SURVIVAL MODELS: TIME-DEPENDENT COVARIATES

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1 SURVIVAL MODELS: TIME-DEPENDENT COVARIATES AND TIME-DEPENDENT EFFECTS An application to the study of prognostic factors of disability in multiple sclerosis ABSTRACT: Background: Several recent studies introduce a two-stage disease process of multiple sclerosis (MS) with different impact of prognostic factors according to the stage. This also raises questions about effectiveness of MS therapy, particularly about initiation of drug intake. Thus, our main objective was to introduce a reflection about multivariate survival analysis in the context of MS data analysis with time-dependent prognostic factors, in order to specifically study impact of early or late drug initiation on MS disability progression. Methods: Using 759 patients with relapsing-remitting multiple sclerosis (RRMS) treated with disease-modifying therapies, three proportional hazards models were developed: a classic Cox model with fixed covariates, a Cox model with time-dependent covariates and a multipleevent model of Prentice Williams and Peterson (PWP). Results: Advanced age at MS onset, annual relapse rate at 1-year 2 and conversion to secondary progressive MS favored a rapid progression of disability with the three models. Inclusion of time-dependent covariates highlighted delayed start of first disease-modifying therapies as factor of poor prognosis, but it remains no significant on the whole. We pointed both classic Cox model and Cox model with time-dependant covariates were not really suitable to study most of MS prognostic factors, and we hypothesized PWP model could be more suitable. Conclusions: This study emphasizes difficult to fit prognostic factors of RRMS with conventional statistical models, particularly because of time-dependent covariates and covariates with time-varying effects. Despite these considerations, long-term benefit of early treatment initiation remains difficult to be highlighted. Keywords: multiple sclerosis, disability, prognostic factors, Cox model, time-dependent covariates, multiple events.

2 INTRODUCTION: Master 2 Modélisation en Pharmacologie Clinique et Epidémiologie In multiple sclerosis (MS), the accumulation of neurological lesions over time usually leads to irreversible disability, and actually leads to high disability or to death after several decades (with a median time from MS onset to cane required to walk around 20 years, and to death around 40 years) 1,2. The natural course of MS and its factors of poor prognostic: progressive form (either primary or secondary), advanced age at onset, male gender, polysymptomatic onset, incomplete remission after the first attack, short time to a second relapse, and high number of relapses during the first two years, are still raising many questions. In fact, several recent observational studies 3-5 conducted on big series of patients and long-term data proposed a novel concept about disability accumulation and prognostic factors in MS with some evidence for a twostage disease progression. Furthermore, disease-modifying therapies (DMT) including immunosuppressive (IS) and immunomodulatory (IM) drugs are widely used in MS patients since the mid-1990s, however efficacy of these immunoactive drugs are not really established 6. The two-stage concept of the disease with a first stage probably dependent on focal inflammation and a second stage probably independent of current focal inflammation, might offer an interesting hypothesis to explain the apparent dissociation between impact of therapeutics on focal inflammatory markers and impact on delaying disability progression. A unifying hypothesis might be that early focal inflammation could be the pivotal event from which all else follows 5,7. Statistical models to analyse MS progression should account for long follow-up periods with possibly censored data. The Cox proportional hazards (PH) model allows one to adequately study this kind of data, and hence to adequately fit prognostic factors of MS into multivariate survival analyses 8. As we see, the study of factors involved in MS disability progression remains a hot spot of debate and discussion. Regarding statistical methods, the long-term study of MS prognostic factors also poses some technical problems in one side, related to variability of patients exposures, habits or drug intake and in other side, related to some evidence MS is a two-stage disease with different impacts of prognostic factors into both stages. The primary Cox model that seems to be adapted to MS factors analyses relies on fundamental assumptions. Primarily, all covariates introduced in the model are fixed from the start of follow-up; taking into account covariates with time-dependent values needs some model adaptations 9. Secondarily, this PH model implies that the factors investigated have a constant impact on the hazard over time 10 and with a two-stage hypothesis of MS the PH assumption may be violated and should be verified. In this work, we wanted to initiate a reflection on assumptions and uses of Cox model for survival analyses of MS risk factors. For this we studied impact of different time-initiations of DMT (early stage against late stage) on MS disability progression as an excuse for illustrating our reflection. So, we specifically pointed our analyses on treated MS patients, we compared estimations of three different survival models, in order to differently account for changes of exposure to DMT and other prognostic factors over time, and we conducted complete checking of the proportional hazards assumption for each of them. PATIENTS AND METHODS: Data: The study population consisted of the patients followed in the Reference Centre for MS in the West France. Patients and data collection were previously presented 5,11. All the patients supported the clinically or laboratory definition of MS according to the Poser criteria 12 and

3 were included in the European Database for Multiple Sclerosis (EDMUS) 13. Individual case reports included identification and demographic data, medical history, key episodes and dates in the MS course (sequelae after the first attacks, relapses, onset of the progressive course, dates of the successive steps of irreversible disability progression, and dates of the treatment start and changes of treatments). The Expanded Disability Status Scale (EDSS) was used to define patients course of disability 14. A given EDSS score was considered as irreversible when it persisted for at least 6 months, excluding any transient worsening of disability related to relapses. In the present work, only patients with a relapsing onset MS and treated for at least 6 months using DMT were included. DMT prescribed in our population were azathioprine, cyclophosphamide, interferons beta, mitoxantrone, methotrexate, and glatiramer acetate. Patients were classified as treated if treatment duration was at least six months, except for mitoxantrone and cyclophosphamide where a cumulative dose of 60 mg and 6 g, respectively, were at least mandatory. Hypothesizing that EDSS 3 corresponded to the key step in the disease process, we defined two phases of MS course: the early phase, Phase 1, from clinical onset to irreversible EDSS 3 and the later phase, Phase 2, from irreversible EDSS 3 to irreversible EDSS 6 5. Primary statistic analysis: After an overall description of the database, we looked for factors that could influence the time from MS clinical onset to EDSS 6 (ability to walk with unilateral support no more than 100 m without rest) using Kaplan-Meier analyses and Log rank tests. The prognostic value of the following factors was evaluated: gender (female or male), age at MS onset (< 20, 20 to 29, 30 to 39, 40), symptoms at MS onset (combination of symptoms, isolated optic neuritis, isolated brain-stem dysfunction, isolated dysfunction of long tracks), incomplete remission after the first attack (no or yes), annual relapse rate at the first year (< 2 or 2), clinical form of MS (RR, SP without relapse, SP with relapses), type of treatment received during followup (IM, IS, both IM and IS), treatment period (first treatment during phase 1 or during phase 2). Cox model: Our initial statistical approach ignored information changes collected during follow-up; we used a conventional Cox model 8. All variables introduced in the model were fixed at the start of follow-up defined as MS clinical onset: gender, age and symptoms at MS clinical onset, degree of remission after the first attack, annual relapse rate at 1 year, conversion to secondary progressive MS, type of treatment received, and treatment period. Those factors corresponded to patients initial characteristics, and past or present exposures at the beginning of follow-up. This model did not take into account changes in exposure over time; especially it did not distinguish between treated periods and therapeutic windows. Considering a single value for treatment exposure during the overall follow-up, the Cox model resulted in a significant approximation of the actual exposure of patients. Cox model and time-dependent covariates: In the second analysis, we used a Cox model with time-dependent covariates, which allow exposure modification over time by a patient follow-up cutting; each time interval was defined by a stable period of exposure to factors. Let A, B, C, D, and E, five relapsing-remitting multiple sclerosis patients (figure 1). Only patients A, C and D had reached EDSS 6 at time T 1, T 2 and T 3, respectively. Several configurations of treatment exposure could be considered. For example in the configuration 1,

4 the patient D was treated from thirteen to thirty years after MS onset and in the configuration 2, the patient D was treated for two periods (6 to 12 and 18 to 30 years after MS onset). Concerning the treatment exposure at time T 1, we could count two really exposed patients in the first configuration against only one patient in the second one. Finally, the average exposure rates of the patients at risk were: - If treatment was considered as a fixed covariate in both configuration, 4 exposed 5 patients patients at T1 + 2 patients at T2 + 2 patients at T at risk at T1 + 3 patients at T2 + 2 patients at T3 3 = If treatment was considered as a time-dependent covariate in configuration 1 and 2 respectively, 2 exposed patients at T1 + 0 patients at T2 and T3 = 2 5 patients at risk at T1 + 3 patients at T2 + 2 patients at T3 10 1exposed patients at T1 + 0 patients at T2 and T3 5 patients at risk at T1 + 3 patients at T2 + 2 patients at T 3 = 1 10 This example confirmed the conventional counting process of Cox model exposure was highly approximated compared with a Cox model allowing for time-dependent covariates. Method for analysing multivariate failure times: In Cox model with time-dependent covariates, only exposure closest to events was considered, meaning that some values of exposure never took part in the counting process (for example in the figure 1, the first treatment of patient B which was stopped before the first event). This was a strong limitation of Cox model, and it led us to foresee another approach. Three principal methods were considered: the Andersen-Gill approach (AG) 15, the marginal data model used by Wei, Lin, and Weissfeld (WLW) 16, and the conditional model developed by Prentice, Williams, and Peterson (PWP) 17. As with time-dependent covariates, the same counting process is used, each subject is represented by a series of observations with time interval of (entry time, first event]; (first event, second event]; ; (n th event, last follow-up] for AG model and PWP model, and with time interval of (entry time, first event]; (entry time, second event]; ; (entry time, last follow-up] for WLW model. At time t, individuals at risk of a second event are: All subjects under observation at time t with the AG model, All subjects under observation at time t and who have not yet experienced a 2 nd event with the WLW model, All subjects under observation at time t and who have not yet experienced a 2 nd event and who have experienced a first event with the PWP model. In our opinion, the PWP approach was the most appropriate one to our context; recurrent events are passages from one disability step to another higher without reversibility; patients at risk into a disability step always come from the step directly below. So we decided to only use

5 the PWP models for our analyses. All along this third analysis, we kept the same time counting process for time-dependent covariates. The results section displays overall analyses from the conventional Cox model (bcox), the Cox model with time-dependent covariates (tcox), and the PWP model. The same covariates were introduced into each model, except for the treatment period and the PWP model where impact of drug intake was analysed step-by-step into each disability stage stratification. The parameter estimates were performed by maximization of the classical partial likelihood 18 for bcox and tcox model, and by maximization of the specific partial likelihood 17 for PWP model. We also used the robust jackknife estimator of the parameter variance 19 for tcox and PWP model because of the dependence between observations of the same individual. We checked PH assumption 10 for all covariates of three models using a graphical strategy by plotting the function log(-log(s(t)): the logarithms of cumulative hazards 20 ; and another method using the scaled Schœnfeld residuals which enables us to test for non-proportionality and to graph a smooth plot of the Schœnfeld residuals to visualize evolution of each estimated coefficients over time (β t ) 21,22. All analyses were performed with R software for Windows 23 and statistical level of significance was 5%. FIGURE 1: Diagram illustrating the counting process with or not time-dependent covariates Configuration 1 Configuration 2 EDSS 6 reached EDSS 6 reached A B End of follow-up Treatment period A B End of follow-up Treatment period C C D D E E 10 T T 2 T 3 40 years 10 T T 2 T 3 40 years Time-dependentcovariate Fixedcovariate Time-dependentcovariate Fixedcovariate Concerning treatment exposures Total Concerning treatment exposures Total Patients at at risk Patients at at risk Event count Event count Exposedpatients patients Exposedpatients patients Average exposure Average exposure RESULTS: Characteristics of the study population: At the database closing in 2004, the Rennes EDMUS cohort included 1609 patients with relapsing onset MS, of whom 759 patients had received at least one treatment. Descriptive characteristics of the 759 patients are presented in Table 1. Two hundred and three patients (27%) had reached EDSS 6 at the end of follow-up after a median time of 12.9 years (min: 0.5; max: 42.5). Regarding DMT, 417 patients (55%) were treated before EDSS 3 and 342

6 patients (45%) received their first treatment after EDSS 3. Nearly half of patients (46%) received only IS drugs, 28% received only IM drugs and 201 patients (27%) were treated by both IM and IS drugs. Bivariate analysis: The Kaplan-Meier estimated median time to reach EDSS 6 from MS onset was 22.3 years [20.9; 27.1]. As shown in Table 2, the following factors: male gender, advanced age at MS onset, incomplete remission after the first attack, annual relapse rate the first year greater than or equal to 2, conversion to secondary progressive phase, IS or both IS and IM drugs intake were significant pejorative factors on the time to reach EDSS 6 from MS onset. Multivariate analyses with the 3 models: Table 3 presents results of the three multivariate survival models. First, the bcox analyses showed that age at onset, annual relapse rate, conversion to secondary progressive phase and type of treatment significantly influenced the time to reach EDSS 6 from MS onset. IS treatments and both IS and IM treatments were factors of poor prognosis (hazards ratio (HR) equal to 2.06 [1.17; 3.60] and 2.28 [1.26; 4.12] respectively) compared with patients only treated by IM drugs. Start of treatment after EDSS 3 was not significant in the bcox model, with HR estimated to 1.12 [0.82; 1.53]. Secondly with the tcox analysis, age at clinical MS onset, and the annual relapse rate were no longer significant. The period of treatment did not influence the time to reach EDSS 6 with HR equal to 1.25 [0.90; 1.72], and treatment by IS drugs remained of poor prognostic (HR: 2.05 [1.48; 2.84]) compared with no treatment. Third, with the PWP model, an increased age at MS clinical onset was a poor prognostic factor of disability progression, as well as a relapse rate at 1 year greater than or equal to 2, and the conversion into SP form. The type of drugs was not found as a significant factor. When we analyzed the impact of treatment at each step of disability, we just revealed a significant protective effect in the early step of the disease. Testing the hypothesis of proportional hazards ratio: All covariates together, the proportional hazards hypothesis was respected for both bcox model (p: 0.721) and tcox model (0.874), but not for the PWP model (p: 0.005). Analysis covariates by covariates did not show anymore-significant test either for bcox or for tcox. Regarding the PWP model, four covariates (incomplete remission, annual relapse rate, clinical form and treatment by IM drugs) did not respect the PH assumption (with respective p values equal to 0.021, <10-3, 0.008, 0.004). Using graphs of the cumulative hazards logarithms, we could highlight junction over time between curves. It was especially obvious for the two covariates (annual relapse rate and clinical form), where there has been a clear decrease of the pejorative effect of the annual relapse rate 2 with time, and even a reverse effect of the SP form over the time. From the smooth scatter plots of β (t), only the annual relapse rate has clearly shown that the proportional hazards ratio condition was not met with time.

7 Table 1: Characteristics of the study population (n=759) Sex Female 543 (71.5%) Male 216 (28.5%) Mean age at onset of multiple sclerosis (years) ± SD 28.8 ± 8.6 Age group at onset of multiple sclerosis <20 years 115 (15.2%) 20 to <30 years 344 (45.3%) 30 to <40 years 204 (26.9%) 40 years 96 (12.6%) Initial symptoms of multiple sclerosis (n=707) Isolated long tracks 323 (45.7%) Isolated brainstem 96 (13.6%) Isolated optic neuritis 181 (25.6%) Combined symptoms 107 (15.1%) Residual deficit from the first relapse No 651 (85.7%) Yes 108 (14.3%) Relapse rate during the first year of multiple sclerosis <2 431 (56.8%) (43.2%) Relapse rate during the first 2 years of multiple sclerosis <2 641 (84.5%) (15.5%) Disease form at end of follow-up Relapsing-remitting form 445 (58.6%) Secondary progressive form 314 (41.4%) Mean follow-up duration from onset (years) ± SD 13.3 ± 9.0 Mean time from onset to secondary progressive conversion of multiple sclerosis (years) ± SD 9.8 ± 6.8 Number of patients to reach EDSS (26.7%) Mean time from onset of multiple sclerosis to EDSS 6 (years) ± SD (n=203) 15.0 ± 8.5 Treatment group First treatment before EDSS (54.9%) First treatment after EDSS (45.1%) Treatment with only immunomodulatory drugs 209 (27.5%) Treatment with only immunosuppressive drugs 349 (46.0%) Treatment with both immunomodulatory and immunosuppressive drugs 201 (26.5%)

8 Table 2 : Assignment of the EDSS score of 6 and time to reach EDSS 6 from MS onset according to demographic and clinical characteristics of the 759 MS patients Sex Age group at onset of multiple sclerosis Initial symptoms of multiple sclerosis (n=707) Residual deficit from the first relapse Relapse rate during the first year of multiple sclerosis Disease form at end of follow-up Treatment period Type of drug intake during follow-up a Kaplan-Meier estimated median with 95% confidence interval. b Comparison of survival curves using Log rank test. n.a: not assessable. Number of patients Number of patients to reach EDSS 6 Kaplan-Meier estimated median time to EDSS 6 from onset of multiple sclerosis a Female (23.8%) 23.0 [21.5 ; 28.8] Male (34.3%) 23.0 [16.5 ; 24.4] <20 years (23.5%) 33.0 [31.0 ; 36.0] 20 to <30 years (27.3%) 22.3 [20.7 ; 28.7] 30 to <40 years (29.9%) 18.0 [16.0 ; 21.4] 40 years (21.9%) 15.3 [12.3 ; 22.7] Isolated long tracks (26.3%) 22.3 [20.0 ; 27.3] Isolated brainstem (31.3%) 23.0 [21.0 ; 28.8] Isolated optic neuritis (30.4%) 22.1 [18.0 ; 27.1] Combined symptoms (21.5%) 30.7 [20.0 ; n.a] No (26.0%) 22.8 [21.0 ; 27.3] Yes (31.5%) 19.5 [16.1 ; 28.7] < (32.0%) 21.0 [19.5 ; 28.8] (19.8%) 22.8 [21.4 ; 28.7] Relapsing-remitting form (8.6%) 35.0 [27.1 ; n.a] Secondary progressive form (52.5%) 19.5 [17.0 ; 21.0] First treatment before EDSS (17.7%) 22.3 [20.0 ; 35.0] First treatment after EDSS (37.7%) 22.3 [20.0 ; 25.0] Only immunomodulatory drugs (6.7%) n.a Only immunosuppressive drugs (37.2%) 21.0 [19.5 ; 22.8] Both immunomodulatory and immunosuppressive drugs (29.4%) 22.3 [17.0 ; 31.5] P-value b 0,023 <10-3 0,442 0,035 0,029 < <10-3

9 Table 3: Results from the 3 multivariate survival models on the time to reach irreversible EDSS score of 6 from multiple sclerosis onset in the 759 MS patients Hazard ratio estimates with bcox model a Hazard ratio estimates with tcox model b Hazard ratio estimates with PWP model c Female Sex Male 1.14 [0.85 ; 1.52] 1.03 [0.76 ; 1.41] 1.07 [0.95 ; 1.20] P-value <20 years to <30 years 1.49 [0.95 ; 2.32] 1.09 [0.68 ; 1.74] 1.42 [1.19 ; 1.69] Age group at onset of 30 to <40 years 2.41 [1.49 ; 3.89] 1.56 [0.94 ; 2.59] 1.60 [1.32 ; 1.93] multiple sclerosis 40 years 3.71 [2.03 ; 6.79] 1.90 [1.00 ; 3.58] 2.06 [1.64 ; 2.57] P value < <10-3 No Residual deficit from the Yes 1.16 [0.80 ; 1.70] 1.04 [0.70 ; 1.56] 1.03 [0.87 ; 1.20] first relapse P value Relapse rate during the < first year of multiple [1.14 ; 2.11] 1.28 [0.93 ; 1.77] 1.31 [1.17 ; 1.47] sclerosis P value <10-3 Relapsing-remitting form Disease form at end of Secondary progressive form 2.89 [1.98 ; 4.20] 9.24 [6.29 ; 13.59] 1.26 [1.07 ; 1.47] follow-up P value <10-3 <10-3 <10-3 First treatment before EDSS Treatment period First treatment after EDSS [0.82 ; 1.53] 1.25 [0.90 ; 1.72] - P value No treatment n.a 1 1 Only immunomodulatory drugs [0.99 ; 2.57] 0.89 [0.74 ; 1.07] Type of drug intake Only immunosuppressive drugs 2.06 [1.17 ; 3.60] 2.05 [1.48 ; 2.84] 0.94 [0.81 ; 1.08] during follow-up Both immunomodulatory and 2.28 [1.26 ; 4.12] n.a n.a immunosuppressive drugs P value < from EDSS 1 to [0.51 ; 0.87] from EDSS 2 to [0.63 ; 1.09] Treatment Hazard Ratio at each EDSS step d from EDSS 3 to [0.77 ; 1.29] from EDSS 4 to [0.79 ; 1.40] from EDSS 5 to [0.96 ; 2.03] a Hazard ratio estimated with 95% confidence interval using a conventional Cox model. b Hazard ratio estimated with 95% confidence interval using a Cox model with time-dependent covariate. c Hazard ratio estimated with 95% confidence interval using a Prentice, Williams and Peterson model. d All confounded treatment hazard ratio estimated with 95% confidence interval using a Prentice, Williams and Peterson model (reference: no treatment). n.a Not assessable.

10 TABLE 4: Assessment of the proportional hazards hypothesis in the 3 multivariate survival models, for the whole model and for each covariate bcox model a tcox model a PWP model a Sex (ref: Female) Male Age group at onset of multiple sclerosis (ref: < 20 years) Residual deficit from the first relapse (ref: No) Relapse rate during the first year of multiple sclerosis (ref: < 2) Disease form at end of follow-up (ref: Relapsing-remitting form) 20 to <30 years to <40 years years Yes <10-3 Secondary progressive form Treatment period (ref: First treatment before EDSS 3) Type of drug intake during follow-up (ref : Immunomodulatory drugs) First treatment after EDSS Only immunosuppressive drugs Both immunomodulatory and immunosuppressive drugs Immunomodulatory drugs b immunosuppressive drugs b Global test a P-value of the proportional hazards test b Reference value: No treatment

11 FIGURE 3: Cumulative hazards logarithms plot for the 4 covariates fitted to the PWP model and with a significant proportional hazards test Graph relating to the presence of residual deficit after the first relapse (A), the relapse rate during the first year of multiple sclerosis (B), the clinical form of multiple sclerosis (C), the type of drug intake during follow-up (D).

12 FIGURE 4: Smooth scatter plot (scaled Schoenfeld residuals + β plotted against time) for the 4 covariates fitted to the PWP model and with a significant proportional hazards test Graph relating to the presence of residual deficit after the first relapse (A), the relapse rate during the first year of multiple sclerosis (B), the clinical form of multiple sclerosis (C), the type of drug intake during follow-up (D).

13 DISCUSSION: Master 2 Modélisation en Pharmacologie Clinique et Epidémiologie In this study, we built three statistical models to address difficulties regarding analysis of MS, particularly regarding analysis about periods of drug intake. We included into analyses the overall traditional prognostic factors of MS, looking specifically their behaviour over time. None of our three models found a significant role of gender and incomplete remission from the first relapse, while they are factors typically found in the literature 4,5,24. It is likely that our results were a reflection of analyses with the inclusion of adjustment between covariates. We showed that patients with an incomplete remission after the first attack had a more advanced age of MS onset (p: 0.003), and that proportion of the secondary progressive phenotype was higher among men than women (p: ). We may conclude an advanced age at MS onset and a high annual relapse rate might play a pejorative role in the disability progression, and gender and degree of remission probably only play a marginal role; in so far as age at MS onset and number of relapses during the early phase of MS, are described as relevant prognostic factors in the literature and our conclusion are comforted by the consistent results of the three models too. Nevertheless, a very recent and complete analysis of MS prognostic factors with the same MS database showed significant and independent impact of gender and residual deficit from the first relapse 5. We could give a start of explanations to understand this difference. The previous study analysed prognostic factors for the whole patients with relapsing onset MS, whether or not they were treated (more than 1600 patients), while our analysis was only performed on 759 treated patients. However, our objectives were not the same: we did not study prognostic factors of MS but impact of treatment periods on MS progression, which justified our selection criteria. The multivariate analysis performed in the previous study was conducted separately for early and late stage of MS using two Cox models 5. It is a very good strategy for analysing disease with several progression stages, as it seems to be emerging for MS 10,25,26. However, in the context of our present study, this strategy could not be introduced for two reasons: firstly, because the study objective was to examine factors comprising the two stages and secondly, because separated analysis could not explore impact of factors throughout the global MS process; hence we needed to introduce and study time-dependent covariates and effects into survival models. The most important and original results of this previous study 5 were factors influencing disability progression were restricted to relapsing onset multiple sclerosis during the early phase of the disease. This finding confirmed other results on the whole multiple sclerosis population 2,4,24,27 and finally, MS prognostic factors comprised gender, age at multiple sclerosis onset and relapse history (relapses within the first 2 years, and residual deficit after the first relapse). We do not question veracity of these prognostic factors in our study and that is why we have chosen to maintain the non-significant covariates into our three statistical models. One main interest of our study was to account for time-dependent covariates into survival analysis of MS, i.e. covariates that take into account change in exposure of patients during their follow-up. From this overall definition, two types of time-dependent covariates can be defined: covariates with unique change, and covariates with multiple changes 9. Secondary progressive phenotype could be considered as a time-dependent covariate with unique change. The three models used for our study found a pejorative role of conversion to SP but estimations differed from one model to another (HR respectively equal to 2.9, 9.2, and 1.3 with bcox, tcox, and PWP models). We think that conversion to SP reflects disease progression as disability increase, and that it is likely to skew estimates. In our opinion,

14 accounting for time with a Cox model for this covariate introduced a systematic bias that may explain the very high HR found with the tcox model. However, it is mostly a general limit of Cox model to study prognostic factor related to model event than a limit related to timedependent counting process. So, we think PWP model was more suitable to estimate effect of SP phenotype: patient follow-up was split in several ways that it allows a risk-estimate at each EDSS step. Evaluation of MS therapies was performed differently according to the model used. Cox model needed two covariates to represent all aspects related to treatment. Period of the first drug intake has been considered as a fixed covariate since start of patient follow-up, while the drug intake (and the kind of drug) has been defined as a time-dependent covariate with multiple changes during follow-up. PWP model allows factor estimates at each stratification of events, so the model allowed DMT impact to be estimated at each MS disability step in our context. A paradoxical effect of drug intake was found with bcox and tcox models. It seems to be another illustration of Cox model limits in this topic. It was difficult to compare results from models with different reference values, but both bcox and tcox models found pejorative effects of treatment, while the PWP model found a protective effect of immunoactive drugs. These results were not always significant and should be interpreted with caution; nevertheless PWP model could be more appropriate for estimating drug outcomes. We assume stratification according to EDSS steps may play an important role in this capacity, as with conversion to SP. A pejorative effect of the late first drug intake was found with both bcox and tcox models, but these estimations remained no significant. The PWP model confirmed this trend by a significant protective effect of drugs intake estimated at the first step of disability, however, insofar as the overall estimates of treatment impact on the time progression of disability was not significant it is not possible to really conclude that to act effectively during the early stages of the disease has an impact on the global time progression of MS disability. It is difficult to conclude about impact of DMT and drug intake period in this work, but it seems DMT of MS are more effective in early disease process. Several clinical trials recently found significant effective immunoactive therapies on disability progression, but these results were frail, in so much as they were identified only on very short periods. As far as we knew, there is no evidence of a real long-term efficacy of immunoactive drugs on MS disability progression 6,28. Some recent pathophysiological arguments could explain DMT to be apparently ineffective and we refer to reading these some paper discussions for more details 5,29. Concerning biostatistical models, classical time counting process into Cox model failed to estimate impact of time-dependent covariates of MS as drug intake or SP phenotype. Counting process of time-dependent covariates seems to bias estimations of the Cox models in our context, because of both disability and the two concerned exposure factors are indicators of the disease progression. In this issue, PWP model appears more appropriate. A second interest of the study concerned covariates with time varying effect. No significant deviation to PH assumption was found with both Cox models, while four covariates (residual deficit after the first relapse, high annual rate of relapses, phenotype and type of treatment) significantly deviate to PH assumption with the PWP model. We think, and it is exemplified by graph of β (t), that these significant deviations from proportional hypothesis mainly reflect the increased test power, consecutively to number increase of the Schœnfeld residuals. Only effect of relapse rate clearly graphically decreases with time, and a high rate only seems to have a pejorative impact on MS with rapid disability progression.

15 As other studies have shown 4,5,27, most known prognostic factors of MS have time-varying effect, including age at MS onset, gender and number of relapses during the first years that would only affect time progression of the early phase. With deviation to the PH assumption, interpretation is a little different: time-varying effect depend on velocity of the disease progression, i.e time to reach EDSS6. The study population included patients with relapsing onset MS followed at the MS clinic of Rennes. Only patients at least once treated by DMT were selected, as our objective was to assess efficacy of early or late drug intake on long-term disability progression. Untreated patients should have different characteristics than treated ones, which imply potential selection bias of our study population hence a natural course of MS a few different than general population of MS patients. Compared with the whole database of the 2054 MS patients of Rennes 11, we found treated patients were younger at MS onset (p: 0.001). We also found patients with an annual rate of relapses greater than or equal to 2 (p: <10-3 ) and patients with a SP form (p: 0.016) were more numerous into our study population. These results confirmed our initial hypothesis that treated patients had an early worse evolution of MS that led neurologists to start DMT drugs. So, it became difficult to consider these two MS populations the same way, for example it was not possible to compare two periods of no drug intake in the same way for the treated population and the never treated population. Moreover, with an average time to EDSS 6 equal to 15 years, disability progression of the study population was similar in times to MS natural course of others studies and the population also kept traditional characteristics of MS patients 1-3. So, our selected study population represented a more homogeneous population without than with untreated patients who did not provide any additional relevant information about the main objective of the study, particularly the impact study of early or late treatment period. To conclude, this work assumed that decrease of the disability progression at the MS early stage could impact the overall disease progression. Our results do not highlight any significant long-term protective effect of early DMT intake, however analysis of the three models tends to show patients with a late treatment start would have a more pejorative global evolution. In the context of MS disease, it should be distinguished two kinds of time-dependent variations related to prognostic factors of MS: covariates with time-varying exposure and covariates with time-varying effect. A specific time counting process allow to introduce timedependent covariates into Cox model, but we have seen Cox model with time-dependent covariates remains inadequate to study certain prognostic factors; Inclusion of time-dependent covariates allows precise exposure value to be accounting for, but some ones may remain conceal; A persistent effect after exposure stop (e.g. after the treatment stop) could not be even accounted for; study of PH assumption allow detecting deviation and time varying effect, however none of the presented models is able to correctly respond to this problematic. We have demonstrated with this work that it is essential to take into account context and disease pathway for statistical analysis, and that statistical methods strongly depend on the clinical situation is being studied. For instance with our current point of interest, abandoning the PH assumption and as such the Cox model might be an option to study drug intake (in multiple sclerosis) in order to address the limitations of models as they were just described above

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