Database Development and Statistical Analysis of Survival in a Clinical and Historical Coort of Dogs Affected by Myxomatous Mitral Valve Disease Treated With Different Therapeutic Protocols Using Causal Inference Techniques

The aim of this work was to retrospectively evaluate the inuence of different therapeutic protocols (loop diuretics, ACE-inhibitors, spironolactone +/- pimobendan) on the survival time (ST) of dogs with myxomatous mitral valve disease at different stages using an Inverse Probability Weighting (IPW) analysis. An IPW method was used to minimize confounding and IPW weighted time-repeated logistic model was used to approximate survival curves (SCs) and calculate survival differences. Subjects were allocated into cases (CA) and controls (CO). Dogs in American College of Veterinary Internal Medicine (ACVIM) B2 class treated with pimobendan (+/- ACE-inhibitors) were selected for the CA group, as well as symptomatic patients (ACVIM class C) threated with triple (furosemide, ACE-inhibitor, pimobendan) or quadruple (furosemide, ACE-inhibitor, pimobendan and spironolactone) therapy. The CO group included ACVIM class B2 dogs not treated with any medication and ACVIM C dogs treated with a combination of furosemide and ACE-inhibitor/spironolactone without pimobendan. The SC of the CA group crossed the CO group at 1634 days. The difference between the two SCs at the time of maximum survival difference in favour of the CO group was 11.3% (CI 1.7%–20.9%) (signicant), in favour of the CA group was 3.9% (CI -8.6%–16.4%) (not signicant) and at the mean ST was 3.6% (CI -8.5%–15.7%) (not signicant) in favour of the CA group. For times greater than 1634 days the survival was in favour of the CA group, there were no statistically signicant differences in survival in favour of the CA group in this clinical population.


Introduction
The cardiovascular activity of pimobendan is known since 1987 and from that time many studies have been performed to de ne its effects on the survival time with different severity of heart diseases in dogs The multicentric blinded, randomized, placebo or positive (benazepril) controlled clinical trials with the highest scienti c evidence were focused on patients affected by MMVD prospectively recruited, considering the inclusion and exclusion criteria de ned before (Boswood et al. 2016, Häggström et al. 2008).
The onset of congestive heart failure (CHF), cardiac-related death or euthanasia were considered the primary and/or secondary endpoint of these studies (Boswood et  The confounding bias that may affect retrospective studies, often in uences the evaluation of the differences in survival times (ST) between treatment groups and the association of the variables of interest with the survival time. In these circumstances a statistical approach coming from the causal inference literature could be applied to determine whether this method leads to results consistent with ndings from randomized studies, also in retrospective data analyses. Moreover, populations included in randomized studies may be very selected and observational data related to populations of patients treated in clinical practice may complement evidence from trials and contribute to generate new evidence on treatment effects.
Among the causal inference methods, the Inverse Probability Weighting (IPW) method uses two regression models, one for the exposure and one for the outcome. The regression model for the exposure is referred to a propensity score (PS) model and estimates the probability of being exposed to the treatment of interest conditional on confounding factors for all subjects in the study population. The model for the exposure is used to construct weights which will be assigned to the subjects in the study population. The second regression model is the outcome model, representing the main analysis model, which aims to estimate the association of the exposures of interest with the outcome variable. The IPW method aims to minimize confounding bias by improving exchangeability between exposed and unexposed subjects with the nal aim to emulate the randomization of the treatment. To reach this aim subjects with lower probability of being exposed will receive a bigger weight to avoid underrepresentation of this part of the population and vice versa subjects with higher probability of being exposed will receive a lower weight. Adjusting for confounding and reproducing a pseudo population where each subject should be potentially exposed and not exposed to the treatment of interest, the IPW method aims to reach a causal interpretation of the ndings under the assumption of no unmeasured confounding and other important assumptions implied by causal inference methods.
An IPW method was used (Cole & Hernán 2008) to estimate the association between the exposure to the type of therapeutic treatment (including or not pimobendan) and death by cardiac or other causes. Speci cally, the aim of this study was to evaluate the in uence of different therapeutic protocols, including loop diuretics (furosemide), ACE-inhibitors, and spironolactone with or without the inodilator pimobendan, on the ST of dogs affected by different stages of MMVD (asymptomatic with cardiac remodelling and symptomatic) via an IPW analysis. To the best of our knowledge this statistical technique has never been used for this type of retrospective study in veterinary medicine.

Material And Methods
Medical records (2000-2020) of client-owned dogs referred to the Cardiology Unit of the Department of Veterinary Medicine of the University of Milan, were retrospectively reviewed.
Owner consent was routinely requested before the rst examination of each dog. The clinical records were selected according to the following inclusion criteria: complete clinical ndings including signalment, history (increased resting respiratory rate, cough, dyspnea) physical examination, thoracic radiographs, and electrocardiogram (ECG). Clinical records of subjects affected by any other heart disease apart from MMVD, clinically signi cant systemic disease, or other signi cant organ dysfunction were excluded. Additionally, subjects with primary hypertension were also excluded from the study (Acierno et al. 2018).
The subjects were then categorized into "case" group (CA) and "control" group (CO).
Dogs belonging to class B2, treated with pimobendan alone or in combination with ACE-inhibitors were included in the CA group, as well as the symptomatic patients (ACVIM class C) threated with triple (furosemide, ACE-inhibitor, pimobendan) or quadruple (furosemide, ACE-inhibitor, pimobendan and spironolactone) therapy. The CO group included untreated ACVIM B2 dogs and ACVIM C patients treated with a combination of furosemide, ACE-inhibitor +/-spironolactone, without pimobendan.
Endpoint of the study was the animal's death (cardiac-related death or euthanasia, and extracardiac causes). Owners were contacted by phone to complete medical records' data and to collect information on subjects' follow up. Dogs lost at follow-up were not included.

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Data obtained from clinical records from 2000 to 2020 were then statistically analysed.

Statistical analysis
Initially, relevant, or confounding variables to be used in the IPW analysis were dichotomized to 1 (higher risk) or 0 (lower risk) levels, according to the risk threshold derived from the literature for each of the covariates. The variables considered to be in uential exclusively on MST were age, cough, dyspnea, and ejection fraction (EF). The confounding variables that affected both survival and treatment assignment were EDVI, LA/Ao ratio, and the presence of PH. Other unmeasured confounding variables for all subjects Survival curves were estimated, both for dogs exposed (CA) and unexposed (CO) to pimobendan treatment, by a IPW weighted model following the method described by Hernán and Robins (Hernán & Robins 2020). Firstly, weights were derived as "stabilized inverse probability weights" (SIPW), i.e., the ratio between the marginal probability density of the exposure and the probability density of the exposure conditional to covariates such as age, pulmonary hypertension, cough, dyspnoea, EDVI, LA/Ao and EF% (Hernán et al. 2001). Survival curves were estimated approximating them with a time-repeated logistic model weighted with the IPW weights and with live/dead as binary outcome. Finally, differences in survival curves among CA and CO groups were estimated using the IPW weighted logistic model and 95% con dence intervals (CIs) were derived based on 100 bootstrap samples.
The difference between the two survival curves at the time of maximum survival difference in favour of the CO group was 11.3% (CI 1.7% -20.9%) (signi cant), while the difference at the time of maximum survival difference in favour of the CA group was 3.9% (CI -8.6% -16.4%) (not signi cant) and at the median survival time was 3.6% (CI -8.5% -15.7%) (not signi cant) in favour of the CA group.
The statistical analysis, carried out using the method proposed by Hernán and Robins, showed a reversal of the trend in the survival curves for CA and CO groups: in a time-frame shorter than 1634 days the CO group had better survival, while the CA had better survival after 1634 days (Fig. 1).

Discussion
The results from this study are consistent with ndings from a prospective, single-blinded, randomized multicenter study trial, showing that causal inference methods can be used to consolidate results from randomized trials (Wess et al. 2020).
Our study has been conducted in a clinical population including patients treated during clinical practice and shows that causal inference methods can be used to analyse data routinely collected in clinical practice to complement evidence coming from randomized trials. Data collected in clinical practice re ects treatment patterns of patients with disease severity and treatment history different from patients included in randomized trials and therefore constitutes a valuable research resource to investigate treatment effects. In clinical practice patients may be treated with different therapeutic protocols (including comedications and treatment changes) and investigating the differences in survival due to different protocols is crucial for contributing to clinical guidelines. Moreover, randomized trials may be often infeasible due to ethical and economic reasons, or they may include very selected populations.
Collecting evidence on treatment effects via observational clinical data routinely collected and analysed with causal inference methods may increase awareness on treatment effectiveness and safety in more general populations encountered during clinical practice.
The IPW analysis attempted to provide a causal interpretation of the association between pimobendan and survival time, however limitations may come from the ful llment of some of the assumptions implied by the methods such as no unmeasured confounders. In case some important confounding factors remain unmeasured the ndings can still retain some residual bias. Indeed, the results of this study on the effect of pimobendan on survival may be affected by differences in disease severity of the dogs in the study population undergoing different treatment strategies. Otherwise, among the advantages of the approach is the possibility to obtain marginal estimates of the potential effect of pimobendan on survival time with respect to traditional methods which conditioning on confounding factors in the outcome model allow to have only conditional estimates. Finally, the approach is novel to veterinary medicine and other applications in the eld are warranted given the increased availability of valuable clinical data routinely collected.

Declarations
Funding: not applicable.
Con icts of interest/Competing interests: not applicable.
Availability of data and material: data is available by upon request.
Code availability: not applicable.
Author contributions  Figure 1