Table 2 Practical guide for how the methods identified can be used and the appropriate situations
Method | Research Question | Strengths | Weaknesses | Recommended uses |
|---|---|---|---|---|
Mutli-level Modelling [13] | How many sessions are needed for 50%* of patients to reach CSI? | -Model captures heterogeneity through random coefficient -Inclusion of multiple characteristics potentially reduces unmeasured confounding | - Cannot make causal inferences regarding dose - Does not deal with selection bias or hidden confounding | This method is suitable for pilot studies aimed at identifying recommended treatment dose to test later in a RCT. All patients would receive treatment and the number of sessions they attend would be recorded. Researchers must collect detailed patient information to enhance the analysis. |
Kaplan-Meier Curve [14] | How many sessions are needed for 50%* of patients to reach clinically significant improvement (CSI)? | - Allows for an exploration of relationships between characteristics and time to CSI -Suitable for analysing observable data without predefined time limits on therapy duration - Uses longitudinal, sessional data to model shape of response without relying on interpolation | - Cannot make causal inferences regarding dose - Sessional outcome data must be collected, which is time consuming - When a participant reaches CSI, this must be maintained until termination of treatment - Does not deal with selection bias or hidden confounding | This method is well-suited for pilot studies aimed at identifying recommended treatment dose to test later in a RCT. All patients would be offered treatment, their outcomes after each session must be collected using a valid psychometric measure. Average time to reach CSI data can be estimated for the sample. The resulting dose-response should be considered as a guideline, rather than an exact estimation of the dose-response relationship. |
Smoothing Splines [16] | What is the potential shape of the dose-response curve? | -Allows for exploration of the potential underlying dose-response curve -Various shapes can be explored and compared using goodness-of-fit indices. | - Cannot make causal inferences regarding dose - The true dose-response curve can be oversimplified or overcomplicated -Goodness-of-fit indices may not reliably identify best more accurate model -Requires large sample size | This method is suited to large, observational studies where researchers want to explore the shape of the dose-response curve. Splines should be applied to observational data, goodness-of-fit indices will help to choose the most plausible shape of response. This is exploratory and should serve as a visualisation before adopting more formal models. |
Propensity Score Method [15] | What is the average effect of dose conditional on propensity score? | - Allows for causal interpretation of the effect of dose - If assumptions are met, outcome is unconfounded by dose, given covariates. - Balances observed covariates between treatment levels | -Requires that outcome is unconfounded given observed variables - Subject to assumptions of overlap and positivity -Misspecification of outcome model leads to bias | This method is suited to observational studies where patients have self-selected varying doses of treatment. The method requires appropriate variables to be collected to create propensity score that balances the covariates that affect self-selection into dose levels. |
Kernel Estimation [17] | What is the dose-response function of a continuous treatment? | - Does not require assumptions about the functional form of the dose-response - Allows for causal interpretation of the effect of dose - Balances observed covariates between treatment levels | -Requires that outcome is unconfounded given observed variables - Dependence on observable variables -Sensitive to sample size | This method is suited to large, observational studies where the relationship between covariates and treatment assignment is complex or poorly understood, such as when patients self-select into varying doses of treatment based on factors that interact in nonlinear or unknown ways. |
SMM(G) IV(2SLS) IV(ATR)† [18] | What is the average treatment effect of the received dose, accounting for non-compliance. | - Allows for causal interpretation of the effect of dose - Possible to accommodate non-linear effects - Handles selection bias that arrives from self-selection into dose | - To identify randomisation as an instrument, we must assume no direct effect of randomisation on outcome (Exclusion restriction) - The functional form of dose must be pre-specified. - To model a non-linear effect, multiple valid instruments must be identified | These methods are best applied to randomised controlled trial data. The method estimates average treatment effects using variable session attendance. When modelling non-linear effects, it may be necessary to identify an additional instrumental variable. |
Stein-Like Estimators [19] | What is the average treatment effect of the received dose, accounting for non-compliance. | - Allows for causal interpretation of the effect of dose - Combination of OLS and 2SLS reduces bias whist mitigating variance - Adapts to the strength of the instrument used - Handles selection bias that arrives from self-selection into dose | - To identify randomisation as an instrument, we must assume no direct effect of randomisation on outcome (Exclusion restriction) - Assumes homogeneity of treatment effects - Assumes linear dose-response relationship | These methods are best applied to randomised controlled trial data. The method estimates average treatment effects using variable session attendance. When modelling non-linear effects, it may be necessary to identify an additional instrumental variable. This method is suitable for when there is a concern between the bias and variance trade-off in standard IV methods. |