Chair of Medical Statistics and Epidemiology, Department of Statistics, University of Milan,
1 Division of Gastroenterology, Unit of Alcohology, Mauriziano Umberto I Hospital, Turin,
2 Division of Internal Medicine, Unit of Alcohology, Saint Orsola Hospital, Bologna,
3 Department of Internal Medicine, School of Medicine, Catholic University, Rome and
4 Service of Psychology, Salvatore Maugeri Foundation, Pavia, Italy
Received 30 October 1998; in revised form 8 March 1999; accepted 4 May 1999
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ABSTRACT |
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INTRODUCTION |
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Many outcome measures proposed in the literature, such as the cumulative abstinence duration (CAD) (Lehert, 1993; Plinius Maior Society, 1994
; Whitworth et al., 1996
; Favre et al., 1997
), are considered as explicit and general treatment objectives. Although abstinence is not necessarily always the only goal of a treatment programme, monitoring abstinence and relapses allows comparison of different therapeutic approaches. This is particularly true under conditions of identical compliance of patients admitted to the treatment programmes. In fact, the unreliability of information on alcohol-intake behaviour of patients who withdraw from therapy limits the possibility of comparing compliant with withdrawn patients and of comparing different approaches under conditions of different compliance.
Compliance, as a proxy measure of the effectiveness of a therapeutic project, does not necessitate an enquiry into alcohol-intake behaviour (Aricò et al., 1994). However, a high degree of compliance does not necessarily reflect the ability of the therapeutic approach to avoid relapse or to maintain abstinence.
There is thus a need to explore more complex procedures, including both alcohol-intake behaviour and compliance with treatment. The aims of our contribution were: (1) to provide guidance to treatment programmes which require self-evaluation; (2) to advance knowledge of the relationship between alcohol-intake behaviour and participation in treatment; (3) to present the use of survival analysis in this setting. For these purposes, we have used data from the ongoing Assessment of Alcoholism Treatment (ASSALT) project. This is an observational prospective study involving 270 alcoholics admitted to 15 alcoholism treatment units throughout Italy in a 1 year period and followed up for 2 years.
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METHODS |
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Follow-up details
A standardized form reporting information about alcohol-intake behaviour and compliance to treatment was compiled for each patient by the ATU staff every 3 months for 2 years from the start of treatment. Information was collected from the treatment registry of the unit, from other units, from other health services and/or self-help groups, directly from the patient, and from his/her relatives. When a patient had withdrawn from treatment or was lost to follow-up, s/he was contacted by telephone or directly at home 2 years after entry and information was collected directly from the patient, and/or from relatives.
Days of abstinence, number and duration of the relapse episodes, compliance to, and causes of withdrawal from, treatment were recorded for the whole 2-year follow-up period. A relapse episode was defined as any interruption of abstinence, and its length was measured by the number of continuous days of alcohol consumption from the start of the episode. Transitory and definitive interruptions of treatment were defined as withdrawal for at least 1 month, then respectively followed or not followed by re-establishment of the planned therapeutic project. Reasons for treatment interruption were classified either as refusal to participate in the therapeutic project (withdrawal for refusal) or as other factors independent of the patient's will (e.g. death, hospitalization, imprisonment, institutionalization: unintentional withdrawal).
Outcome variables
Four types of outcome variables were independently assessed. The first one is represented by recurrence and the other three by withdrawal from treatment. The specifications on definition of failure, of censoring and of the considered covariates are reported in Table 1.
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For the withdrawal-failure type analyses, the length of time between the start of the treatment and the first (model 2) or the definitive (model 3) episode of withdrawal for refusal was considered. For each failure type, a variable named cumulative proportion of abstinence duration (CAD) was calculated as the ratio of the number of days of abstinence before withdrawal (or censoring) and the number of days between the start of treatment and occurrence of the specific failure (or censoring).
Since compliance can change over the course of the observation period, so that a patient can interrupt and subsequently resume the treatment programme, a special survival analysis procedure, namely survival analysis for repeated events, was applied to measure the strength of association between CAD and the risk of each episode of withdrawal (model 4). A number of observations was generated for each patient equal to the number of treatment resumptions, so that the analysis was performed with reference to treatment cycles, rather than to patients (such as for the previously described analyses).
Survival analysis techniques
The cumulative proportion of patients free from the first episode of relapse or of withdrawal was estimated by the product-limit method. Subsequently, several extensions of the basic Cox's proportional hazard model were used to estimate the strength of association between CTD (or CAD) and the risk of failure (recurrence or withdrawal).
Firstly, we reasoned that CTD and CAD are time-dependent variables, since the duration of both received treatment and abstinence may change over the course of observation time. Thus, all the models were fitted considering a time-dependent covariate as the explanatory variable (Kalbfleisch and Prentice, 1980).
Secondly, we noticed that the 15 ATUs differed for the values of both CAD (explanatory variable) and the risk of withdrawal (failure). Under these conditions, the ATU may be considered as confounding the effect of the explanatory variable on the risk of failure. On the other hand, we also noticed that withdrawal rates were not proportionally distributed over time among the ATUs. In fact, in some units several early withdrawals occurred, whereas in other units later failures were observed. This is the classical situation in which adjustment should not be performed by modelling the confounder as a covariate, since the assumption of proportionality of the hazard functions among the levels of confounding is likely to be violated. Thus, all the models were fitted considering the ATU as a stratification variable in order to obtain adjusted estimates unaffected by time-interacting covariates (Marubini and Valsecchi, 1995).
Thirdly, when the model was fitted including as the unitary observation every treatment cycle, several observations could be referred to a particular patient, so that the basic assumption that each observation was independent from each other was systematically violated. We used the method proposed by Wei et al. (1989), correcting the estimates for dependence among multiple event times. The advantage of this technique (known as the WLW method, but also described as marginal or population-averaged method) is that there is no need to make assumptions about the nature or the structure of the dependence. Larger confidence intervals are expected when adjusting coefficients for dependence.
For all the considered models, the parameters and the corresponding standard errors were estimated by maximizing the logarithm of the partial likelihood function (Kalbfleisch and Prentice, 1980). The likelihood ratio test (LRT) was performed to evaluate whether the covariates explained a significant portion of the risk of failure. LRT has asymptotic
2 distribution with degrees of freedom (df) equal to the number of estimated parameters (Collett, 1994
).
The corresponding calculations were carried out using the Statistical Analysis System (SAS) package (Allison, 1995). For all hypothesis tests, P < 0.05 was considered as significant.
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RESULTS |
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The cumulative proportions of abstainers and of compliant patients during follow-up are shown in Fig. 1. The cumulative proportions of abstainers [and the corresponding 95% confidence interval (CI)] were 58% (5264%), 48% (4255%) and 45% (3951%) after 6 months, 1 year and 2 years from the start of treatment respectively. The cumulative proportions of compliant patients (and the corresponding 95% CI) were 71% (6676%), 63% (5769%) and 53% (4760%) after 6 months, 1 year and 2 years from the start of treatment respectively.
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DISCUSSION |
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The clinician who wants to offer a treatment to his alcoholic patients should have information on the probability that different kinds of failure might occur during treatment. The crucial issue in the monitoring strategy is the a priori choice of the failure events. The characteristics of the patients and of the therapeutic project that might modify the response must be carefully considered. The final goal is to know which is the best treatment for the individual alcoholic patient.
The ASSALT project has been designed as a natural experiment involving the planned observation of the usual therapeutic activity of the alcoholism treatment units who voluntarily agreed to participate in the project (Treatment Evaluation Group of GESIA, 1994). Comparison of the treatments' effectiveness between alcoholism units and/or between different therapeutic approaches was not suitable, however, by the observational design of the study, in the absence of a random allocation of patients into different therapeutic approaches (Plinius Maior Society, 1994). Moreover, the results of the ASSALT project cannot be generalized to the population of alcoholics treated in Italy since a selected group of the more motivated and better-organized alcoholism units has voluntarily participated in the project.
Despite these limitations, the observational approach of the ASSALT project is the most rational tool for characterizing and monitoring alcoholics and for identifying factors associated with the risk of failure of the therapeutic project. However, only questions regarding the choice and the statistical management of the outcome variables were addressed here. Since the observational approach of the ASSALT project can be considered as a realistic simulation of the usual therapeutic activity of an alcoholism unit, these questions are not restricted to this specific project. It has been stated that, since the basis for selection and timing of interventions in observational studies is not precisely specified, sophisticated statistical analyses are necessary to attribute to a specific cause the success (or the failure) of a therapeutic programme (Bull and Spiegelhalter, 1997). Survival analysis is a powerful and versatile tool widely used in several fields to study the occurrence and timing of different kinds of events. Surprisingly, it has found rare applications in the monitoring of alcoholics during treatment (Fuller and Willford, 1980
; Aricò et al., 1994
). The main reason why survival analysis seems particularly suitable in this field is that treatment of alcoholics can never be considered wholly successful. In other words, all the observations are necessarily right-censored and survival analysis is particularly suitable in the statistical treatment of censored data.
In this paper, several survival analysis techniques have been used and particular attention has been given to the putative response variables. This is a crucial point in planning prospective observational studies for which survival analysis techniques are suitable. The strict pre-definition of the outcome variables and of their putative determinants should be made on the basis of the characteristics of treatment programmes, but also considering the realistic possibility to collect and to define reliable response data.
In a first approach, the length of time between the start of treatment and first episode of relapse was explored as the cardinal variable. Using this variable as the outcome in a survival analysis model, it is possible to describe the alcohol-intake behaviour of patients over time, rather than only at the end of observation. However, the first episode of relapse is not informative about treatment failure. In fact, an early relapse episode followed by abstinence may be considered as a good result by many clinicians. We observed that patients with lower compliance to treatment paradoxically showed significantly lower risk of relapse in the use of alcohol. One might think that this unexpected result means that shorter interventions could be more effective in obtaining abstinence than intensive treatments. However, all the therapeutic projects considered here were planned as long-term interventions. Another theoretical possibility is that patients with moderate or slight severity of alcohol dependence were less motivated to comply with treatment and more likely to be abstinent after withdrawal. In other words, severity of alcohol dependence might be considered as a confounding variable of the effect of compliance on the risk of relapse. However, since similar results were observed independently from severity of alcohol dependence, this possibility also seems unlikely. We suspect therefore that the unexpected result is explained by the questionable reliability of data on alcohol-intake behaviour of patients withdrawn from the treatment. In fact, while self-reported alcohol-intake behaviours during treatment were always comparable with those referred by operators, only self-reported and unverifiable information was available after withdrawal. Under these conditions, the estimate of the proportion of abstainers over the time can be considered biased and cannot be used as an indicator of success of the therapeutic project. We cannot state the generalizability of this finding in settings different from that considered here, but we suspect that this is a problem common to many multi-centre data-bases.
These considerations justify the second approach used here, where the length of time between start of treatment and its withdrawal was considered as the cardinal variable. The estimate of the cumulative proportion of patients compliant to treatment is realistically unbiased, since all cases of treatment interruption were captured. In correlating this new outcome variable with alcohol-intake behaviour, two problems should be considered. Firstly, since validity of information is questionable after withdrawal from treatment, alcohol-intake behaviour should be considered only in the period in which the patient is in treatment. This recommendation is also justified by the observation that a lower goodness-of-fit of the model was obtained when considering as the outcome the definitive episode of withdrawal, rather than the first one. This could be explained by the fact that periods free from treatment (and therefore characterized by less reliable data on alcohol-intake behaviour) are also included in this case. Secondly, we can reasonably assume that the period of observation is strongly associated with abstinence duration. The longer the period of observation, the more likely the relapse. Thus, variables nominally similar to CAD should be considered as time-dependent covariates. Considering these two aspects in a model of proportional hazards, we observed, as expected, that patients with a lower proportion of abstinence duration during treatment showed a significantly higher risk of withdrawal. These findings suggest that the relationship between recurrence and treatment withdrawal should be considered as a realistic and accurate tool for monitoring treatment.
Survival analysis is able to take into account that some individuals experience more than one failure event during the follow-up period (repeated events analysis). This is the case for patients with more than one withdrawal, each followed by resumption of treatment. In our series, we did not observe a better fitting for the model that considers repeated events in comparison with the conventional model. This is likely to be due to the adjustment for the lack of independence between observations that lead to increasing standard errors of the estimates (Wei et al., 1989). The small number of patients (21) with intermittent treatment is also likely to be involved in this result. However, since intermittence in treatment increases at increased periods of observation, the usefulness of repeated events analysis should be explored for a longer duration of observation.
A crucial problem in the application of survival techniques to analyse data from observational studies is the adjustment for confounding variables. In fact, since patients are not randomly assigned to treatments, several variables associated both with the covariate of interest and with the response variable might confound the observed effect. This typically occurs for the centre, in multi-centre data-bases, but also for several characteristics of the patients, such as demographic and social co-ordinates and initial severity of dependence, that might act as confounders. Proportional hazards models are able to adjust the estimates of interest for the effect of confounding, but several cautions in the choice of the adjustment method are needed.
In conclusion, this first application of survival analysis techniques to the combined study of alcohol-intake behaviour and of adherence to treatment for alcoholics can improve our knowledge on treatment evaluation. The availability of statistical packages allows an easy application of these techniques to the analysis of data. Furthermore, our results suggest that compliance to treatment is an objective and versatile outcome measure in monitoring alcoholics' treatment. The high risk of withdrawal for patients who are not able to maintain abstinence suggests that compliance could be considered as a proxy variable of a treatment's success. Long-term follow-up studies to elucidate the determinants of withdrawal should be performed.
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ACKNOWLEDGEMENTS |
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FOOTNOTES |
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Assessment of Alcoholism Treatment Group: Co-ordination: G. Corrao (Milano); I. Giorgi (Pavia). Design: Epidemiological and statistical aspects: G. Corrao (Milano). Psychological aspects: I. Giorgi (Pavia) and D. Orlandini (Mestre, Venezia). Internal medical aspects: G. Vittadini (Pavia); Psychometric aspects: G. Vidotto (Padova). Supervision: G. Gasbarrini (Roma). Management: A. Zambon (Milano); O. Omodeo (Pavia). Collaborative group: M. Sforza, I. Alunno Serpini (Casa di Cura Le Betulle, Appiano Gentile), L. Piloni, C. Brambilla, L. Toniolo (Servizio Tossicodipendenze e Alcolismo, Bassano del Grappa), M.T. Salerno, T. Radicione, A. Erbi (Università, Bari), A. Noventa, M. Mortella, M. Riglietta (Servizio Tossicodipendenze, Bergamo), G. F. Stefanini, F. Caputo, C. Dall'Aglio (Ospedale Sant'Orsola, Bologna), A. Allamani, M. C. Sarni (Ospedale Careggi, Firenze), A. Lucchini, M. Torriani, C. Biscaro (Servizio Tossicodipendenze, Gorgonzola), E. Ferrari, N. M. Lopez, M. Studer (Nucleo Operativo Alcoldipendenze, Lodi), G. Fiorelli, T. M. De Feo, C. Viganò (Università, Milano), F. Madeddu, M. G. Movalli, S. M. Angelone (IRCCS San Raffaele, Milano), C. Malandrino, P. Burra, D. Mioni (Università, Padova), P. P. Vescovi, C. Di Gennaro, C. Giuffredi (Università, Parma), A. Albergati, D. Soragna, P. Bo (Fondazione Istituto Neurologico C. Mondino, Pavia), G. Belfiore, A. Bianchi, D. Bencivenni (Ambulatorio Alcologia, Pavia), G. Vittadini, O. Nervi, O. Omodeo (Fondazione S. Maugeri, Pavia), G. Cerizza, P. Rapuzzi (Nucleo Operativo Alcoldipendenze, Rivolta D'Adda), M. Salvagnini, P. Dotto (Ospedali Sandrigo e Vicenza), D. Agostini, N. Moroni, C. Lenci (Casa di Cura Villa Silvia, Senigallia). The order of authorship in the paper was designated by the following criteria: (a) the first author has taken principal responsibility for organizing and writing the research work and for the epidemiological and statistical aspects; (b) second and third authors have collaborated with the first author in the statistical treatment of the material and have developed the software for his management; (c) the remaining authors have reviewed the paper and its findings in accordance with accuracy and representation of their data and project goals; (d) all the participants of the ASSALT group are cited above according to their role in the project.
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