A flexible analytical framework for reference-based imputation, delta adjustment and tipping-point stress-testing

This paper addresses the challenge of implementing the treatment policy strategy when subjects are not followed up after treatment discontinuation. This problem can be addressed using reference-based imputation, delta adjustment, and tipping-point analysis. Our new framework tackles this problem analytically. We characterize the process that measures the response regardless of drug discontinuation, Z(t), using its association with two observable processes: time to drug dropout (T*), and the variable representing the response in a hypothetical world without drug discontinuation Y(t). We define the intervention discontinuation effect (IDE) as the unobservable process that quantifies the difference between Y(t) and Z(t) after T*. We express various well-known imputation rules as forms of the IDE. We model Y using mixed models and T* with the Royston-Parmar model. We build estimators for the marginal mean of Z given the estimated parameters for Y and T*. We demonstrate that this simple estimator building suits all studied rules and provide guidance to extend this methodology. With the proposed framework, we can analytically resolve a broad range of imputation rules and have right-censored treatment discontinuation. This methodology is more efficient and computationally faster than multiple imputation and, unlike Rubin’s variance estimator, presents no standard error over-estimation.</p

Random effects model fit to the natural anti-RhD titer decline of donors in the absence of boostering.

<p>A jitter of 1.75 was applied to the titer change measurements to enhance interpretability of the data. For individual fits, the line ends at a donor’s maximum time of measurement. Note that for 5% of donors a small positive annual change is modelled due to measurement errors and since it is not possible to restrict the model to negative values.</p

Predicting anti-RhD titers in donors: Boostering response and decline rates are personal

<div><p>Background</p><p>Anti-RhD immunised donors provide anti-RhD immunoglobulins used for the prevention of rhesus disease. These donors are periodically hyper-immunised (boostered) to retain a high titer level of anti-RhD.</p><p>Study design and methods</p><p>We analysed anti-RhD donor records from 1998 to 2016, consisting of 30,116 anti-RhD titers from 755 donors, encompassing 3,372 booster events. Various models were fit to these data to allow describing the anti-RhD titers over time.</p><p>Results</p><p>A random effects model with a log-linear anti-RhD titer decline over time and a saturating titer response to boostering is shown to fit the data well. This model contains two general model parameters, relating timing and maximum of the booster effect, as well as two parameters characterizing the individual donor, namely how fast the booster effect saturates with current titer and the anti-RhD decline rate. The average individual log₂ decline is 0.55 per year, i.e. a 32% decline in absolute titer, with half of the donors declining between 13% and 41% per year. Their anti-RhD titer peaks around 26 days following a booster event. Boostering response reduces with higher titers at boostering; at median titer (log₂ 11) the mean increase per booster is log₂ 0.38, that is from an absolute titer of 2048 to 2665 (+30%), with half of all donors increasing between 16% and 65% in their titer.</p><p>Conclusion</p><p>The model describes anti-RhD titer change per individual with only four parameters, two of which are donor specific. This information can be used to enhance the blood bank’s immunisation programme, by deriving individualized immunization policies in which boostering is adjusted to the anticipated anti-RhD decline, effectiveness of boostering and titer levels required.</p></div

Four examples of model fits to individual donor titers observed over time.

<p><b>(</b>See <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0196382#pone.0196382.s006" target="_blank">S5 Fig</a> for the model fits for all individual donors).</p

Peak in anti-RhD titer gain after boostering.

<p>A jitter of 1.95 was applied on the measurements of both titer change and titer at boostering to enhance interpretability of the data. Individuals were not boostered in the 50 days preceding the booster of interest. Black circles denote the approximate peak in increase assumed at 26–50 days from boostering (see Step 2A results), when a donor was boostered only once. Blue crosses denote this increase when one or more boosters were given subsequent to the booster of interest. Our best model fit to all these data-points together (shown for <i>t</i> = 26) hence represents an overestimate of the titer gain from boostering once. Also shown is the fit dependence from our final model (see Step 3 in the main text, shown for an average individual and also for 26 days from boostering).</p

Sum Score during pregnancy and post partum ^a.

<p>^a The repeated measures analysis has been performed using linear mixed effects models. Data are presented in mean and 95% Confidence Interval. Abbreviations: pp, post partum, HELLP, Hemolysis Elevated Liver enzymes Low Platelets.</p

EEG Sum Score ^a.

<p>^a EEG Sum Score is the sum of items 1 to 6, ranging 0–17 points.</p

Alpha Peak Frequency during pregnancy and post partum ^a.

<p>^a The repeated measures analysis has been performed using linear mixed effects models. Data are presented in mean and 95% Confidence Interval. Abbreviations: Hz, Hertz; pp, post partum, HELLP, Hemolysis Elevated Liver enzymes Low Platelets.</p

Course of Alpha Peak Frequency in a patient who developed Severe Preeclampsia ^a,b,c.

<p>^a Data of patient is presented in red dots. ^b Black line and dotted lines are data of Severe Preeclampsia + HELLP, as presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0155299#pone.0155299.g002" target="_blank">Fig 2</a>. ^c Blue line and dotted lines are data of Normotensive women, as presented in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0155299#pone.0155299.g002" target="_blank">Fig 2</a>. ^d Red line: patient developed Severe Preeclampsia. Abbreviations: Hz, Hertz; pp, post partum; HELLP, Hemolysis Elevated Liver Enzymes Low Platelets.</p

Additional file 1: Table S1. of Cost-effectiveness of enzyme replacement therapy with alglucosidase alfa in adult patients with Pompe disease

Survival: Cox regression estimates. Table S2. Quality of life: regresssion estimates conceptual disease model. Table S3. Costs: regression estimates healthcare costs and productivity costs and input cost parameters. Figure S1. Double loop model structure. (PDF 394 kb