A note on Australian AIDS survival

Transcription

1 A note on Australian AIDS survival B.D. Ripley 1 and P.J. Solomon 2 1. Department of Statistics, University of Oxford, 1 South Parks Road, Oxford OX1 3TG, UK 2. Department of Statistics, University of Adelaide, South Australia, Australia Address for correspondence: Dr P.J. Solomon, Department of Statistics, University of Adelaide, Australia 5005

2 Abstract Understanding factors important for AIDS survival is crucial for planning and modelling. In this article, we present the results of a registry-based study of the survival of Australian residents diagnosed by July 1991 and reported by January We fit semi-parametric Cox models incorporating temporal trends associated with changes in the Australian Government s treatment policy for HIV/AIDS, and other available covariates. We also describe a special study of age effects, and demonstrate the power of sophisticated statistical analyses to provide insight into complex data that may be missed by a more naive analysis. We find a significant reduction in the hazard of death associated with the widespread introduction of zidovudine into clinical practice in mid-1987 for people with advanced HIV disease. The Australian Government s treatment policy was broadened in August 1990 to make zidovudine available to people whose CD4 cell/mm 3 counts persist below 500, but there was no further change in the hazard associated with the policy change. People infected via heterosexual contact have significantly improved survival over homosexual/bisexual males, whereas people with haemophilia have significantly poorer survival. Queensland has a significantly increased hazard over that for New South Wales, the largest Australian state. The very young have a greatly increased hazard of death, which increases steadily from about aged two years at diagnosis to 75 years, followed by a sharp increase. We find no real evidence that the survival of people infected via contaminated blood or blood-products decreases with age. A parametric analysis suggests that an exponential survival distribution is reasonable and that the baseline hazard is constant. This may provide insight into underlying trends in the disease process. Key words: Australian AIDS survival nonstationarity, treatment effects, age effects; Cox model; Weibull survival model. 1

3 1 INTRODUCTION It is important that we understand factors affecting the survival of people with AIDS. Its importance stems from the evolving definition of AIDS which has implications for defining and estimating the incubation distribution. It is also important for health-care planning, predicting deaths and prevalence of AIDS, and for providing accurate information to people with HIV disease. As our knowledge of some features of the epidemic, such as HIV prevalence, increases, our knowledge about the incubation distribution is increasingly uncertain (1). Incubation for AIDS is believed to depend, at least in part, on treatments, age and possibly diseases at diagnosis. Understanding factors associated with AIDS survival can therefore provide crucial information about the pattern of disease from initial infection to death. The purpose of this note is two-fold. Firstly, we describe the results of our recent study of Australian AIDS survival up to Using a time-dependent Cox model, we investigate covariates related to survival and incorporate temporal trends associated with changes in the Australian Government s treatment policy. We also present a special study of age effects. Secondly, we demonstrate the power of sophisticated statistical analyses in providing insight into factors important for survival that may be missed by a more naive approach. 2 METHODS 2.1 The data There were 2,843 Australian AIDS cases diagnosed prior to 30 June 1991 and reported to the National Centre in HIV Epidemiology and Clinical Research in Sydney, by 31 January The first case was diagnosed in December 1982 and by the study s endpoint, 1,787 of the 2,843 individuals had died. The HIV epidemic started in New South Wales and spread to Victoria, followed by Queensland and then the smaller States and Territories. NSW and Victoria are the first and second largest Australian states. There is considerable regional variability in the epidemic in Australia, but otherwise the pattern of spread amongst the population is typical of socalled Western countries, where the majority of AIDS cases have been seen amongst men who have sex with men, and more recently amongst injecting drug users. However, there have been relatively few cases in this risk group in Australia compared with other countries. Yearly AIDS incidence for the three largest Australian States and the remainder are shown in Figure 1. In all 29 patients were diagnosed with AIDS after death and therefore have zero survival times. Most of these cases occurred early in the epidemic when AIDS was still being recognised and are disproportionally distributed amongst the transmission categories: 22 of the cases were homosexual/bisexual males, 6 were infected by blood transfusions or blood products, and one case was an infant with an infected mother. 2.2 Data quality AIDS is a notifiable disease in all States and Territories of Australia, and the data are therefore believed to be relatively complete compared with other countries. However, we adjusted the endpoint of the study by six months since there are some delays in death notifications, and to a lesser extent, delays in reporting of AIDS cases. The delay between diagnosis of AIDS and reporting is variable, which can be seen in figures published regularly by the NCHIVECR. But reporting delay data are available 2

4 NSW VIC QLD Other Figure 1: Annualized yearly AIDS incidence by state in Australia. only for the recent past, and are not collected or entered into the database in a systematic way. Direct modelling of the reporting delay distribution is therefore unlikely to be fruitful. Under-reporting of AIDS is believed to be of the order of 15% (2). The quality of the death data is less certain and there is no recent published information on this, although some death certificate checking is undertaken. The implications of delays in death reporting, as well as of under-reporting, for estimating survival probabilities have been discussed recently in the Australian context (3). The national database does not identify non-aids deaths, so that all deaths are assumed to be AIDS deaths for the purposes of the present analysis. Survival time is calculated as the number of days between a diagnosis of AIDS and death or 30 June 1991, whichever is the sooner. The covariates available to us are sex, age at diagnosis, reported transmission category, State or Territory of diagnosis, and information on the availability of zidovudine in Australia. 2.3 The model and analysis We begin with a time-dependent Cox model (4,5) which includes all the available covariates. We refer to this as the full model. Detailed descriptions of the covariates now follow. state or Territory of diagnosis: The Australian Capital Territory is a small enclave within NSW and is combined with NSW for the purposes of our analysis. The States and Territories are then 3

5 NSW New South Wales and Australian Capital Territory VIC Victoria QLD Queensland WA Western Australia SA South Australia TAS Tasmania NT Northern Territory. Each State or Territory is compared to NSW. trans The transmission categories are: hs male homosexual or bisexual contact hsid as hs and also intravenous drug user id female or heterosexual male intravenous drug user het heterosexual contact haem haemophilia or coagulation disorder blood receipt of blood, blood components or tissue mother mother with or at risk of HIV infection other other or unknown. Here the baseline for comparison is the male homosexual or bisexual contact group. Temporal effects The Australian AIDS survival experience shows significant nonstationarity. A dramatic improvement in survival coincided with, although may not be entirely attributable to, the widespread introduction of zidovudine into clinical practice in mid-1987 (6), and the increased use of prophlyactic treatments for opportunistic infections. Early clinical trials (7) established that ZDV considerably enhances the survival of people with AIDS. Later evidence (8) suggested that taking ZDV during the symptom-free period might delay the onset of an AIDS-defining illness. On the basis of these findings, the Australian government amended its treatment policy in August 1990 to make ZDV available to people whose CD4 cell counts per mm 3 persist below 500. The results of the recent Concorde trial (9) have again thrown open the question of the effects of anti-retroviral treatment on the symptomfree period, and we pursue this point further in the Discussion. We have modelled directly the observed nonstationarity in AIDS survival by allowing a proportional change in the hazard from 1 July 1987 to 30 June 1990 (zdv1(t)) and another from 1 July 1990 (zdv2(t)). These time-dependent covariates represent temporal changes in survival on a population basis. Detailed data on individual ZDV use are not available to us. The full Cox model includes the covariates described above as well as sex (male = 1, female = 0) and age in years at diagnosis. The hazard is then h(t; Z()) = h 0 (t) exp( 1 sex+ 2 age + 3 state + 4 trans + 5 zdv1(t) + 6 zdv2(t)); (1) where h 0 (t) is the baseline hazard, Z() is the covariate vector and 3 and 4 are vector parameters. Using a stepwise regression procedure based on the partial likelihoods, we obtained as parsimonious a Cox model as possible. We call this the reduced model. In addition, we compared the results of the Cox model with a parametric Weibull survival model. 4

6 Special study of age effects Age is known to be important for survival, with the very young and very old having relatively poor prognoses. We examined linearity in the hazard of death with age by examining the martingale residual plot in the first instance. We then split the data into six age groups as shown below and re-fitted the reduced model. The knots were chosen from prior experience, giving numbers in each group of In each case the baseline for comparison is the year-old group, and we compared the results from both the Cox and the parametric Weibull models. We then went on to consider parametric nonlinear functions of age using a spline function. The blood-transfusion and blood-product data are quite different and should be considered separately. We investigated the question of whether the survival of patients infected via blood or blood products decreases with age by splitting the 139 patients concerned into for age groups: 0 20, 21 40, and 61+ and then fitting the Cox model including the time-dependent covariates zdv1(t) and zdv2(t). Computing The analyses were done using S-PLUS functions survival3 written by Terry Therneau (Mayo Foundation). Note that zero survival times are avoided by shifting the deaths by 0.9 days to occur after other events (i.e. deaths or censorings) on the same day. We used stratified Cox models to examine the separate effects graphically. The S-PLUS algorithms for the analyses described in this paper are contained in (10) where they are used for a disguised and simplified version of this data set, and the exact code used is available from the first author. 3 RESULTS Fitting the full Cox model (1) gives the regression estimates shown in Table 1. Sex is not a significant factor, with a relative risk for males of 1.01 (95% confidence limits (0.72, 1.41)). Age at diagnosis of AIDS is highly significant, although the increased relative risk of for each additional year is relatively slight (we explore the age effects in more detail later). Queensland, which is the third largest state following NSW and Victoria, has significantly poorer survival than NSW (95% c.i. for relative risk (1.00,1.41)). The survival trends in the other states are suggestive although not statistically significant. Figure 2 shows the relative survival pattern adjusted for the presence of the other covariates. The median survival time for Queensland is 1.15 years, compared with that for NSW of 1.31 years. The heterosexual transmission group has significantly improved survival over that of homosexual and bisexual males (the relative risk is reduced by more than half to 0.452, P -value 0.004) whereas people with haemophilia have a significantly increased hazard of death, corresponding to an increased relative risk of (P -value 0.04). Trends in survival by transmission category are shown in Figure 3. Injecting drug users also do better than homosexual and bisexual men, although not significantly, and children infected via a mother with HIV/AIDS, or people infected via blood or blood products (who are not haemophiliacs) do worse, although again not significantly. The hazard of death is reduced by half with the introduction of the first time-dependent covariate in mid-1987 and this effect is highly significant. However, there is no further 5

7 TABLE 1. Australian AIDS survival: results of fitting the full Cox model (1). Covariate ^ Standard error ^ exp( ^) P -value sex age ?6 state.nt state.qld state.sa state.tas state.vic state.wa trans.hsid trans.id trans.het trans.haem trans.blood trans.mother trans.other zdv zdv NSW QLD VIC months since diagnosis Figure 2: Survival curves for AIDS in Australia by state, adjusted for other covariates. change in the hazard with the introduction of the second time-dependent covariate in mid

8 hs hsid id het hs haem blood other months since diagnosis months since diagnosis Figure 3: Survival curves for AIDS in Australia by transmission category, adjusted for other covariates. Reduced model Since any effect of sex will be confounded with that of transmission category, we dropped sex from the model. Removing sex and zdv2, the difference in zdv at 1 July 1990, makes virtually no difference to the partial likelihood ratio statistic: on 17 degrees of freedom changes to on 15 df. A stepwise elimination procedure indicated that state could also be removed (likelihood ratio test on 9 df), which leaves the reduced model: h(t; Z()) = h 0 (t) exp( a age + T trans + z zdv1(t)): (2) Table 2 sets out the results of fitting the reduced Cox model. TABLE 2. Australian AIDS survival: results of reduced model (2). Covariate ^ Standard error ^ exp( ^) P -value age ?6 trans.hsid trans.id trans.het trans.haem trans.blood trans.mother trans.other zdv Age at diagnosis and the proportional change in the hazard corresponding to zdv1 7

9 remain highly significant. The effects of the other covariates are not much changed from the full model. Parametric analysis The survival curves suggest the Weibull survival distribution is appropriate. The Weibull distribution is both a proportional hazards and an accelerated life model (see, for instance, 11) and we included the observed temporal effect by assuming a doubling of survival from July The resulting parameter estimates show excellent agreement with the Cox model for both the full and reduced models, and are not given here. The Weibull index parameter is estimated to be 0.97 (P -value = 0.11 for a test of being an exponential distribution) which suggests a monotone decreasing hazard for survival in the presence of the covariates fitted. Removing the 29 zero survival times, the exponential survival distribution gives an excellent fit (Weibull index parameter 1.02, P -value = 0.30), suggesting that in practice, it is reasonable to assume a constant baseline hazard. The implications of this are outlined in the Discussion. Analysis of age effects We now consider the possible nonlinearity of the log-hazard with age. As a first step, we replaced a linear term in age by a step function with the knots as given in the Methods, and re-fitted the reduced Cox model. The results are set out in Table 3. The difference in partial likelihoods over the reduced model was 8.24 on 4 df. TABLE 3. Australian AIDS survival: study of nonlinear age effects. Covariate ^ Standard error ^ exp( ^) P -value trans.hsid trans.id trans.het trans.haem trans.blood trans.mother trans.other age age age age age zdv Compared to the age-group, people aged over 50 years at diagnosis of AIDS have significantly poorer survival. Other trends are suggestive, such as younger people aged up to 15 also have poorer survival, but the effect is not statistically significant. People infected via heterosexual contact still do significantly better than homosexual/bisexual men, however haemophiliacs no longer have a significantly increased hazard. We also fitted a smooth nonlinear function of age using splines. This shows significantly better fits with the smoothed age effects with the difference in partial likelihoods over the reduced model of on 7 df. Figure 4 shows a greatly increased hazard at age zero, a decreased hazard in teenage years then a steady increase to age 75, followed by a sharp 8

10 increase. Confidence intervals are shown, and the reference is to a 21 year old. For this model, haemophiliacs again have a significantly increased hazard. predicted change in hazard age Figure 4: Relative hazard curves with 95% confidence intervals (dashed) for age, relative to a 21 year old. The rug shows the distribution of ages. Age-dependence for blood-contaminated cases Finally, we investigate whether the survival of the 139 people infected with HIV via blood or blood products in Australia decreases with age. Table 4 sets out the marginal survival experience in different age-groups. TABLE 5. Age-dependence for blood-contaminated cases of AIDS in Australia (days) n events mean s.e.(mean) median 95% c.i. up to (257,1) 20+ to (196, 507) 40+ to (79, 512) 60+ to (110, 479) The evidence of Figure 5 is suggestive, and for comparison, the survival curve of a healthy US 65-year-old male is shown. However, a formal analysis comparing the partial likelihoods for comparable Cox models shows no real evidence of an age effect (see Table 5). (The log partial likelihood ratios were 12.0 on 4 df and 10.8 on 2 df for these models against 8.6 on 1 df for a model with no age effect.) This is probably due to the relatively small numbers of patients involved. 9

11 normal months since diagnosis Figure 5: Survival curves for AIDS in Australia for people infected via blood contamination, adjusted for other covariates. The curves shown are grouped by age, with a healthy 65-year old US male for comparison. TABLE 5. Study of age-dependence for blood-contaminated cases, comparing two Cox models. Covariate ^ Standard error ^ P -value zdv to to zdv age reference is to the 0 to 20 age group. 4 DISCUSSION The results of our population-based study have established that there are significant temporal trends in survival in Australian AIDS patients. These trends may, at least in part, be attributable to the effects of available treatments for people with HIV/AIDS and remain important in the presence of other factors important for survival. Although such registrybased studies cannot directly assess treatment effects, an advantage is that the data are broadly representative of the population being treated in medical practice. Of the 41 people infected via heterosexual contact, 21 are females and 20 are males. The hazard is reduced by more than half of that for homosexual/bisexual males and the effect is the same for both males and females. The reasons for Queensland s relatively poor survival remain obscure and require further 10

12 investigation. We considered the possibility that it might be due to a high proportion of blood-contaminated cases: 8.3% of cases diagnosed in Queensland are due to contaminated blood or blood products, whereas in NSW (which is the largest state, and where most blood is donated) the figure is 5.8%. Our methodology adjusts for this proportion, but as figure 3 shows, the proportional hazards hypothesis fails for these transmission categories in so far as the early hazard rate is much larger. However, removing the blood-contaminated cases from the study only reduced slightly the difference in Queensland. It is interesting to note that there was no significant effect of the second time-dependent covariate i.e. that the nonstationarity was captured by the change modelled in mid-1987, when the hazard was reduced by half, but that there was no further significant change in the hazard associated with an effect modelled in mid Both of these time-dependent covariates reflect changes in the Australian Government s treatment policy: in June 1987, zidovudine was made widely available to people with advanced HIV disease and then in August 1990, zidovudine became available in Australia to people with CD4 cell counts less than 500 per mm 3. Our findings contribute to the still incomplete knowledge of the pattern of survival from initial infection with HIV to death. The European Concorde study (9) suggests that taking zidovudine early does not prolong life, nor significantly prolong the incubation period for AIDS. However, questions about the precise effects of anti-retroviral and other treatments on the incubation period for AIDS remain. Our analysis suggests that, on a population basis, starting zidovudine in the asymptomatic period has no survival benefit over starting zidovudine later, when the patients is suffering advanced HIV disease. These results appear to be in broad agreement with Concorde, although it may be too soon to detect an effect on a population basis. Data on individual treatment patterns are, unfortunately, not available, nor are data on diseases or CD4 cell counts at diagnosis of AIDS available to us. Previous studies have shown that men presenting with Kaposi s sarcoma have improved survival over those who present with opportunistic infections such as PCP (see 12, among others). Moreover, the AIDS incubation distribution may vary by disease at diagnosis, and possibly by detailed infection distribution, so that study of subsequent survival by these criteria is of interest. Nevertheless, we believe that the findings of our study are of interest in their own right. The results of the parametric analysis suggest that an exponential survival distribution is a reasonable model i.e., the baseline hazard of death is constant. This raises the question of what part of the disease process, if any, is constant. For instance, changes in the disease process coinciding with the external temporal effects we have modelled cannot be separately estimated on the basis of the available data. One interpretation is that there have not been significant trends in the disease process, nor in the effects of treatment on the incubation period for AIDS, but there are other possible interpretations. In particular, for people taking zidovudine early, i.e. pre-aids, poorer survival following a diagnosis of an AIDS-defining illness could be disguised by cases being detected at an earlier stage of disease. Since the definition of AIDS in Australia has not changed in recent years, it seems more likely that the survival pattern has remained relatively constant as the model suggests. Our study of age at diagnosis showed, in the first instance, that it is a highly significant effect, but that overall, the hazard increases only slightly with age. Age has a small effect on state and transmission category (trans), except for cases infected via mother which have relatively poor survival although the effect was not statistically significant (see Tables 1 and 2). The step-function and spline analyses confirmed that it is the very young and very old who are at significantly higher risk of death than people who are infected in middle-age. We also found some evidence that the hazard of blood-contaminated cases of AIDS 11

13 increases with age, but the effect is not statistically significant within this rather small group of 139 patients. Acknowledgements This work was supported in part by the Australian Research Council. We are grateful to the National Centre in HIV Epidemiology and Clinical Research for making the data available to us. Bibliography 1. Bacchetti P, Segal M, Jewell N. Backcalculation of HIV infection rates (with discussion). Statistical Science 1993; 8: AIDS Bureau, NSW Health Department. Report on planning for HIV/AIDS care and treatment services in New South Wales. State Health Publication (AIDS) 1990; Solomon PJ, Wilson SR. Predicting AIDS deaths and prevalence in Australia. Med J Aust 1992; 157: Cox, DR. Regression models and life tables (with discussion). J R Statist Soc B 1972; 34: Cox, DR. Partial likelihood. Biometrika 1975; 62: Solomon PJ, Wilson SR, Swanson CE, Cooper DA. Effect of zidovudine on survival of patients with AIDS in Australia. Med J Aust 1990; 153: Fischl MA, Richman DD, Grieco MH, et al. The efficacy of azidothymidine (AZT) in the treatment of participants with AIDS and AIDS-related complex: a double-blind, placebo-controlled trial. N Eng J Med 1987; 317: Volberding PA, Lagakos SW, Koch MA et al. Zidovudine in asymptomatic human immunodeficiency virus infection: a controlled trial in persons with fewer than 500 CD4-positive cells per cubic millimeter. N Eng J Med 1990; 322: Seligmann M, Warrell DA, Aboulker J-P, et al. Concorde: MRC/ANRS randomised double-blind controlled trial of immediate and deferred zidovudine in symptom-free HIV infection. The Lancet 1994; 343: Venables WN, Ripley BD Modern applied statistics with S-Plus. Springer, New York Cox DR, Oakes D. Analysis of survival data. Chapman and Hall, London Rothenberg R, Woelfe M, Stoneburner R, Milberg J, Parker R, Truman B. Survival with the acquired immunodeficiency syndrome. N Eng J Med 1987; 317: