Sampling strategies to measure the prevalence of common recurrent infections in longitudinal studies

The prevalence of common recurrent infections such as diarrhoea and respiratory infections in field studies is commonly estimated using repeated measurements in the same individuals. Many studies have used intensive surveillance, for example by conducting twice-weekly home visits to measure prevalence on every single day over the study period [1, 2]. In other studies prevalence was measured at intervals, for example during only four home visits at 4-week intervals [3]. The differences in logistical effort are considerable. A study of 100 households over one year with twice-weekly surveillance visits would require 52 × 2 × 100 = 10,400 visits. Conducting only four visits per household in total requires only 4 × 100 = 400 visits. It has been shown that close surveillance can be inefficient with regard to study power [4]. To facilitate logistics and limit the impact of study procedures on participants' risk behaviour, it can be preferable to sample less frequently and recruit a somewhat larger study population to offset the loss of power incurring with fewer measurements [4].

Using an empirical mathematical model this paper explores the question of how many more participants are needed for infrequent sampling to achieve the same study power as frequent sampling. Furthermore, we tested the effect of recall error, and whether the use of daily point prevalence data offers any advantages over weekly period prevalence data [3, 5]. Recording weekly period prevalence [3, 5] may be simpler, but is less precise. Finally we explored the implications of clustering at group level (e.g. household or village) for sampling strategies.

Repeated prevalence measurements allow the calculation of the "longitudinal prevalence" (i.e. the proportion-of-time-ill), a measure that in the case of diarrhoea has been shown to correlate better with adverse outcomes than incidence [6, 7]. The longitudinal prevalence (LP) of a disease in an individual is a continuous outcome that can take values between 0% (never diseased) and 100% (always diseased) [4, 6]. For sufficiently large studies, standard formulae for the calculation of the required sample size for the comparison of two means (e.g. in a control and intervention arm) can be used, such as

wheren is the sample size per arm, the term (0.84+1.96) corresponds to 80% power and p = 0.05, σ₁ and σ₂ are the standard deviations of the LP in the two groups, is the mean longitudinal prevalence in the control arm, andLPR the ratio of the mean LP between intervention and control arm [8].

The standard deviation can also be expressed in terms of the "coefficient of variation" (CV), useful for sample size calculations based on limited data (see below).

The sample size calculation for studies using LP as an outcome is not straightforward because the assumed standard deviation of critically depends on how disease is distributed between individuals. For many common recurrent infections disease prevalence is highly clustered in individuals [9]. The more the disease is concentrated in high risk individuals, the easier it is to predict an individual's future disease evolution based on previous measurements, thus limiting the gain in study power from many repeat measurements.

There are several epidemiological characteristics of common recurrent infections like diarrhoea and respiratory infections that increase the clustering of disease in individuals, i.e. increase the standard deviation of the longitudinal prevalence, thereby making individuals more "different" from each other [9]. Episode incidence is typically highly clustered in high risk individuals [9]. Also, individuals with more episodes tend to experience longer episodes than those with fewer episodes [9]. This also concentrates disease days in high risk individuals. These and other characteristics can be specified in a mathematical model allowing the comparison of different surveillance strategies with regard to study power under controlled conditions [4,9].

Our model simulates the occurrence of recurrent infections in a population of hypothetical individuals over 365 days. For a detailed description of the model see [9]. The models were implemented inStata 10. The model was parameterized by specifying three major characteristics disease distribution.

In a first step, we built a set of models simulating 20,000 individuals with increasingly complex assumptions on how disease is distributed over the follow-up period of 365 days, based on a stepwise parameterization of the model described above. The aim of these models (four in total, named models A to D) was to illustrate how the three different model parameters (episode incidence, episode duration and correlation between incidence and episode duration) affect the dependency of study power on sampling frequency.

The parameters for this set of models were estimated from a single field study from Brazil, testing the effect of Vitamin A on diarrhea in children under 5 [10]. As observed in the study, we assumed a 5% prevalence of diarrhea in models A to D. The differences between models A to D are described in the next section. After generating the models A to D based on the model parameters, we simulated different sampling frequencies ranging between daily sampling to sampling only once every 28 days. For simplicity, we assumed a 24 h recall period without recall error. We then calculated the longitudinal prevalence (proportion of time ill) in each individual, the mean and standard deviation of the LP of the simulated population, and finally the required sample size for the different sampling intervals based on the formula above. For illustration, we assumed a 20% reduction of LP in one arm (LPR = 0.8, this value was not critical to the models' output).

For the sample size calculation in practice, an investigator must first identify a reasonable estimate of the baseline mean LP in the population, which can be acquired from cohort or cross sectional data. The challenge lies in the determination of the standard deviation of LP which depends on factors that are often unknown, unless high quality longitudinal data are available. Field data [9] suggest that the ratio of the SD of LP to the mean LP (the CV) will decrease from model scenario 1 to 4. A range of CV values estimated from studies available to the authors are listed in Table5. Typical CV values for model scenarios 1 (LS) and 2 (LL) range between 2.5 (Guatemala and Pakistan diarrhoea data) and 2.9 (Ghana ALRI data). For model scenarios 3 (HS) and 4 (HL) one may assume CVs of about 0.9 to 1.3 (Ghana diarrhoea and Brazil 2 diarrhoea data). These large differences in the standard deviations between the scenarios highlight the difficulty in estimating the required sample size.

Sampling at long intervals to measure the prevalence of common infections may not only reduce the number of visits and costs, but could also improve participants' willingness to cooperate and decrease the potential for changing risk behaviours due to close surveillance. The findings of this study could be used to inform on the choice of the most appropriate sampling strategy and its implications for sample size and sampling frequency. Infrequent sampling is less suitable when the aim of a study is to measure the incidence of infection.

Sampling strategies are ideally chosen to maximise study power given the available budget. The choice of a particular sampling strategy in terms of costs and logistics is highly context specific. In some settings, recruiting and supervising a large group of field workers (needed for intensive follow-up) can be straightforward, in other settings very difficult. Sometimes, recruiting additional study participants can be the dominant logistical challenge. In this case it may be better to choose close follow-up to maximise study power given a limited number of participants.

The final choice of the sampling frequency may often depend on the research question. If microbiological data are to be collected, frequent sampling may be necessary to maximize study power particularly for uncommon pathogens. Long sampling intervals may be ideal for example to explore the effect of large scale-environmental health interventions, where the causative pathogen is often of minor interest and the study population is too large to allow frequent sampling. But regardless of the study question, it should be useful to compare the statistical power of different sampling frequencies (for example by using Tables3 and4).

In the past, large-scale trials have often opted for close surveillance of a subset of the population [14]. In many circumstances it may be better to sample disease at long intervals in the whole study population to save staff costs and to avoid influencing risk and reporting behavior of study participants by frequent visits. A recent trial on water treatment in Kenya in which participants were randomized to two different diarrhoea surveillance schemes (intensive vs. infrequent sampling) found strong evidence for the latter (Michael Kremer, Claire Null, personal communication).

The following example illustrates the profound implications on study planning of choosing infrequent sampling. Emerson and colleagues conducted a large cluster-randomised trial to measure the impact of fly control and latrine construction on trachoma [21]. Diarrhoea was originally included as a secondary outcome but then dropped because the logistical effort of conducting weekly follow-up visits was deemed prohibitive (Emerson, personal communication). However, our results suggest that the additional costs of visiting each household 6 to 12 times over the study period of 6 months would have been small, and - given the large number of already recruited participants - could have allowed estimating the effect size of sanitation on diarrhoea with sufficient accuracy. Given the clustered design of the trial, close surveillance of participants for diarrhoea symptoms would have gained little power over less frequent sampling, as was shown in Table4. Jenkins and colleagues conducted a study on the impact of a household water filter on diarrhoea [22]. Due to lack of funding, the study was originally planned as an acceptability study, only. However, after considering different surveillance strategies as described in this paper the budget was judged sufficient to conduct 6 visits per household at monthly intervals.

Some interventions or risk factors (e.g. micronutrient supplements) partly or primarily affect the duration rather than the incidence of infections [10]. Some interventions can also alter the average duration of disease by selectively reducing short or long episodes as observed in a household water treatment trial study in Guatemala [13]. Period prevalence data may at times be more efficient in terms of study power and are easier to collect. However, it will often be difficult to exclude prior to a study that an intervention affects episode duration, which would not be captured fully by recording period prevalence. The results indicate that in most circumstances, applying a 7-day recall period using point prevalence data may be the preferred choice for measuring prevalence. However, the choice of the length of the recall period depends on the situation. For example, in urban settings people may be used to Monday-Friday work weeks and shop opening hours and might 'think' in weekdays more than some poor rural populations, which may facilitate disease recall.

We identified several epidemiological characteristics of recurrent infections that needed to be included in the simulations in order to achieve estimates on the association between sampling frequency and sample size. A large number of parameter combinations would have been possible, and it could be argued that the simulation should have focused on changing these parameters individually. However, different settings commonly do not differ in a single parameter but in several of them jointly. For example, children in high incidence settings often have longer episodes than in low incidence settings [9]. We limited the number of scenarios to just four, covering a fairly wide range of epidemiological settings and conditions. As with any more complex model the choice of these scenarios was to some extent arbitrary. As in the above example of a sample size calculation many epidemiological settings will fall in between the scenarios, so that the sample size calculation will still contain a fair amount of guess-work. Future work could explore a wider range of model scenarios, including other types of infections and conditions, which in this analysis we largely restricted to diarrhoea and respiratory infections as the most important in terms of morbidity and mortality [23].

As demonstrated in Figure1 the simulated datasets used in this analysis allowed us to explore the role of different parameters of disease distribution under "controlled conditions". Real datasets would have been unsuitable for this purpose because it would have been very difficult to infer from them a similar understanding of the stochastic processes that may influence the choice of the appropriate sampling strategies. However, simulation models by definition simplify the dynamics of disease occurrence and as such they provide an approximation of the real data. For example, the model does not allow for missing data, which occur in most datasets collected in the field. The validation of the model using the real datasets (which all contained missing data of up to 10%) revealed that missing data do not systematically influence the association between sampling frequency and sample size in studies with a typical loss-to-follow up (see the comparison of real and simulated data shown in Figure1). For this reason, we did not further explore the complex issue of missing data.

As described in the sensitivity analysis section, our assumptions regarding recall error were relatively straightforward. For example, we assumed the same recall error for recording point prevalence and period prevalence data. Obtaining point prevalence data will require a more thorough questioning of study participants compared to period prevalence (which can be obtained with a single question). Spending more time with the interviewees may reduce recall error.

In real datasets, recall error may also vary between different villages/clusters and increase during the course of a study due to a number of factors. Towards the end period of a study, prevalence estimates are often low suggesting that participants or field staff lose interest in reporting disease [11]. Some studies found that the first (or a single) surveillance visit provides higher, at times implausible prevalence estimates compared to subsequent visits [24,25]. Our model did not account for these factors. However, the sensitivity analysis showed that recall error hardly influences the model results. Also, recall error could be less important for calculating LP than incidence of disease because the timing of disease occurrence is less relevant. A recent study found that mothers often misplaced the day at which disease occurred in a child, but this error had little effect on the overall prevalence estimate [26].

Choosing the optimal approach to measure recurrent infections in epidemiological studies greatly depends on the setting, the study objectives, study design and budget constraints. Our findings may contribute to making epidemiological studies more efficient, valid and cost-effective. They may also encourage more researchers to include diarrhea or respiratory infections as a health outcome in the first place, which previously have often been thought to require a high logistical effort. As shown in this paper, this need not necessarily be the case.