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Evaluating dose response from flexible dose clinical trials.

Lipkovich I, Adams DH, Mallinckrodt C, Faries D, Baron D, Houston JP - BMC Psychiatry (2008)

Bottom Line: Dose profiles for mean changes from baseline were evaluated using weighted MSM with a repeated measures model.To adjust for selection bias due to non-random dose assignment and dropouts, patient-specific time-dependent weights were determined as products of (i) stable weights based on inverse probability of receiving the sequence of dose assignments that was actually received by a patient up to given time multiplied by (ii) stable weights based on inverse probability of patient remaining on treatment by that time.Results were compared with those by unweighted analyses.

View Article: PubMed Central - HTML - PubMed

Affiliation: Lilly Research Laboratories, Eli Lilly and Company, Indianapolis Indiana, USA. lipkovichia@lilly.com

ABSTRACT

Background: The true dose effect in flexible-dose clinical trials may be obscured and even reversed because dose and outcome are related.

Methods: To evaluate dose effect in response on primary efficacy scales from 2 randomized, double-blind, flexible-dose trials of patients with bipolar mania who received olanzapine (N = 234, 5-20 mg/day), or patients with schizophrenia who received olanzapine (N = 172, 10-20 mg/day), we used marginal structural models, inverse probability of treatment weighting (MSM, IPTW) methodology. Dose profiles for mean changes from baseline were evaluated using weighted MSM with a repeated measures model. To adjust for selection bias due to non-random dose assignment and dropouts, patient-specific time-dependent weights were determined as products of (i) stable weights based on inverse probability of receiving the sequence of dose assignments that was actually received by a patient up to given time multiplied by (ii) stable weights based on inverse probability of patient remaining on treatment by that time. Results were compared with those by unweighted analyses.

Results: While the observed difference in efficacy scores for dose groups for the unweighted analysis strongly favored lower doses, the weighted analyses showed no strong dose effects and, in some cases, reversed the apparent "negative dose effect."

Conclusion: While naïve comparison of groups by last or modal dose in a flexible-dose trial may result in severely biased efficacy analyses, the MSM with IPTW estimators approach may be a valuable method of removing these biases and evaluating potential dose effect, which may prove useful for planning confirmatory trials.

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Marginal structural model with IPTW. A. Cumulative potential dose effect profiles by dose groups for Study A (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated from marginal structural model with IPTW for reduction in the Young Mania Rating Scale (YMRS) total score in patients with bipolar disorder. Olanzapine (Olz): For 20 vs. 5–10 mg, overall dose effect NS; significant negative dose effect (p < .05) at Weeks 4, 7, 8, 10. B. Cumulative potential dose effect profiles by dose groups for Study B (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated by marginal structural model with IPTW for reduction in the Positive and Negative Syndrome Scale (PANSS) total score in patients with schizophrenia. Olanzapine (Olz): no significant overall dose effect; significant negative dose effect (p < .05) at Weeks 20, 24.
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Figure 1: Marginal structural model with IPTW. A. Cumulative potential dose effect profiles by dose groups for Study A (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated from marginal structural model with IPTW for reduction in the Young Mania Rating Scale (YMRS) total score in patients with bipolar disorder. Olanzapine (Olz): For 20 vs. 5–10 mg, overall dose effect NS; significant negative dose effect (p < .05) at Weeks 4, 7, 8, 10. B. Cumulative potential dose effect profiles by dose groups for Study B (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated by marginal structural model with IPTW for reduction in the Positive and Negative Syndrome Scale (PANSS) total score in patients with schizophrenia. Olanzapine (Olz): no significant overall dose effect; significant negative dose effect (p < .05) at Weeks 20, 24.

Mentions: Assuming that (i) all relevant time-dependent confounders were correctly accounted for in estimating probabilities for dose assignments and for patient discontinuation, and that (ii) the MSM model was correctly specified, the evaluation of dose-response relationship from MSM allows for causal interpretation [3]. Using expression (1) we can estimate the potential outcomes over time (dose profiles) for any given pre-specified dose sequence and baseline severity (Y0). For example, if we are interested in estimating causal effect (by time t) of continuously receiving high versus low dose by an average patient all we need to do is to (i) evaluate the expected outcomes under high dose by plugging dose = 3 (the code for high level) in all terms involving dose in equation (1), including the interaction terms if present; (ii) then do the same for dose = 1 (low), and subtract one outcome from the other. Assuming (for simplicity) that there are no interaction terms, the causal dose effect would be constant over time and simply equal to the sum of estimated coefficients γ1(3) + γ2(3) + γ3(3) + γ4(3), as all other terms not involving dose will cancel out. If any dose by time interaction terms are present, dose effect would change over time. The significance of any such causal effect can then be easily evaluated by testing a hypothesis that the sum of the parameters as shown above is different from zero. The expected potential outcomes for a hypothetical patient at specific level of baseline severity who would have been continuously assigned the same dose (d) throughout the study can be estimated (and associated 95% confidence intervals and p-values can be obtained) from the output of proc GENMOD by performing inference on linear predictors at specific values of predictor variables (e.g. by creating a data set with such hypothetical records of subjects whose baseline covariates are fixed at their mean levels and the current and all previous doses fixed at level d and passing it to GENMOD for evaluation). To account for the correlation in repeated measures and the fact that the subject weights depend on previous data points we used robust conservative estimates of standard errors. Examples of such estimated potential outcomes are given in Figure 1.


Evaluating dose response from flexible dose clinical trials.

Lipkovich I, Adams DH, Mallinckrodt C, Faries D, Baron D, Houston JP - BMC Psychiatry (2008)

Marginal structural model with IPTW. A. Cumulative potential dose effect profiles by dose groups for Study A (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated from marginal structural model with IPTW for reduction in the Young Mania Rating Scale (YMRS) total score in patients with bipolar disorder. Olanzapine (Olz): For 20 vs. 5–10 mg, overall dose effect NS; significant negative dose effect (p < .05) at Weeks 4, 7, 8, 10. B. Cumulative potential dose effect profiles by dose groups for Study B (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated by marginal structural model with IPTW for reduction in the Positive and Negative Syndrome Scale (PANSS) total score in patients with schizophrenia. Olanzapine (Olz): no significant overall dose effect; significant negative dose effect (p < .05) at Weeks 20, 24.
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Figure 1: Marginal structural model with IPTW. A. Cumulative potential dose effect profiles by dose groups for Study A (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated from marginal structural model with IPTW for reduction in the Young Mania Rating Scale (YMRS) total score in patients with bipolar disorder. Olanzapine (Olz): For 20 vs. 5–10 mg, overall dose effect NS; significant negative dose effect (p < .05) at Weeks 4, 7, 8, 10. B. Cumulative potential dose effect profiles by dose groups for Study B (each dose profile is estimated from MSM model for a hypothetical patient of average baseline severity who would have continuously received the same dose throughout the study); estimated by marginal structural model with IPTW for reduction in the Positive and Negative Syndrome Scale (PANSS) total score in patients with schizophrenia. Olanzapine (Olz): no significant overall dose effect; significant negative dose effect (p < .05) at Weeks 20, 24.
Mentions: Assuming that (i) all relevant time-dependent confounders were correctly accounted for in estimating probabilities for dose assignments and for patient discontinuation, and that (ii) the MSM model was correctly specified, the evaluation of dose-response relationship from MSM allows for causal interpretation [3]. Using expression (1) we can estimate the potential outcomes over time (dose profiles) for any given pre-specified dose sequence and baseline severity (Y0). For example, if we are interested in estimating causal effect (by time t) of continuously receiving high versus low dose by an average patient all we need to do is to (i) evaluate the expected outcomes under high dose by plugging dose = 3 (the code for high level) in all terms involving dose in equation (1), including the interaction terms if present; (ii) then do the same for dose = 1 (low), and subtract one outcome from the other. Assuming (for simplicity) that there are no interaction terms, the causal dose effect would be constant over time and simply equal to the sum of estimated coefficients γ1(3) + γ2(3) + γ3(3) + γ4(3), as all other terms not involving dose will cancel out. If any dose by time interaction terms are present, dose effect would change over time. The significance of any such causal effect can then be easily evaluated by testing a hypothesis that the sum of the parameters as shown above is different from zero. The expected potential outcomes for a hypothetical patient at specific level of baseline severity who would have been continuously assigned the same dose (d) throughout the study can be estimated (and associated 95% confidence intervals and p-values can be obtained) from the output of proc GENMOD by performing inference on linear predictors at specific values of predictor variables (e.g. by creating a data set with such hypothetical records of subjects whose baseline covariates are fixed at their mean levels and the current and all previous doses fixed at level d and passing it to GENMOD for evaluation). To account for the correlation in repeated measures and the fact that the subject weights depend on previous data points we used robust conservative estimates of standard errors. Examples of such estimated potential outcomes are given in Figure 1.

Bottom Line: Dose profiles for mean changes from baseline were evaluated using weighted MSM with a repeated measures model.To adjust for selection bias due to non-random dose assignment and dropouts, patient-specific time-dependent weights were determined as products of (i) stable weights based on inverse probability of receiving the sequence of dose assignments that was actually received by a patient up to given time multiplied by (ii) stable weights based on inverse probability of patient remaining on treatment by that time.Results were compared with those by unweighted analyses.

View Article: PubMed Central - HTML - PubMed

Affiliation: Lilly Research Laboratories, Eli Lilly and Company, Indianapolis Indiana, USA. lipkovichia@lilly.com

ABSTRACT

Background: The true dose effect in flexible-dose clinical trials may be obscured and even reversed because dose and outcome are related.

Methods: To evaluate dose effect in response on primary efficacy scales from 2 randomized, double-blind, flexible-dose trials of patients with bipolar mania who received olanzapine (N = 234, 5-20 mg/day), or patients with schizophrenia who received olanzapine (N = 172, 10-20 mg/day), we used marginal structural models, inverse probability of treatment weighting (MSM, IPTW) methodology. Dose profiles for mean changes from baseline were evaluated using weighted MSM with a repeated measures model. To adjust for selection bias due to non-random dose assignment and dropouts, patient-specific time-dependent weights were determined as products of (i) stable weights based on inverse probability of receiving the sequence of dose assignments that was actually received by a patient up to given time multiplied by (ii) stable weights based on inverse probability of patient remaining on treatment by that time. Results were compared with those by unweighted analyses.

Results: While the observed difference in efficacy scores for dose groups for the unweighted analysis strongly favored lower doses, the weighted analyses showed no strong dose effects and, in some cases, reversed the apparent "negative dose effect."

Conclusion: While naïve comparison of groups by last or modal dose in a flexible-dose trial may result in severely biased efficacy analyses, the MSM with IPTW estimators approach may be a valuable method of removing these biases and evaluating potential dose effect, which may prove useful for planning confirmatory trials.

Show MeSH
Related in: MedlinePlus