Abstract

Background A reduction in cause-specific mortality may be the most important public health measure of the efficacy of a new vaccine. However, in developing countries, assignment of causes of deaths occurring outside hospitals can be assessed often only through the questioning of relatives about the signs and symptoms leading to death (‘post-mortem questionnaire’). Causes assigned in this way have poor sensitivity and specificity. We illustrate the effects of this misclassification on the power of a large trial of a pneumococcal polysaccharide/protein conjugate vaccine with a mortality endpoint.

Methods Required sample sizes to achieve a study with specified power were calculated for all-cause and acute lower respiratory tract infection (ALRI) mortality for different levels of sensitivity and specificity of post-mortem questionnaires. Data from active community-based surveillance and post-mortem questionnaires collected 1989–1993 from the study area were used in the calculations.

Findings The mortality rate among children aged 6–29 months from all causes was 34.2 per 1000 child-years; 19% of deaths were attributable to ALRI. Assuming that pneumococci would be responsible for 50% of ALRI deaths and that the vaccine would cover 70% of disease serotypes and would be 90% effective against these serotypes, the expected efficacy of the vaccine would be 6.0% (19% × 50% × 70% × 90%) against all causes combined and 31.5% (50% × 70% × 90%) against deaths from ALRI. If, as suggested by various reports, the sensitivity and specificity of assigning a death to ALRI by post-mortem questionnaire are about 40% and 90% respectively, then the observed vaccine efficacy against ALRI (as classified using the post-mortem questionnaire) would fall to 20%, and the power to detect this would be reduced by approximately 40%. Furthermore, low sensitivity of diagnosis would lead to a falsely low estimate of the burden of ALRI mortality in the population and the trial might have greater power to detect a reduction in mortality from all causes combined than that estimated at the outset.

Conclusions Low sensitivity and specificity of diagnosis by post-mortem questionnaire may mean that the power of a trial to detect a reduction in all-cause mortality is similar to that to detect a reduction in ALRI mortality. Since the latter is more susceptible to bias from misclassification of cause of death, all-cause mortality may be the most suitable endpoint. Similar considerations apply to trials of interventions against other diseases for which a cause-specific endpoint is subject to substantial misclassification.

A reduction in mortality may be the most important public health measure of the efficacy of new vaccines or therapies and research trials powered to demonstrate an impact on mortality are important for informing policy. Most interventions are directed at particular causes of morbidity or mortality and thus, in general, the impact of an intervention on cause-specific mortality is more biologically meaningful than overall mortality. Also, the relative impact on cause-specific mortality will be greater and consequently trials using this endpoint are often much smaller in size than trials that use overall mortality. However, in developing countries causes of deaths are often difficult to ascertain because most deaths occur at home and funerals are held promptly. Generally, no clinical assessment is made of the cause of death. In some research studies, attempts have been made to establish the causes of death using post-mortem questionnaires (also known as ‘verbal autopsies’), in which information on signs and symptoms leading up to the death is collected from bereaved relatives by trained interviewers. The data collected are reviewed independently by a group of physicians, usually three, to assign a cause of death.1 However, the ability of this technique to diagnose accurately causes of death in African populations is questionable2–6 and the impact of this misclassification on the statistical power of interventions trials is unclear.

We illustrate the effects of misclassification of causes of death on the estimation of power and efficacy of a large-scale trial of a pneumococcal conjugate vaccine underway in a rural region of The Gambia.

Background

Pneumococcal disease may account for up to 2 million deaths of young children annually. The possibility of protection of these children is now provided by the development of pneumococcal polysaccharide/protein conjugate vaccines,7–9 which are immunogenic in infants. Against this background, trials of pneumococcal conjugate vaccines commenced in a number of settings, including California, Finland, and South Africa, with each measuring impact against disease. Measuring the efficacy of this vaccine against mortality is particularly important in developing countries where the burden of pneumococcal disease is highest. Thus, a large-scale randomized, double-blind trial of pneumococcal polysaccharide/conjugate vaccine is being undertaken in the Upper River and Central River Divisions of The Gambia where acute lower respiratory tract infection (ALRI) mortality is high.10–12 In planning this trial, sample size calculations were compared for the endpoints of either deaths from ALRI or all-cause mortality, taking into account the likely misclassification around the diagnosis of deaths from ALRI in this setting; this paper presents those comparisons.

The study site was chosen for a number of reasons. The area is representative of a rural African setting, the population is relatively stable, coverage with vaccines in the routine Expanded Programme of Immunizations (EPI) schedule is high,10,11,13 a basic level of laboratory and clinical infrastructure is available, and large-scale research studies including the aetiology of ALRI6,9,14,15 have been conducted in the area. Between 1989 and 1993, births and deaths of children under the age of 5 years were recorded through active community surveillance and causes of death were assigned using the post-mortem questionnaire technique.10,11 The birth rate was 37.5 births per 1000 population per year. Table 1 shows the age-specific mortality rates. Deaths due to ALRI were estimated to account for 19% of the deaths.

Since the trial started, deaths have been identified by active surveillance of the study population and causes of deaths are being assessed through post-mortem questionnaires. The trial is randomized and double-blinded. Vaccination with the pneumococcal conjugate vaccine is integrated into the EPI and scheduled to be given at the ages of 6, 10, and 14 weeks. The 9-valent vaccine being used is produced by Wyeth Lederle Pediatrics and contains pneumococcal types 1, 4, 5, 6B, 9V, 14, 18C, 18F, and 23F polysaccharides conjugated to the diphtheria toxoid derived protein CRM 197. The pneumococcal vaccine is mixed with diphtheria/pertussis/tetanus/Haemophilus influenzae type b (TETRAMUNER) produced by the same manufacturer. Infants attending for vaccinations are randomized to receive either the pneumococcal vaccine mixed with TETRAMUNER or placebo mixed with TETRAMUNER. The primary analysis will be among children who receive all three vaccine doses, for whom calculations below are given. Analyses will also be conducted according to which group the children were randomized irrespective of the number of doses that they received.

Calculations of sample size were conducted using the methods described in Smith and Morrow1 with power calculated for comparing two incidence rates. A 5% two-sided significance level was used. The assumptions underlying the calculations are presented below.

Results

Study size calculations

The data in Table 1 and hospital data (unpublished) indicated that the major burden of deaths from ALRI was among those aged under about 30 months and that the efficiency of an efficacy trial increased if it was confined to this age group.

The population of the Upper River and Central River Divisions in mid-2000 was 383 000, as estimated from national census data. Approximately 14 000 births were expected to occur annually. Sample size calculations (see below) had indicated that more than 60 000 child-years of follow-up of the trial cohort might be required to achieve reasonable power to detect a significant effect of the vaccine on overall mortality. It was considered that this would be most easily achieved logistically by increasing the duration of recruitment of the trial rather than by expanding the study area.

It was estimated that children would be fully vaccinated with the pneumococcal conjugate vaccine, on average, by the age of 6 months, that approximately 850 (6.1%) infants would die annually before reaching this age, that 5% of infants would fail to receive a complete series of vaccinations, that 8% of mothers would refuse to allow their child to join the trial (figures based on the experience in a large Hib vaccine trial conducted previously in The Gambia),16 and that a further 10% of children would be lost to follow-up each year. This would leave approximately 10 600 children who would contribute fully to the post-vaccination surveillance period each year. It was planned that the recruitment for the trial would continue for a period of 3½ years after the first child was fully vaccinated, and that this would be followed by a final 6-month period of follow-up. Based on the numbers of children entering the trial, the length of time until they reach the age of 30 months and their estimated mortality rates, a total of 1065 deaths, of which 203 (19%) would be attributed to an ALRI, were expected in the control group over a follow-up of 31 137 child-years.

Anticipated reduction in mortality likely to be achieved by an effective pneumococcal vaccine

The impact of a pneumococcal vaccine on overall mortality will depend on a number of factors including the proportion of deaths due to ALRI, the proportion of ALRI deaths due to pneumococci, the proportion of pneumococcal deaths attributable to serotypes included in the vaccine, and the vaccine’s efficacy against those serotypes. Our assumptions for the trial and the basis for these are as follows:

  • Data collected from the Upper River Division suggest that ALRI account for 19% of all deaths in the region.10,11

  • There are no data on the proportion of ALRI deaths due to pneumococci but studies conducted in The Gambia suggest that around 50% of invasive disease is due to pneumococci.14,17 We assumed that pneumococci will account for somewhere between 30% and 70% of ALRI deaths in young Gambian children.

  • Data from The Gambia suggest that the serogroups represented in the 9-valent Wyeth Lederle vaccine account for 74% of cases of invasive pneumococcal disease seen in the study area.14 The level of cross-protection that each serotype might provide against others within each serogroup is not clear. Factor typing of 260 isolates obtained from children presenting with pneumococcal disease at the MRC hospital in the western division was conducted for the purposes of the trial; 204 (78%) isolates were of vaccine serotype (unpublished). For the purposes of this paper we assumed that the vaccine is equally effective against pneumonia with or without accompanying bacteraemia. Therefore, we assumed that the vaccine will cover 70% of pneumococcal serotypes responsible for disease in the trial area.

  • A study conducted in the US suggests that the pneumococcal conjugate 7-valent vaccine is more than 95% effective in preventing disease against homologous pneumococcal serotypes.8 We assumed that that the efficacy of the 9-valent vaccine against mortality from pneumococcal serotypes in the vaccine will be 90% in this trial.

Assuming that 19% of deaths are attributed to ALRI, 50% of ALRI deaths are due to pneumococci, and that the vaccine covers 70% of serotypes and is 90% effective against those, then vaccination would be expected to reduce overall mortality by 6.0% (0.19 × 0.5 × 0.7 × 0.9) and ALRI attributed mortality by 31.5% (0.5 × 0.7 × 0.9). With the assumptions that 70% or 30% of ALRI deaths are attributed to pneumococci in young Gambian children (with the other assumptions remaining the same), pneumococcal vaccination might be expected to reduce overall mortality by 8.4% and 3.6% respectively and ALRI-attributed mortality by 44.1% and 18.9% respectively.

An important consideration with respect to these assumptions is that the proportion of deaths from ALRI was estimated from post-mortem questionnaires. If the sensitivity of these is low, ALRI may have accounted for a higher proportion of deaths than indicated by this estimate and, if the specificity of this technique is less than 100%, then other causes of deaths may have been incorrectly assigned as ALRI deaths. A wide combination of sensitivities and specificities are compatible with an observed ALRI death rate of 19%, each corresponding to a different ‘true’ ALRI mortality rate in this population. Thus, for example, for the tabulation shown in Table 2, and for the case when the sensitivity is 0.4 and the specificity 0.9, the equations would need to satisfy the conditions below:

 

\[a{/}{(}a{+}b{)}\ {=}\ 0.4\]

 

\[d{/}{(}c{+}d{)}\ {=}\ 0.9\]

 

\[a\ {+}\ c\ {=}\ 203\]

 

\[b\ {+}\ d\ {=}\ 862\]

Solving these equations gives a = 129, b = 193, c = 74, and d = 669. Thus, in this scenario, the true proportion of deaths due an ALRI would have been 30% (19% as classified using the post-mortem questionnaire). If ALRI account for 30% of deaths, 50% of which are caused by pneumococci, and the vaccine covers 70% of pneumococcal serotypes and is 90% effective against these, vaccination might be expected to reduce overall mortality by 9.5% (0.3 × 0.5 × 0.7 × 0.9). If the sensitivity was 30% and the specificity 90%, then the true proportion of deaths due to an ALRI would have been 45%. Figure 1 shows the true underlying proportion of deaths due to an ALRI when 19% of deaths are recorded as such for a range of sensitivities and specificities in diagnosis.

Implications of poor sensitivity and specificity of the post-mortem questionnaire technique for the power of the trial

The greater the proportion of deaths caused by ALRI, the greater will be the expected impact of the vaccine in reducing all-cause mortality. Misclassification of causes of deaths will reduce the difference in cause-specific mortality rates that can be measured between the vaccinees and controls and thereby reduce the power to detect an effect against ALRI mortality. For example, for the scenario of 40% sensitivity and 90% specificity, the 203 ALRI deaths recorded by post-mortem questionnaire (cells a and c in Table 2) would comprise only 129 which were actually due to an ALRI (cell a in Table 2) and 74 which were from other causes (cell c in Table 2), against which the pneumococcal vaccine would not be expected to have any effect. Thus, if the vaccine reduces the ALRI mortality by 31.5%, the number of deaths expected in the pneumococcal vaccine group will be 129 × 0.685 + 74 = 162.4, and the measured vaccine efficacy will be 20.0% and not 31.5%. The power to detect a vaccine efficacy of 20.0% is 54% (as opposed to 93% power to detect a 31.5% vaccine efficacy). On the other hand, the power to detect a 9.5% vaccine efficacy against overall mortality is 60% (as opposed to 28% power to detect a vaccine efficacy of 6.0%). Table 3 shows the true underlying ALRI mortality for different levels of sensitivity and specificity assuming that the proportion of deaths attributed to ALRI by post-mortem questionnaires is 19%, anticipated reductions which might be measurable in a trial under different assumptions of vaccine efficacy, and the power to detect such reductions.

Discussion

We have calculated the power of a trial of a pneumococcal conjugate vaccine among Gambian infants to assess the efficacy of the vaccine in preventing ALRI specific and all-cause mortality. Background cause-specific death rates were estimated prior to the start of the trial using post-mortem questionnaires. Such questionnaires are also being used to assess cause-specific mortality during the trial. The power to detect efficacy against ALRI mortality is reduced substantially because of the likely low sensitivity and specificity of a post-mortem questionnaire diagnosis. When the sensitivity of post-mortem questionnaires is 40% and the specificity is 90%, which is plausible for the setting in The Gambia,5,6 the expected efficacy against deaths classified as due to ALRI would fall from 31.5% to 20%, leading to loss in power of about 40% (from 93% to 54%). Some of the misclassification arises because of the overlap of symptoms between malaria (which is common in the area10,11) and ALRI,18 although the sensitivity and specificity of post-mortem questionnaires in non-malarious areas is also poor.19–21 A further factor contributing to the high misclassification may be that a proportion of deaths occur from multiple causes. A possibility is to enhance malaria control activity in the region for the purposes of the trial so as to prevent deaths from malaria which might increase the specificity for the diagnosis of deaths from ALRI. However, even if specificity of the post-mortem questionnaires was 95% and the sensitivity remained at 40%, the reduction of power for the ALRI endpoint would still be substantial.

If our assumptions regarding the sensitivity and specificity of the post-mortem questionnaires are correct, the overall proportion of deaths truly due to ALRI might be as high as 30%. If this is so, the impact of the vaccine on all-cause mortality would be higher than estimated at the outset and the power to detect this would be similar to that for detecting an effect against ALRI mortality as assessed through post-mortem questionnaires. The estimate of vaccine efficacy, which is crucial for calculating the burden of disease and the cost effectiveness of the vaccine, would be unbiased for all-cause mortality but biased for ALRI mortality and the extent of this bias would be unclear. A biased estimate showing, for example, a low efficacy of the vaccine against ALRI mortality may affect decisions relating to the public health priority of interventions against pneumococcal disease.

There are other advantages for using all-cause mortality as the primary endpoint. It is plausible that the benefits of the vaccine may extend beyond the target disease if, for example, it reduces measles mortality or deaths are prevented in children in whom ALRI is a secondary infection.

It is plausible that the benefits (or risks) of a vaccine may extend beyond the target disease.22–25 The pneumococcal vaccine is also likely to prevent deaths from pneumococcal meningitis, which although rare, has a high case fatality rate. The verbal autopsy methodology would not be able to distinguish between different forms of meningitis and so it would be difficult to include meningitis-specific mortality in a cause-specific endpoint. Finally, the mortality from pneumococcal disease may be substantial in this setting and so a demonstration of an effect against overall mortality, even in the absence of an indirect effect against other causes of death, would have important implications for public health policy. This would greatly enhance the pressure on governments, donor agencies, and pharmaceutical companies to produce and deliver this vaccine to children in developing countries. For all these reasons, the primary endpoint chosen for the trial in The Gambia was all-cause mortality.

These findings have important implications for other trials designs involving mortality endpoints. When cause-specific mortality is used as the endpoint, it is important to consider the sensitivity and specificity of the endpoint diagnosis. Our findings also have implications for other trials where there is uncertainty about the accuracy of the measurement of the endpoint, including, for example, trials of interventions against HIV-associated opportunistic infections, or trials of vaccines against specific aetiologies of diarrhoeal disease. A recent trial of a 7-valent pneumococcal polysaccharide/protein conjugate vaccine conducted in South Africa showed an efficacy of about 20% against radiologically confirmed pneumonia with consolidation (K Klugman; personal communication). This is lower than had been expected. One interpretation of the findings is that the pneumococcus causes a lower proportion of cases of radiological pneumonia than previously considered. On the other hand, the apparently low vaccine efficacy could be biased by poor specificity of diagnosis of radiological pneumonia. The difficulty of interpreting the data from disease endpoints which are subject to misclassification argues further for a trial of this vaccine with overall mortality as a primary endpoint.

A number of potential biases need to be considered in interpreting our findings. Our assumptions that the sensitivity and specificity of the post-mortem questionnaire for diagnosing ALRI are about 40% and 90% respectively were based on a small study conducted in The Gambia,6 and a study in Kenya5 where the spectrum of disease in children and therefore the ability to predict the cause may differ from The Gambia. Further, both studies used hospital diagnoses as the gold standard against which to compare the diagnoses from the post-mortem questionnaire. It is possible that some of the ‘hospital assessed’ causes of the death were incorrect and patients presenting to hospital may not have been representative of those in the wider population, which will have biased the estimates of sensitivity and specificity.

A number of other assumptions were made when calculating the power of the trial, including the proportion of eligible children entering the trial, the losses to follow-up, the likely proportion of ALRI that are caused by pneumococci, and the vaccine serotype coverage. These assumptions were based on previous experience of research conducted in the country but they may not hold during the present trial for a number of unforeseen reasons. For example, mortality may fall, perhaps from increased surveillance and improved medical care put in place for the trial, which would lower the power of the trial. We have also assumed that the efficacy of the vaccine will be 90% against pneumococcal serotypes contained in the vaccine, which we inferred from trials of a pneumococcal conjugate 7-valent vaccine against invasive disease conducted in the US.7 Whether high efficacy of the vaccine against disease would be seen in The Gambia, where the pressure of infection from pneumococci, the distribution of other pathogens, the mechanisms for vaccine delivery, and host immune responses may differ from the US population, is not clear. It is also plausible that the efficacy of the pneumococcal vaccine against mortality is lower than for disease if, for example, the vaccine does not protect against non-invasive ALRI disease, as is the case for the polysaccharide pneumococcal vaccine.26 In this event, the sample size of our trial may prove to be inadequate. However, for the purpose of illustrating the effect of misclassification, we assumed a vaccine efficacy of 90% in this paper.

Our findings highlight the difficulties of calculating sample sizes even in a setting such as ours where surveillance studies for disease and mortality were conducted over several years in preparation for this trial. One important strategy for dealing with uncertainty in the degree of misclassification of the endpoint is to conduct an interim analysis and re-estimate sample sizes at that time. This should be done using a low significance so that it does not affect appreciably the significance in the final analysis.27

In summary, low sensitivity and specificity of diagnosis by post-mortem questionnaire may mean that the power of a trial to detect a reduction in all-cause mortality is similar to that to detect a reduction in cause-specific mortality. Since the latter is more susceptible to bias from misclassification of causes of death, all-cause mortality may be the most suitable endpoint. Our investigations highlight the importance of taking diagnostic sensitivity and specificity into account when designing efficacy trials against disease-specific endpoints.

Appendum

Since writing this paper, the primary endpoint of the trial was changed from overall mortality to radiological pneumonia, for a number of reasons including a desire to allow completion of the trial in a shorter time frame.

Table 1

Mortality rates per 1000 child-years at risk recorded in children in Upper River Division, The Gambia, during the period 1989–1993

 Overall ALRIa  
Age group (months) No. of deaths Rate per 1000 child-years No. of deaths Rate per 1000 child-years Percentage of deaths due to ALRI 
a Acute lower respiratory tract infection (assessed using post-mortem questionnaires). 
0–5 1584 117.8 311 23.2 20.2 
6–11 572 42.6 138 10.2 23.9 
12–17 411 33.2 72 5.8 17.5 
18–23 365 29.6 60 4.8 16.2 
24–29 341 28.4 38 3.2 11.3 
30–35 186 15.6 17 1.42 9.1 
36–41 161 13.8 20 1.70 12.3 
42–47 71 6.0 0.68 11.3 
48–53 60 5.2 0.44 8.5 
54–59 25 2.2 0.17 7.7 
Overall 3776 33.4 671 5.9 17.7 
 Overall ALRIa  
Age group (months) No. of deaths Rate per 1000 child-years No. of deaths Rate per 1000 child-years Percentage of deaths due to ALRI 
a Acute lower respiratory tract infection (assessed using post-mortem questionnaires). 
0–5 1584 117.8 311 23.2 20.2 
6–11 572 42.6 138 10.2 23.9 
12–17 411 33.2 72 5.8 17.5 
18–23 365 29.6 60 4.8 16.2 
24–29 341 28.4 38 3.2 11.3 
30–35 186 15.6 17 1.42 9.1 
36–41 161 13.8 20 1.70 12.3 
42–47 71 6.0 0.68 11.3 
48–53 60 5.2 0.44 8.5 
54–59 25 2.2 0.17 7.7 
Overall 3776 33.4 671 5.9 17.7 
Table 2

The expected ‘true’ underlying number of deaths from acute lower respiratory tract infection (ALRI) and that expected to be recorded by the post-mortem questionnaire technique in the control group over the course of the pneumococcal vaccine trial

  ‘True’ cause of death  
  ALRI Non-ALRI Total 
Cause of death as ascertained by post-mortem questionnaire ALRI 203 
 Non-ALRI 862 
 Total a + b c + d 1065 
  ‘True’ cause of death  
  ALRI Non-ALRI Total 
Cause of death as ascertained by post-mortem questionnaire ALRI 203 
 Non-ALRI 862 
 Total a + b c + d 1065 
Table 3

The expected vaccine efficacy (VE) for all-cause and acute lower respiratory tract infection (ALRI) mortality according to different levels of sensitivity and specificity of the post-mortem questionnaire technique and the resulting power to detect such effects assuming that, in the absence of vaccination, the measured proportion of deaths attributed to an ALRI would be 19%, pneumococci would account for 30 or 50 or70% of these, that the vaccine will cover 70% of pneumococcal serotypes and would provide 90% protection against these serotypes

  Anticipated VE if pneumococci account for 30% of ALRI mortality Anticipated VE if pneumococci account for 50% of ALRI mortality Anticipated VE if pneumococci account for 70% of ALRI mortality 
  Overall mortality ALRI mortality Overall mortality ALRI mortality Overall mortality ALRI mortality 
Sensitivity Specificity VE Power VE Power VE Power VE Power VE Power VE Power 
20 90 17.1 98 18.0 46 28.7 100 30.0 90 40.0 100 42.0 100 
 95 17.7 99 18.6 50 29.6 100 31.0 92 41.4 100 43.4 100 
30 90 9.1 56 13.5 27 14.3 93 22.3 64 20.0 100 31.2 92 
 95 10.6 71 16.7 40 17.7 99 27.8 84 24.8 100 38.9 99 
40 90 5.8 27 12.0 22 9.5 60 20.0 54 13.2 88 28.0 85 
 95 7.9 45 15.9 37 12.6 85 26.5 80 17.6 99 37.1 98 
50 90 4.3 16 11.2 20 7.2 38 19.2 49 10.0 65 26.9 82 
 95 5.9 27 15.9 37 9.8 63 25.9 78 13.7 90 36.3 98 
60 90 3.5 12 10.8 16 5.8 26 18.0 46 8.1 47 25.2 76 
 95 4.8 19 15.2 34 8.0 46 25.5 77 11.2 75 35.7 97 
70 90 2.8 10.9 19 4.7 19 17.9 45 6.6 33 25.1 76 
 95 4.1 15 15.1 33 6.8 33 25.1 76 9.5 60 35.1 97 
80 90 2.4 10.6 18 4.0 15 17.4 43 5.6 25 24.4 73 
 95 3.6 13 14.4 31 5.9 27 24.8 74 8.2 48 34.7 97 
90 90 2.1 10.1 17 3.6 13 16.8 40 5.0 21 23.5 69 
 95 3.1 10 14.7 32 5.17 22 24.7 74 7.2 39 34.6 97 
100 100 3.6 13 18.9 50 6.0 28 31.5 93 8.4 50 44.1 100 
  Anticipated VE if pneumococci account for 30% of ALRI mortality Anticipated VE if pneumococci account for 50% of ALRI mortality Anticipated VE if pneumococci account for 70% of ALRI mortality 
  Overall mortality ALRI mortality Overall mortality ALRI mortality Overall mortality ALRI mortality 
Sensitivity Specificity VE Power VE Power VE Power VE Power VE Power VE Power 
20 90 17.1 98 18.0 46 28.7 100 30.0 90 40.0 100 42.0 100 
 95 17.7 99 18.6 50 29.6 100 31.0 92 41.4 100 43.4 100 
30 90 9.1 56 13.5 27 14.3 93 22.3 64 20.0 100 31.2 92 
 95 10.6 71 16.7 40 17.7 99 27.8 84 24.8 100 38.9 99 
40 90 5.8 27 12.0 22 9.5 60 20.0 54 13.2 88 28.0 85 
 95 7.9 45 15.9 37 12.6 85 26.5 80 17.6 99 37.1 98 
50 90 4.3 16 11.2 20 7.2 38 19.2 49 10.0 65 26.9 82 
 95 5.9 27 15.9 37 9.8 63 25.9 78 13.7 90 36.3 98 
60 90 3.5 12 10.8 16 5.8 26 18.0 46 8.1 47 25.2 76 
 95 4.8 19 15.2 34 8.0 46 25.5 77 11.2 75 35.7 97 
70 90 2.8 10.9 19 4.7 19 17.9 45 6.6 33 25.1 76 
 95 4.1 15 15.1 33 6.8 33 25.1 76 9.5 60 35.1 97 
80 90 2.4 10.6 18 4.0 15 17.4 43 5.6 25 24.4 73 
 95 3.6 13 14.4 31 5.9 27 24.8 74 8.2 48 34.7 97 
90 90 2.1 10.1 17 3.6 13 16.8 40 5.0 21 23.5 69 
 95 3.1 10 14.7 32 5.17 22 24.7 74 7.2 39 34.6 97 
100 100 3.6 13 18.9 50 6.0 28 31.5 93 8.4 50 44.1 100 
Figure 1

Proportion of overall mortality caused by ALRI assuming that 19% was attributed to ALRI by post-mortem questionnaire. The curves are shown for different levels of sensitivity and specificity of post-mortem questionnaires.

Figure 1

Proportion of overall mortality caused by ALRI assuming that 19% was attributed to ALRI by post-mortem questionnaire. The curves are shown for different levels of sensitivity and specificity of post-mortem questionnaires.

We thank the people of URD who took part in these studies. We also thank Professor Richard Hayes, Dr Steven Obaro, Dr Orin Levine, and Dr Akram Zaman for helpful discussions. Shabbar Jaffar is supported by a grant from UK Medical Research Council.

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