Model selection process for objective 4

Due to the causal inference nature of objective 4 of the thesis, the methods that account for treatment selection bias in observational studies had to be

a sensitivity analysis) were adopted over the multivariable model risk adjustment (the conventional modelling approach) for the thesis.

Propensity scoring (with the propensity score been defined as the probability of receiving treatment conditioning on observed baseline patient characteristics (139)) only removes overt bias conditional on observed covariates, however because the propensity score model can be adjusted for as many observed patient characteristics as available if a large comprehensive dataset is used (in this instance MINAP registry) bias may be removed adequately. The score from propensity scoring is used to create comparable treatment groups in terms of baseline covariates by either matching, stratification, inverse probability of treatment weighting on the propensity score or covariate adjustment using the propensity score(139). For the thesis weighting using the inverse of probability of treatment was used. This is because inverse probability weighting is the most robust way of balancing covariates without losing patient information as matching and stratification involve excluding patients that fail to match on the propensity score, thereby potentially losing important information as well as reducing study power. The primary outcome for this objective of the thesis was one year all-cause mortality. Secondary outcomes included six months and 30 day mortality. Due to the survival nature of the study, a survival model had to be employed and this case a survival model under propensity scoring modelling. The survival-time inverse-probability weighting propensity score analysis was adopted for propensity scoring survival modelling. This method was adopted as it incorporates propensity scoring for survival data for causal inference. The method works by estimating the treatment effects as Average Treatment Effects (ATE) and Average Treatment Effect on the Treated (ATET) through two models: 1) the treatment assignment model which estimates the propensity for treatment assignment and 2) the survival model which is the outcome model

were the treatment effects estimated(140, 141). The ATE coefficients derived are the absolute difference in survival times when all patients receive treatment compared to when all the patients do not receive treatment. The ATET is then the absolute difference in survival time only for those who were treated compared to when they did not receive treatment. The ATE and ATET are derived as follows:

Each patient, the treatment effect is a difference of two potential outcomes which can be denoted by the equation below:

𝑌𝑖 (1) − 𝑌𝑖 (0) 3.6

Where 𝑌𝑖 (0) : outcome (survival time) when the patient does not receive treatment.

𝑌𝑖 (1): outcome (survival time) when the patient receives treatment. The ATE is the average of moving the entire population from treated to untreated as shown by the equation below:

𝐸 [𝑌𝑖 (1) − 𝑌𝑖 (0)] 3.7

The ATET is then the average treatment on the treated patients only, i.e. the conditional expectation as shown below:

𝐸 [𝑌𝑖 (1) − 𝑌𝑖 (0)| 𝑍 = 1] 3.8

where 𝑍 = 1 : is for the treated patients only(142).

The treatment assignment model (propensity scoring model) is used to derive inverse-probability weights that are used to weight the data before the survival model is fitted in order to balance the systematic differences between the treatment and control observations so that the treatment effects can only be attributed to the treatment administered.

For this thesis a non-parsimonious multivariable logistic regression model was adopted as the treatment assignment model and a Weibull model for

factors (diabetes, hypercholesterolaemia, hypertension, smoking status, COPD, family history of coronary heart disease), cardiovascular history (cerebrovascular disease, peripheral vascular disease), hospital discharge medications (statins, aspirin, P2Y12 inhibitors, ACEi/ARBs), adjusted mini- GRACE risk score variables (age, cardiac arrest, elevated enzyme, systolic blood pressure and heart rate at hospitalisation and creatinine) and care by cardiologist. The treatment assignment model should be adjusted for as many pre-treatment covariates (that can potentially predict treatment assignment) as possible in order to ensure the propensity scores derived can be adequately used to even out the systematic differences between the treated vs. the non-treated, such that the treatment effects observed can be accurately attributed to the care intervention under investigation(138). The 24 variables adjusted for in the model were the pre-treatment variables available in the data source (MINAP) used for the analysis. Choice of variables to add to the treatment assignment model was also guided by literature and clinical input from Professor CP Gale.

Using the inverse probability weights derived from the treatment assignment model to balance the covariate distribution between the treated vs. the non-treated, the survival model was fitted also adjusted for the earlier mentioned covariates as well as cardiac rehabilitation. This further adjustment of the covariates was done to reduce residual confounding in the survival model and cardiac rehabilitation was only included in the survival model as it was a post treatment variable and could therefore not predict treatment assignment. Adjusted Kaplan-Meier curves to assess survival differences between patients who received β blockers and those who did not were derived using the survci command. The models were adjusted for the propensity scores derived from the non-parsimonious multivariable logistic regression model, i.e. the treatment assignment model.

As mentioned earlier in this section, propensity scoring adjusts for measured confounding adequately especially in the incidence of use of large comprehensive datasets. However, because unmeasured confounding is also a major problem when analysing observational data instrumental variable analysis had to be employed as a sensitivity analysis. The method allows for the determination of treatments effects that are similar to those obtained from randomised clinical trials by the use of an instrumental variable that behaves like a natural randomisation of patients to “treatment groups” that differ in their likelihood of receiving care(138). The instrumental variable acts as an unconfounded proxy of treatment and allows for comparison of groups of patients that differ in their likelihood of receiving treatment instead of comparing the actual treatment groups(143). This allows for the estimation of causal effects after accounting for measured and unmeasured confounding(143). However, for the analysis to be robust the instrument should be a strong predictor of treatment and should not be associated with the outcome of interest(138).

In literature several examples of instrumental variables have been employed which include: physician prescribing preferences, differential distances, density of cardiologists, distance to healthcare facilities, personal beliefs, calendar time, exogenous shocks (sudden shift in patient or physician behaviour) and state laws/policies(143, 144). Physician Prescribing Preferences (PPP) has been found to be a good instrument in clinical epidemiology for investigating drug effectiveness when using instrumental variable analysis(143). So for the current thesis PPP was chosen as the instrumental variable. However, because in MINAP there is not actual data capture of PPP a proxy was derived using hospital prescribing rates of guideline-indicated hospital discharge medications (aspirin, P2Y12 inhibitors, β blockers, statins and ACEi/ARBs).

potential for survivorship bias as it does not consider follow-up time. In order to avoid this survivorship bias a Poisson regression modelling approach with an offset of the log of survival time was used for the thesis as has been adopted in other studies(145). To further mitigate potential bias from residual confounding the 24 case mix variables were also adjusted for in the Poisson model.

For both the instrumental variable analysis and survival-time inverse- probability weighting propensity score analysis, the analyses were conducted by overall AMI cohort and stratified by AMI phenotype (STEMI and NSTEMI) for three survival time points (one month, six months and one year).