Study Population and Definitions

We conducted a retrospective observational cohort study among persons treated at the Comprehensive Care Center, an outpatient clinic in Nashville, TN. The study population included all patients who established care and had at least 2 provider visits from 1998 to 2007. Eligible individuals were those with no prior antiretroviral use at the Center who had at least one CD4 measurement in the range 200–749 before experiencing an AIDS-defining event or initiating HAART. Study entry was the date of the first CD4 level between 200–749. Follow-up ended at death, 31 December 2007, or the last clinic visit for persons lost to follow-up. During the study period, healthcare coverage was available to virtually all HIV-infected Tennesseans.^{13}

AIDS-defining events were based on U.S. Centers for Disease Control and Prevention classification criteria, excluding CD4<200 cells/mm

^{3}.

^{14} Non-AIDS events were based on recommendations of an endpoints committee comprised of infectious disease clinicians. Examples include acute myocardial infarction and cirrhosis of liver; a complete list of non-AIDS events considered for this study is found in the

eAppendix (

http://links.lww.com). Subjects were considered lost to follow-up if they had no clinic encounter for more than a year before date of death or 31 December 2007, whichever came first. The precision of all measurements involving time is in units of days. HAART was defined as any regimen containing 3 or more active antiretroviral therapy agents.

^{3} The study was approved by the Vanderbilt University Medical Center Institutional Review Board.

Statistical Methods

Given a set of candidate rules, “start HAART within 3 months of first CD4 measured below *x*,” where *x* = 201,202,…,750, we sought to estimate which value of *x* would result in the best expected patient health *k* months after study entry. To address this question, we followed the methodology of Robins et al.^{8} This methodology requires specifying a measurement of patient health at *k* months (the outcome variable), and the treatment rules, *x*, that are compatible with each patient’s CD4 and HAART initiation history (the explanatory variable). We considered *k* = 6, 12, 24, and 36 months and employed inverse probability weights to account for potential bias due to non-random assignment of treatment rules and patient drop-out.

Outcome Variables

Our analyses required specifying a metric of each patient’s health at time *k* months. This outcome, *y*, is termed a “utility” or “health metric” and in our analysis was a function of death, AIDS-defining events, non-AIDS-defining events, and CD4 if asymptomatic. The utility was an arbitrary but reasoned quantity; in our analyses we used the following utilities:

- CD4 count-based:
*y* = most recent CD4 at or before month *k* if patient alive and asymptomatic at month *k*, *y* = 100 if subject had an AIDS or non-AIDS event by month *k* but was not deceased, *y* = 100×(*t*−12−*k*)/18 if subject was deceased before month *k* where *t* = months to death (see ). - Quality of life: Based on a validated quality-of-life scale incorporating death, type of AIDS or non-AIDS event, and CD4 at month
*k* (see and eAppendix [http://links.lww.com] for formula).^{15} In this utility death was assigned *y* = 0, AIDS or non-AIDS events were assigned *y* between 0.56 and 0.65 depending on the specific type of event, and asymptomatic patients were assigned *y* between 0.78 and 0.95 depending on their most recent CD4 at or before month *k*.

For both utilities, a low value of *y* corresponded to a poor outcome. Utility 1 was elicited a priori from consultations with the Vanderbilt-Meharry Center for AIDS Research Epidemiology/Outcomes group. This utility was based on CD4 count and assigned a patient with an AIDS or non-AIDS event by month *k* the same utility as an asymptomatic patient with CD4=100; individuals who died were assigned negative utility scores, with those who died earliest given larger negative values. Utility 2 also incorporated death, AIDS and non-AIDS events, and CD4, but was based on a published quality-of-life scale^{15} and used type of first AIDS event. In both utilities, if a patient had either type of event and subsequently died before time *k*, then the death was recorded. If both AIDS and non-AIDS events occurred, the earlier took precedence.

Regimen Rules

Following Robins et al,^{8} consider a multi-armed trial where each patient is randomly assigned a value of *x* between 201 and 750, and then asked to follow the rule “start HAART within 3 months of first CD4 measurement below *x*.” In such a trial, suppose a patient was assigned the rule with *x* = 400. If this patient’s first CD4 measurement below (but not equal to) 400 was 350, and if he started HAART within 3 months of this measurement, then this patient was adherent to his assigned rule. Notice that although this patient was randomized to the rule “start HAART within 3 months of the first CD4 measured below 400,” his CD4/treatment history was also consistent with the rules “start HAART within 3 months of the first CD4 measured below 399, 398,…, 351.” In contrast, if this patient had not started HAART within 3 months of his CD4 measurement of 350 or had started HAART before his CD4 was measured below 400, he would have been non-adherent to his assigned rule.

Using this model, we examined each patient’s CD4 and HAART initiation history and determined compatible rules for each patient. It should be noted that for the purpose of computing rules, follow-up stopped at the earliest of date of HAART initiation, first AIDS event, last visit, death, or *k* months.

contains some hypothetical examples matching treatment histories to regimen rules. Consider Patient A: his first CD4 measurement was 400, his next was 350 at month 3, and he then started HAART in month 4. This patient’s data were compatible with the rules “start HAART within 3 months of first CD4 measured below *x* = 351,…,400.” Had this patient been assigned the rule with *x* = 400, he would have been compliant because the first CD4 measured below (but not equal to) 400 was 350, and he started HAART one month after this observation. However, this patient’s data were not compatible with the rule “start HAART within 3 months of first CD4 measured below *x* = 401,” because his first CD4 measurement below 401 (CD4 = 400 at month 0) was taken more than 3 months before he started HAART. Similarly, this patient’s data were not compatible with the rule “start HAART within 3 months of first CD4 measured below *x* = 350” because he started HAART without ever having a CD4 measured below 350.

| **Table 1**Assigning regimen rules compatible with patients’ data; some examples when *k* = 6 months. |

Patients whose data were not compatible with any regimen rule were artificially censored at the date their data became incompatible. For example, Patient B did not start HAART within 3 months of CD4=250, but then started HAART in month 4, one month after CD4=300. Therefore, his data were not consistent with any *x*, and he was artificially censored when he started HAART. Patient C’s data were also inconsistent with all rules as he started HAART more than 3 months after his last CD4 measurement. Patient D failed to start HAART within 3 months of his first CD4 below 201, so his data were not consistent with any rule and he was artificially censored 3 months after his first CD4 below 201. In contrast, Patient E was consistent with *x*=201,…,350.

It should be noted that regimen rules were based on measured rather than actual CD4. For example, Patient F started HAART within 3 months of his first CD4 measured below 750 although it is likely that his CD4 dropped below 750 cells more than 3 months before initiating HAART, but was not observed. Patient G’s history is similar to Patient F’s with the additional CD4 measurement of 250 taken at month 1. Although this measurement may have prompted the initiation of HAART, Patient G also started HAART within 3 months of his first CD4 measured below 750. Similarly, patient H was assigned all rules

*x* = 201,…,750. Patient I was also assigned all treatment rules as the study ended less than 3 months before his first CD4 measurement and it is therefore unclear whether he was deferring treatment until a lower CD4 or preparing to start. Finally, Patients J, K, and L never started HAART, but were consistent with the rules “start HAART within 3 months of the first CD4 measured below

*x* = 201,…,250”—Patient J because he never had a CD4 measurement below 250 and Patients K and L because their next measurements were less than 3 months before

*k* = 6. The complete algorithm used for determining compatible rules is given in the

eAppendix (

http://links.lww.com).

Weighted Regression Models

To find the rule for starting HAART that maximized health at k months, we regressed

*y* on

*x* and found the value of

*x* that achieved the maximum predicted value of

*y*. Each individual contributed as many values of (

*x*,

*y*) as the number of rules compatible with their data. For example, a person who had data compatible with starting HAART within 3 months of their first CD4 below

*x* = 201,…,250 contributed 50 data points (

*x*,

*y*) to the analysis: (201,

*y*), (202,

*y*),…, (250,

*y*); their outcome

*y* was the same for all

*x*. We fit a curve to the (

*x*,

*y*) pairs of all eligible patients using weighted least squares regression, with

*x* expanded using restricted cubic splines to allow the relationship between

*x* and

*y* to be non-linear. Our splines used 6 knots, at default positions of the Design package

^{16} of R statistical software version 2.8.1 (

http://www.r-project.org).

Inverse Probability Weights

Persons whose data were compatible with a given rule may have had characteristics different from those whose data were compatible with other rules. To address this potential source of bias, we employed inverse probability weighting methods in the manner described by Cain et al.^{17} Briefly, for months 0,1,…, *k*, we estimated the probability of initiating HAART using logistic regression and the covariates age, sex, race, injection drug use as HIV risk factor, most recent CD4, CD4%, and HIV-1 RNA, time since most recent laboratory measurements, and time in care. Months were included in the model using restricted cubic splines. For each compatible treatment rule *x* per person, we then computed the predicted probability of remaining compatible with *x* for each month of follow-up. Based on CD4 history, if a patient could not be artificially censored from a particular rule *x* at a given month, then the probability of remaining compatible with *x* for that patient in that month was 1, otherwise it was one minus the probability of initiating HAART. Weights were computed as the product of the inverse of these probabilities over the *k* months of follow-up.

Some patients’ health at time *k* months was unknown, due either to loss to follow-up or end-of-study censoring. Separate stabilized inverse-probability weights to address loss to follow-up and end-of-study censoring were computed. Our final weights were the product of the multiple inverse-probability weights. In order to reduce variability, the product of the weights was truncated at the 2.5th and 97.5th percentiles.^{18}