the EU. The individuals born outside Europe who are enrolled in the cohort may, however, constitute a limited and privileged portion of the immigrant population, those who have access to care30 and who are therefore more motivated to follow provider prescription. These results shed light on the possibility of a differential bias due to missingness. This bias appears to have been ignored in previous studies, which suggested a possible association between social status (or a proxy for it) and nonadherence.13,31-33 This result confirms the difficulty in predicting adherence solely on the basis of simple social and demographic factors.19 Because the French Social Security guarantees free-of-charge access to care, including antiretroviral treatment, to all HIV-infected individuals, unprivileged populations are more represented in the APROCO cohort than in other longitudinal studies performed in countries where such access is denied. Our data suggest that these individuals were less likely to fill in adherence questionnaires whether they adhere or not.

These results confirm the importance of the number of self-reported side effects in poor adherence during the maintenance phase. This result confirms previous analyses, limited to the early phase of HAART,9,34 which reported that self-reported side effects are more predictive of nonadherence than medically recorded side effects. Characteristics of the regimen also influence adherence significantly: as shown in a previous study,35 a PI in the regimen had a quite negative impact on adherence, perhaps because it represents both the impact of perceived side effects that remain "uncaptured" by the number of symptoms as well as of food constraints, which are most often associated with PI combinations. This study confirms the long-term negative impact on adherence of complex regimens,36,37 ie, those requiring dosing ≥3 times a day. Conversely, patients with once-daily regimens were, somewhat surprisingly, nonadherent more often than those on twice-daily schedules. As there has been considerable enthusiasm for the once-daily strategies with the aim of improving adherence,38 one likely explanation is that such regimens may have been prescribed more frequently to patients who have been or are thought likely to be nonadherent. In any case, though, our results do not indicate any guaranteed adherence for such a simplification strategy.

Previous results have shown the impact of depression39,40 and the presence of a stable partner41 on survival. The present study suggests that adherence behavior may mediate the relation between these psychosocial factors and survival and that adherence is enhanced more by the partner s support than by the simple existence of a stable relationship. This study also confirms the close interrelationship between depression and nonadherence previously reported,13,42 a relation that persists even after controlling for self-reported symptoms.

Some limitations must be acknowledged. First, the study is based on data from the APROCO cohort of patients, who began a PI-containing regimen in 1996-1997. They are thus representative of the first generation of HAART patients but are not completely representative of patients who are on antiretroviral therapy today. Moreover, the PIs prescribed in this study are likely to differ from those used today in clinical practice.

Conversely, the statistical approach adopted to correct for the bias induced by missing data allowed us to use the entire original cohort population. All patients with at least 12 months of clinical follow-up were included. In addition, this method enabled us to demonstrate the presence of a significant bias due to missing data in the analysis of the factors associated with nonadherence. Adjustment or correction for this bias resulted in a different pattern of predictors for nonadherence. This study is, to our knowledge, the first application of the Heckman approach to longitudinal sociobehavioral data. Further methodologic work is needed to overcome some of the method s limitations. Specifically, more consistent standard errors of the model s parameter estimates are necessary, and it would be extremely useful to unravel the bias due to missed clinical visits from that due to nonresponse to the self-administered questionnaires. Even if we cannot disentangle the influence of dropped clinical visits from that of nonresponse to adherence questionnaires on parameter estimates in the model, the method adopted, however, allows us correct for the overall bias due to the aggregated missing data.

We also note that this study shares with others some of the general methodologic problems related to data based on patients self-reports, which may be affected by social desirability and recall bias.43 Various studies of HAART-treated patients show that self-reports tend to estimate adherence as slightly higher than alternative methods of measurement (such as unannounced pill counts and electronic medication monitors).44,45 Nevertheless, most of these studies have also confirmed that self-reports are reasonably reliable and that self-reports of nonadherence correlate well with undetectable plasma PI levels.46-48

The study shows that reasons for nonadherence in the maintenance phase are multifactorial. Only 2 of these sets of factors are amenable to public health interventions: firstly, depression should be recognized and treated in a timely way; secondly, self-reported side effects need to be taken into account both in day-to-day care and in clinical research by recording them for effective comparison of different treatment options. A multidisciplinary approach involving psychosocial interventions and identification of better-tolerated regimens is needed to improve the long-term adherence of HIV-infected patients to their life-long treatment.

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APPENDIX A

It is known that misleading results (inconsistent estimates) can be obtained in longitudinal studies under the MNAR hypothesis when the occurrence of missing data is not taken into account. This appendix describes the Heckman15,27 2-step method used to control for the bias entailed by missing outcome data.

Let us define patient adherence as:

Equation (Uncited)
Equation (Uncited)
Image Tools

and the nonmissingness index variable as:

Equation (Uncited)
Equation (Uncited)
Image Tools

The 2-step estimation procedure can be described as follows. The first stage is based on estimating the probability of nonmissing data in the outcome variable with a probit model and taking all possible scheduled visits into account. The model is specified by the following selection equation:

Equation (Uncited)
Equation (Uncited)
Image Tools

where Wit is the covariate matrix and γit is the error term.

The predicted probabilities derived from the previous model are used to compute the IMR) λit (the IMR can also be computed using residuals instead of predicted probabilities):

Equation (Uncited)
Equation (Uncited)
Image Tools

where φ is the standard normal density and Φ is the cumulative standard normal distribution function. In other words, the IMR variable represents the response hazard rate: it measures the probability of nonmissing adherence data for ith individual at time t given that he or she was "at risk" (still in the cohort at time t).

The second-stage equation corresponds to estimating the probability of nonadherence through a probit link function, where only the visits corresponding to an observed Ait are used:

Equation (Uncited)
Equation (Uncited)
Image Tools

where Xit is the matrix of observed explanatory variables.

The error term of the second equation is supposed to be related to the error term of the first equation such that cov(γit, &epsiv;it′) = 0, for tt′. Both models in stages I and II were estimated by GEE with unstructured within-subject covariance matrix to account for correlated responses within individuals.

Note that identification issues require that the first-stage selection equation include at least 1 covariable that is not a part of the matrix Xit. If the same set of variables would be used in both equations, the IMR would simply be a nonlinear function of Xit. In this case, IMR would be extremely colinear with the linear function βXit in the rest of the equation (it would be perfectly colinear if IMR were a linear function of Xit, but the nonlinearity attenuates this colinearity). Including in the selection equation variables that are not correlated with outcome level allows us to improve the precision of Heckman parameter estimates and to overcome the usual problem caused by multicolinearity (high standard errors).

Using the truncated normal distribution theory, we can'show that the following conditional mean function is given by:

Equation (Uncited)
Equation (Uncited)
Image Tools

Consequently, we can see that there is a problem of missingness bias whenever the final term is not zero, ie, when the errors in the equation of interest and the selection equation are correlated: cov(γit, &epsiv;it) ≠ 0. Entering the IMR variable as an additional regressor in the second-stage equation allows us to correct for potential bias due to missing data: the IMR term incorporates the effect of unobserved factors that can affect both the missingness process and the outcome, as its computation is based on the residuals (or the predicted values) of the first-stage model (see IMR definition).

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APPENDIX B

The APROCO-COPILOTE Study Group is composed of the following:

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Steering Committee

Principal Investigators: C. Leport, F. Raffi

Methodology: G. Chêne, R. Salamon

Social Sciences: J-P. Moatti, J. Pierret, B. Spire

Virology: F. Brun-Vézinet, H. Fleury, B. Masquelier

Pharmacology: G. Peytavin, R. Garraffo

Scientific Committee: members of Steering Committee, and other members: D. Costagliola, P. Dellamonica, C.'Katlama, L. Meyer, M. Morin, D. Salmon, A. Sobel

Project Coordination: F. Collin

Events Validation Committee: L. Cuzin, M. Dupon, X. Duval, V. Le Moing, B. Marchou, T. May, P. Morlat, C. Rabaud, A. Waldner-Combernoux

Clinical Research Group: V. Le Moing, C. Lewden

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Data Monitoring and Statistical Analysis

C. Alfaro, F. Alkaied, C. Barennes, S. Boucherit, A.D. Bouhnik, C. Brunet-François, M.P. Carrieri, J.L. Ecobichon, V. El Fouikar, V. Journot, R. Lassalle, J.P. Legrand, M. François, E. Pereira, M. Préau, V. Villes, C. Protopopescu, H. Zouari

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Promotion

Agence Nationale de Recherches sur le Sida (ANRS, Coordinating Action n° 7).

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Keywords:

HIV; adherence; missing data; selection models; cohort; Highly Active Antiretroviral Treatment

© 2006 Lippincott Williams & Wilkins, Inc.

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