Handling missing quality of life data in HIV clinical trials: what is practical?

Abstract

Aims

Missing health-related quality of life (HRQOL) data in clinical trials can impact conclusions but the effect has not been thoroughly studied in HIV clinical trials. Despite repeated recommendations to avoid complete case (CC) analysis and last observation carried forward (LOCF), these approaches are commonly used to handle missing data. The goal of this investigation is to describe the use of different analytic methods under assumptions of missing completely at random (MCAR), missing at random (MAR), and missing not at random (MNAR) using HIV as an empirical example.

Methods

Medical Outcomes Study HIV (MOS-HIV) Health Survey data were combined from two large open-label multinational HIV clinical trials comparing treatments A and B over 48 weeks. Inclusion in the HRQOL analysis required completion of the MOS-HIV at baseline and at least one follow-up visit (weeks 8, 16, 24, 40, 48). Primary outcomes for the analysis were change from week 0 to 48 in mental health summary (MHS), physical health summary (PHS), pain and health distress scores analyzed using CC, LOCF, generalized estimating equations (GEE), direct likelihood and sensitivity analyses using joint mixed-effects model, and Markov chain Monte Carlo (MCMC) multiple imputation. Time and treatment were included in all models. Baseline and longitudinal variables (adverse event and reason for discontinuation) were only used in the imputation model.

Results

A total of 511 patients randomized to treatment A and 473 to treatment B completed the MOS-HIV at baseline and at least one follow-up visit. At week 48, 71% of patients on treatment A and 31% on treatment B completed the MOS-HIV survey. Examining changes within each treatment group, CC and MCMC generally produced the largest or most positive changes. The joint model was most conservative; direct likelihood and GEE produced intermediate results; LOCF showed no consistent trend. There was greater spread for within-group changes than between-group differences (within MHS scores for treatment A: −0.1 to 1.6, treatment B: 0.4 to 2.0; between groups: −0.7 to 0.4; within PHS scores for treatment A: −1.5 to 0.4, treatment B: −1.7 to −0.2; between groups: 0.1 to 1.1). The size of within-group changes and between-group differences was of similar magnitude for the pain and health distress scores. In all cases, the range of estimates was small <0.2 SD (less than 2 points for the summary scores and 5 points for the subscale scores).

Conclusions

Use of the recommended likelihood-based models that do not require assumptions of MCAR was very feasible. Sensitivity analyses using auxiliary information can help to investigate the potential effect that missing data have on results but require planning to ensure that relevant data are prospectively collected.

Appendix

• Endpoint models: Last change score:

  $$ (Y_{{{\text{ij}}}} - Y_{{{\text{i0}}}} ) = \beta _{0} + \beta _{1} TRT + \varepsilon _{{\text{i}}} $$

  where $\varepsilon_{{\text{i}}} \,\sim\, N (0,\sigma ^{2} )$ Y _i0 is the baseline score and Y _ij is the 48-week or last observed score for the ith patient.

  TRT = 1 if treatment A, 0 otherwise.

• Repeated measures models: Repeated change scores:

  $$ (Y_{{{\text{ij}}}} - Y_{{i0}} ) = \beta _{{{\text{0j}}}} + \beta _{{{\text{1j}}}} TRT + \varepsilon _{{{\text{ij}}}} , $$

  where $\varepsilon _{{{\text{ij}}}} \,\sim\,{}N(0,\Upsigma )$

  Y _i0 is the baseline score and Y _ij is the observed score at the j = 8, 16, 24, 40, and 48 week assessment for the ith patient.

  TRT = 1 if treatment A, 0 otherwise.

• Growth curve models (piecewise linear models with knots at 8 and 16 weeks): Scores:

  $$ Y_{{{\text{ij}}}} = \beta _{0} + \beta _{1} WEEK_{{{\text{ij}}}} + \beta _{2} WEEK_{{{\text{ij}}}} ^{ * } TRT + \beta _{3} WEEK8_{{{\text{ij}}}} + \beta _{4} WEEK8_{{{\text{ij}}}} ^{ * } TRT + \beta _{5} WEEK16_{{{\text{ij}}}} + \beta _{6} WEEK16_{{{\text{ij}}}} ^{ * } TRT + \varepsilon _{{{\text{ij}}}} $$

  where ε _ij ∼ N(0, Z _ij DZ _ij + σ ² I), Z_ij = (1 WEEK_ij) and D is the variance of the random effects.

  Y _ij is the observed score at the j = 8, 16, 24, 40, and 48 week assessment for the ith patient.

  WEEK_ij is time from randomization to the jth MOS-HIV assessment

  WEEK8_ij = max(WEEK_ij − 8, 0); WEEK16_ij = max(WEEK_ij − 16, 0);

  TRT = 1 if treatment A, 0 otherwise.

• Joint model:

  $$ \begin{array}{*{20}c} {{Y_{{{\text{ij}}}} = X_{{{\text{ij}}}} \beta + Z_{{{\text{ij}}}} d_{{\text{i}}} + \varepsilon _{{{\text{ij}}}} }} \\ {{T_{{\text{i}}} = M_{{\text{i}}} \mu + r_{{\text{i}}} }} \\ \end{array} ,{\left[ {\begin{array}{*{20}c} {{d_{{\text{i}}} }} \\ {{r_{{\text{i}}} }} \\ {{\varepsilon _{{{\text{ij}}}} }} \\ \end{array} } \right]} \approx N{\left[ {{\left( {\begin{array}{*{20}c} {0} \\ {0} \\ {0} \\ \end{array} } \right)},{\left( {\begin{array}{*{20}c} {D} & {{\sigma ^{'}_{{{\text{dt}}}} }} & {0} \\ {{\sigma _{{{\text{dt}}}} }} & {{\sigma ^{2}_{{\text{t}}} }} & {0} \\ {0} & {0} & {{\sigma ^{2}_{{\text{e}}} }} \\ \end{array} } \right)}} \right]} $$

  where T _i is the log time to the last MOS-HIV assessment.