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Table 1 Description of the estimation methods used for dealing with treatment nonadherence in pragmatic trials with point-treatment settings

From: Analysis approaches to address treatment nonadherence in pragmatic trials with point-treatment settings: a simulation study

Name of the method

Description

Naïve methods

 

ITT

It models the randomization variable (Z) on the outcome (Y) without adjustment for measured confounders L. This method does not consider whether individuals adhered to the treatment [6].

Naïve PP

It models Z on Y among those subjects who receive the treatment according to the protocol but without adjustment for L. This method excludes those subjects who deviated from the protocol.

Naïve AT

It models the treatment actually received (A) on Y without adjustment for L. This method does not consider whether individuals randomized to the treatment groups.

Adjusted methods

 

Baseline-adjusted ITT

The same as ITT but it adjusts for L.

Baseline-adjusted PP

The same as naïve PP but it adjusts for L.

IP-weighted PP

This method creates inverse probability adherence weights to generate a pseudo population to estimate the treatment effect by removing the effect of nonadherence [25]. We used a logistic model that adjusts for L to estimate the probabilities, and then used the marginal structural model to estimate the parameters of interest. The stabilized weights were used to prevent from extreme weights [7, 30].

IV-methods

 

Naïve 2SLS

The instrument (Z) is modelled to the treatment (A) in the first stage, and then the predicted treatment is modelled to the outcome (Y) in the second stage [31]. There was no adjustment for L in either stage of the model.

First-stage adjusted 2SLS

The same as naive 2SLS except it adjusts for L in the first stage of the model [28, 29].

Both-stages adjusted 2SLS

The same as naive 2SLS except it adjusts for L in both stages of the model.

Naïve 2SRI

The instrument (Z) is modelled to the treatment variable (A) in the first stage, and then the residuals from the first stage and the treatment variable are modelled to the outcome (Y) in the second stage [22]. There was no adjustment for L in either stage of the model.

First-stage adjusted 2SRI

The same as naive 2SRI except it adjusts for L in the first stage of the model [29].

Both-stages adjusted 2SRI

The same as naive 2SRI except it adjusts for L in both stages of the model [22].

NPCB

This nonparametric method uses a constrained probability statement to provide bounds on the estimated treatment effect rather than a point estimate [18, 19].

  1. Note: The 2SLS, 2SRI, and NPCB are IV-based methods. Whether there is any adjustment for covariates, the 2SLS/2SRI are not termed as the naive, first-stage adjusted, or both-stages adjusted 2SLS/2SRI in the literature. For comparison purposes, we termed these methods as the naive, first-stage adjusted, or both-stages adjusted 2SLS/2SRI;
  2. Abbreviations: ITT: intention-to-treat; PP: per-protocol; AT: as-treated; IP-weighted PP: inverse probability weighted per-protocol; 2SLS: two-stage least square; 2SRI: two-stage residual inclusion model; NPCB: non-parametric causal bound.
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BMC Medical Research Methodology

ISSN: 1471-2288

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