163 Antidepressant therapy prescription, do psychologists help? Evidence from Portugal Yit =β0 +β1(Pit − ¯Pi)+β2 ¯Pi + (W′ it − ¯W′ i)β3 + ¯W′ i β4 +εijt (2) Where W′ it includes X′ it, Z′ ijt and θt and ¯W′i includes ¯X′ i, ¯Z′ ij and ¯θ; all explanatory variables – both the number of psychologists but also covariates - are replaced by their GP-specific means over time and deviation from this mean. For better estimation of the partial association captured by the between term β2 we adjusted for the patient case mix, and for GP, GP practice and local context characteristics described in section 2.2.1. Finally, we controlled for year ( θt ) to account for time trends and (policy) shocks that are common to all GPs, practices, and local groups. Importantly, we have adjusted standard errors by clustering at the local group level, which is the level at which the psychologist’s number is defined. All analyses were performed using STATA 16 software. Heterogeneity and robustness analyses We conducted several heterogeneity analyses to explore the potential mechanisms driving the relationship of interest, particularly looking at heterogeneity in the within estimates. First, we explored whether any changes in prescription was due increased number of psychologists overtime would have a different magnitude for GPs in local groups with higher vs. lower average number of psychologists. We hypothesize that such non-linearities might exist because some local groups have a very low (or zero) number of psychologists, where adding 1 psychologist/100,000 patients leads to a much larger relative increase in psychotherapy supply than adding the same 1 psychologist in an established team of n psychologists. Furthermore, pharmacotherapy and psychotherapy might be used as substitutes (mild patients) or in combination (moderate patients). When used in combination, no (immediate) reduction in prescription would be observed due to additional psychotherapy. Depending on their preferences and beliefs about the effectiveness of psychotherapy as a single or combined therapeutic approach GPs might choose to prioritize additional psychotherapy supply differently depending on the previous (un)availability of such resources in their local groups. We classified GPs in quartiles of the average number of psychologists they are exposed to in the local group during the study period and estimated our main model stratified by quartile. Second, we conducted additional stratified analysis by determinants of antidepressant prescription described in the literature: GP sex, GP age, GP length of tenure in NHS, patient list size and urbanization degree of the practice location [14, 24]. With these analyses, we aimed at understanding whether GPs with certain (practice) characteristics were more prone to respond to the changes in the psychotherapy supply over time. Following a similar rationale, we have conducted stratified analysis by dividing GPs into quartiles of antidepressant prescription (average over the study period). This analysis aimed at exploring heterogeneity by unmeasured GP characteristics that influence prescription behaviour, such as their personal history of depression or personal experience with pharmacotherapy and psychotherapy [14, 23]. 5
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