A note on Australian AIDS survival

B.D. Ripley and P.J. Solomon

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 5005

3. Address for correspondence: Dr P.J. Solomon, Department of Statistics, University ofAdelaide, Australia 5005

Abstract

Understanding factors important for AIDS survival is crucial for planning andmodelling. In this article, we present the results of a registry-based study of thesurvival of Australian residents diagnosed by July 1991 and reported by January 1992.We fit semi-parametric Cox models incorporating temporal trends associated withchanges in the Australian Government’s treatment policy for HIV/AIDS, and otheravailable covariates. We also describe a special study of age effects, and demonstratethe power of sophisticated statistical analyses to provide insight into complex data thatmay bemissed by a more naive analysis. We find a significant reduction in the hazard ofdeath associated with the widespread introduction of zidovudine into clinical practicein mid-1987 for people with advanced HIV disease. The Australian Government’streatment policywas broadened in August 1990 tomake zidovudine available to peoplewhose CD4 cell/mm counts persist below , but there was no further change inthe hazard associated with the policy change. People infected via heterosexual contacthave significantly improved survival over homosexual/bisexual males, whereas peoplewith haemophilia have significantly poorer survival. Queensland has a significantlyincreased hazard over that for New South Wales, the largest Australian state. Thevery young have a greatly increased hazard of death, which increases steadily fromabout aged two years at diagnosis to 75 years, followed by a sharp increase. Wefind no real evidence that the survival of people infected via contaminated blood orblood-products decreases with age. A parametric analysis suggests that an exponentialsurvival distribution is reasonable and that the baseline hazard is constant. This mayprovide insight into underlying trends in the disease process.

Key words:

Australian AIDS survival – nonstationarity, treatment effects, age effects; Cox model;Weibull survival model.

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1 INTRODUCTION

It is important that we understand factors affecting the survival of people with AIDS. Itsimportance stems from the evolving definition of AIDS which has implications for definingand estimating the incubation distribution. It is also important for health-care planning,predicting deaths and prevalence of AIDS, and for providing accurate information to peoplewith 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). Incubationfor AIDS is believed to depend, at least in part, on treatments, age and possibly diseasesat diagnosis. Understanding factors associated with AIDS survival can therefore providecrucial 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 recentstudy of Australian AIDS survival up to 1992. Using a time-dependent Cox model, weinvestigate covariates related to survival and incorporate temporal trends associated withchanges in the Australian Government’s treatment policy. We also present a special studyof age effects. Secondly, we demonstrate the power of sophisticated statistical analyses inproviding insight into factors important for survival that may be missed by a more naiveapproach.

2 METHODS

2.1 The data

There were 2,843 Australian AIDS cases diagnosed prior to 30 June 1991 and reported tothe National Centre in HIV Epidemiology and Clinical Research in Sydney, by 31 January1992. The first case was diagnosed in December 1982 and by the study’s endpoint, 1,787of the 2,843 individuals had died.

The HIV epidemic started in New South Wales and spread to Victoria, followed byQueensland and then the smaller States and Territories. NSW and Victoria are the first andsecond largest Australian states. There is considerable regional variability in the epidemicin Australia, but otherwise the pattern of spread amongst the population is typical of so-called Western countries, where the majority of AIDS cases have been seen amongst menwho have sex with men, and more recently amongst injecting drug users. However, therehave 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 shownin 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 stillbeing recognised and are disproportionallydistributed amongst the transmission categories:22 of the cases were homosexual/bisexual males, 6 were infected by blood transfusions orblood 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 aretherefore believed to be relatively complete compared with other countries. However, weadjusted the endpoint of the study by six months since there are some delays in deathnotifications, and to a lesser extent, delays in reporting of AIDS cases.

The delay between diagnosis of AIDS and reporting is variable, which can be seenin figures published regularly by the NCHIVECR. But reporting delay data are available

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1982 1983 1984 1985 1986 1987 1988 1989 1990 1991

010

020

030

040

0

NSWVICQLDOther

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 systematicway. 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 % (2).

The quality of the death data is less certain and there is no recent published informationon this, although some death certificate checking is undertaken. The implications of delaysin death reporting, as well as of under-reporting, for estimating survival probabilities havebeen discussed recently in theAustralian context (3). The national database does not identifynon-AIDS deaths, so that all deaths are assumed to be ‘AIDS deaths’ for the purposes ofthe present analysis.

Survival time is calculated as the number of days between a diagnosis of AIDS anddeath or 30 June 1991, whichever is the sooner. The covariates available to us are sex, age atdiagnosis, reported transmission category, State or Territory of diagnosis, and informationon the availability of zidovudine in Australia.

2.3 The model and analysis

Webeginwith a time-dependentCoxmodel (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 withNSW for the purposes of our analysis. The States and Territories are then

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NSW New South Wales and Australian Capital TerritoryVIC VictoriaQLD QueenslandWA Western AustraliaSA South AustraliaTAS TasmaniaNT Northern Territory.

Each State or Territory is compared to NSW.

trans

The transmission categories are:hs male homosexual or bisexual contacthsid as hs and also intravenous drug userid female or heterosexual male intravenous drug userhet heterosexual contacthaem haemophilia or coagulation disorderblood receipt of blood, blood components or tissuemother mother with or at risk of HIV infectionother 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 dramaticimprovement in survival coincided with, although may not be entirely attributable to,the widespread introduction of zidovudine into clinical practice in mid-1987 (6), and theincreased use of prophlyactic treatments for opportunistic infections. Early clinical trials(7) established that ZDV considerably enhances the survival of people with AIDS. Laterevidence (8) suggested that taking ZDV during the symptom-free period might delay theonset of anAIDS-defining illness. On the basis of these findings, the Australian governmentamended its treatment policy in August 1990 to make ZDV available to people whose CD4cell counts per mm persist below . The results of the recent Concorde trial (9) haveagain thrown open the question of the effects of anti-retroviral treatment on the symptom-free period, and we pursue this point further in the Discussion.

We have modelled directly the observed nonstationarity in AIDS survival by allowing aproportional change in the hazard from 1 July 1987 to 30 June 1990 (zdv1 t ) and anotherfrom 1 July 1990 (zdv2 t ). These time-dependent covariates represent temporal changesin survival on a population basis. Detailed data on individual ZDV use are not available tous.

The full Cox model includes the covariates described above as well as sex (male ,female ) and age in years at diagnosis. The hazard is then

; exp(1)

where is the baseline hazard, is the covariate vector and and are vectorparameters.

Using a stepwise regression procedure based on the partial likelihoods, we obtained asparsimonious a Cox model as possible. We call this the reduced model. In addition, wecompared the results of the Cox model with a parametric Weibull survival model.

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Special study of age effects

Age is known to be important for survival,with the very young and very old having relativelypoor prognoses. We examined linearity in the hazard of death with age by examining themartingale residual plot in the first instance. We then split the data into six age groups asshownbelowand re-fitted the reduced model. The knotswere chosen from prior experience,giving numbers in each group of

0–15 16–30 31–40 41–50 51–60 61+39 1022 1583 987 269 85

In each case the baseline for comparison is the 31–40 year-old group, and we compared theresults from both the Cox and the parametric Weibull models. We then went on to considerparametric nonlinear functions of age using a spline function.

The blood-transfusion and blood-product data are quite different and should be consid-ered separately. We investigated the question of whether the survival of patients infectedvia blood or blood products decreases with age by splitting the 139 patients concerned intofor age groups: 0–20, 21–40, 41–60 and 61+ and then fitting the Cox model including thetime-dependent covariates zdv1(t) and zdv2(t).

Computing

The analyses were done using S-PLUS functions written by Terry Therneau(Mayo Foundation). Note that zero survival times are avoided by shifting the deaths by 0.9days 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-PLUSalgorithms for the analyses described in this paper are contained in (10) where they are usedfor a disguised and simplified version of this data set, and the exact code used is availablefrom the first author.

3 RESULTS

Fitting the full Cox model gives the regression estimates shown in Table 1. Sex is not asignificant 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 1.014for 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 signifi-cantly poorer survival than NSW (95% c.i. for relative risk (1.00,1.41)). The survival trendsin the other states are suggestive although not statistically significant. Figure 2 shows therelative survival pattern adjusted for the presence of the other covariates. The mediansurvival 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 ofhomosexual and bisexual males (the relative risk is reduced by more than half to 0.452,-value 0.004) whereas people with haemophilia have a significantly increased hazard

of death, corresponding to an increased relative risk of 1.465 ( -value 0.04). Trends insurvival by transmission category are shown in Figure 3. Injecting drug users also do betterthan homosexual and bisexual men, although not significantly, and children infected viaa mother with HIV/AIDS, or people infected via blood or blood products (who are nothaemophiliacs) do worse, although again not significantly.

The hazard of death is reduced by half with the introduction of the first time-dependentcovariate in mid-1987 and this effect is highly significant. However, there is no further

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TABLE 1. Australian AIDS survival: results of fitting the full Cox model (1).

Covariate Standard error exp -valuesex 0.0046 0.1716 1.005 0.98age 0.0136 0.0025 1.014 0.04state.NT -0.2968 0.5801 0.743 0.61state.QLD 0.1715 0.0871 1.186 0.054state.SA -0.1059 0.1414 0.900 0.45state.TAS 0.1596 0.3388 1.173 0.64state.VIC 0.0057 0.0608 1.006 0.93state.WA -0.0720 0.1162 0.931 0.54trans.hsid -0.1175 0.1521 0.889 0.44trans.id -0.3472 0.2405 0.707 0.15trans.het -0.7932 0.2888 0.452 0.006trans.haem 0.3816 0.1868 1.465 0.041trans.blood 0.1675 0.1362 1.182 0.22trans.mother 0.4182 0.5898 1.519 0.48trans.other 0.0964 0.1639 1.101 0.56zdv1 -0.6951 0.0660 0.499 0.00zdv2 -0.7305 0.0748 0.482 0.00

months since diagnosis0 20 40 60

0.0

0.2

0.4

0.6

0.8

1.0

NSWQLDVIC

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-1990.

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months since diagnosis0 20 40 60

0.0

0.2

0.4

0.6

0.8

1.0

hshsididhet

months since diagnosis0 20 40 60

0.0

0.2

0.4

0.6

0.8

1.0

hshaembloodother

Figure 3: Survival curves for AIDS inAustralia by transmissioncategory, adjusted for othercovariates.

Reduced model

Since any effect of sex will be confounded with that of transmission category, we droppedsex from the model. Removing sex and zdv2, the difference in zdv at 1 July 1990, makesvirtually no difference to the partial likelihood ratio statistic: 179.53 on 17 degrees offreedom changes to 179.13 on 15 df. A stepwise elimination procedure indicated that statecould also be removed (likelihood ratio test 173.59 on 9 df), which leaves the reducedmodel:

; exp (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 -valueage 0.0136 0.0025 1.014 0.03trans.hsid -0.1172 0.1520 0.889 0.44trans.id -0.3673 0.2261 0.693 0.11trans.het -0.7840 0.2686 0.457 0.004trans.haem 0.3838 0.1851 1.483 0.033trans.blood 0.1769 0.1219 1.193 0.15trans.mother 0.4055 0.5839 1.500 0.49trans.other 0.0931 0.1608 1.098 0.56zdv1 -0.7016 0.0635 0.496 0.00

Age at diagnosis and the proportional change in the hazard corresponding to zdv1

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remain highly significant. The effects of the other covariates are not much changed fromthe full model.

Parametric analysis

The survival curves suggest the Weibull survival distribution is appropriate. The Weibulldistribution 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 fromJuly 1987. The resulting parameter estimates show excellent agreement with the Coxmodelfor both the full and reduced models, and are not given here. The Weibull index parameteris estimated to be 0.97 ( -value = 0.11 for a test of being an exponential distribution)which suggests a monotone decreasing hazard for survival in the presence of the covariatesfitted. Removing the 29 ‘zero’ survival times, the exponential survival distribution gives anexcellent fit (Weibull index parameter 1.02, -value = 0.30), suggesting that in practice, itis reasonable to assume a constant baseline hazard. The implications of this are outlined inthe Discussion.

Analysis of age effects

We now consider the possible nonlinearity of the log-hazard with age. As a first step, wereplaced a linear term in age by a step function with the knots as given in the Methods, andre-fitted the reduced Cox model. The results are set out in Table 3. The difference in partiallikelihoods over the reduced model was 8.24 on 4 df.

TABLE 3. Australian AIDS survival: study of nonlinear age effects.

Covariate Standard error exp -valuetrans.hsid -0.133 0.152 0.875 0.38trans.id -0.390 0.227 0.677 0.085trans.het -0.794 0.269 0.452 0.003trans.haem 0.220 0.198 1.246 0.27trans.blood 0.003 0.136 1.003 0.98trans.mother -0.229 0.645 0.796 0.72trans.other 0.019 0.164 1.019 0.91age.0-15 0.210 0.288 1.234 0.47age.16-30 -0.094 0.062 0.910 0.13age.41-50 0.061 0.061 1.063 0.32age.51-60 0.376 0.095 1.457 0.000075age.61+ 0.746 0.157 2.109 0.000002zdv1 -0.702 0.064 0.496 0

Compared to the 31–40 age-group, people aged over 50 years at diagnosis of AIDS havesignificantly poorer survival. Other trends are suggestive, such as younger people aged upto 15 also have poorer survival, but the effect is not statistically significant.

People infected via heterosexual contact still do significantly better than homosex-ual/bisexual men, however haemophiliacs no longer have a significantly increased hazard.

We also fitted a smooth nonlinear function of age using splines. This shows significantlybetter fits with the smoothed age effects with the difference in partial likelihoods over thereduced model of 27.87 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

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increase. Confidence intervals are shown, and the reference is to a 21 year old. For thismodel, haemophiliacs again have a significantly increased hazard.

age

pred

icte

d ch

ange

in h

azar

d

0 20 40 60 80

-2-1

01

23

4

Figure 4: Relative hazard curves with 95% confidence intervals (dashed) for age, relativeto 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 bloodor blood products in Australia decreases with age. Table 4 sets out the marginal survivalexperience 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 20 30 21 618 115 366 (257, )20+ to 40 37 26 384 60 268 (196, 507)40+ to 60 47 27 335 49 210 (79, 512)60+ to 80 25 23 326 84 222 (110, 479)

The evidence of Figure 5 is suggestive, and for comparison, the survival curve of ahealthy US 65-year-old male is shown. However, a formal analysis comparing the partiallikelihoods for comparable Cox models shows no real evidence of an age effect (see Table5). (The log partial likelihood ratios were 12.0 on 4 df and 10.8 on 2 df for these modelsagainst 8.6 on 1 df for a model with no age effect.) This is probably due to the relativelysmall numbers of patients involved.

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months since diagnosis0 10 20 30 40 50

0.0

0.2

0.4

0.6

0.8

1.0

0-2021-4041-6060+normal 65

Figure 5: Survival curves for AIDS inAustralia for people infected via blood contamination,adjusted for other covariates. The curves shown are grouped by age, with a healthy 65-yearold US male for comparison.

TABLE 5. Study of age-dependence for blood-contaminated cases, comparing two Coxmodels.

Covariate Standard error -valuezdv1 -0.573 0.214 0.007520+ to 40 0.312 0.298 0.2940+ to 60 0.334 0.278 0.2360+ 0.557 0.306 0.07zdv1 -0.536 0.211 0.011age 0.0073 0.0049 0.132

reference is to the ‘0 to 20’ age group.

4 DISCUSSION

The results of our population-based study have established that there are significant temporaltrends in survival in Australian AIDS patients. These trends may, at least in part, beattributable to the effects of available treatments for people with HIV/AIDS and remainimportant in the presence of other factors important for survival. Although such registry-based studies cannot directly assess treatment effects, an advantage is that the data arebroadly representative of the population being treated in medical practice. Of the 41 peopleinfected via heterosexual contact, 21 are females and 20 are males. The hazard is reducedby more than half of that for homosexual/bisexual males and the effect is the same for bothmales and females.

The reasons for Queensland’s relatively poor survival remain obscure and require further

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investigation. We considered the possibility that it might be due to a high proportion ofblood-contaminated cases: 8.3% of cases diagnosed in Queensland are due to contaminatedblood or blood products, whereas in NSW (which is the largest state, and where most bloodis donated) the figure is 5.8%. Our methodology adjusts for this proportion, but as figure 3shows, the proportional hazards hypothesis fails for these transmission categories in so faras the early hazard rate is much larger. However, removing the blood-contaminated casesfrom the study only reduced slightly the difference in Queensland.

It is interesting to note that there was no significant effect of the second time-dependentcovariate 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 inthe hazard associated with an effect modelled in mid-1990. Both of these time-dependentcovariates 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 inAugust 1990, zidovudine became available in Australia to people with CD4 cell counts lessthan 500 per mm .

Our findings contribute to the still incomplete knowledge of the pattern of survival frominitial infection with HIV to death. The European Concorde study (9) suggests that takingzidovudine early does not prolong life, nor significantly prolong the incubation period forAIDS. However, questions about the precise effects of anti-retroviral and other treatmentson the incubation period for AIDS remain.

Our analysis suggests that, on a population basis, starting zidovudine in the asymp-tomatic period has no survival benefit over starting zidovudine later, when the patientsis suffering advanced HIV disease. These results appear to be in broad agreement withConcorde, although it may be too soon to detect an effect on a population basis. Data onindividual treatment patterns are, unfortunately, not available, nor are data on diseases orCD4 cell counts at diagnosis of AIDS available to us. Previous studies have shown that menpresenting with Kaposi’s sarcoma have improved survival over those who present with op-portunistic infections such as PCP (see 12, among others). Moreover, the AIDS incubationdistribution may vary by disease at diagnosis, and possibly by detailed infection distribu-tion, so that study of subsequent survival by these criteria is of interest. Nevertheless, webelieve that the findings of our study are of interest in their own right.

The results of the parametric analysis suggest that an exponential survival distributionis a reasonable model i.e., the baseline hazard of death is constant. This raises the questionof what part of the disease process, if any, is constant. For instance, changes in thedisease process coinciding with the ‘external’ temporal effects we have modelled cannotbe separately estimated on the basis of the available data. One interpretation is that therehave not been significant trends in the disease process, nor in the effects of treatment onthe 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 ofan AIDS-defining illness could be disguised by cases being detected at an earlier stage ofdisease. Since the definition of AIDS in Australia has not changed in recent years, it seemsmore 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 significanteffect, but that overall, the hazard increases only slightlywith age. Age has a small effect onstate and transmission category (trans), except for cases infected ‘via mother’ which haverelatively poor survival—although the effect was not statistically significant (see Tables1 and 2). The step-function and spline analyses confirmed that it is the very young andvery 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

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increases with age, but the effect is not statistically significant within this rather small groupof 139 patients.

Acknowledgements

This work was supported in part by the Australian Research Council. We are grateful to theNational Centre in HIV Epidemiology and Clinical Research for making the data availableto us.

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