Digestor discontinuo En un sistema discontinuo, la curva de evolución

A double sample procedure divides the total sample into two parts, and these parts are then surveyed sequentially - whether the second part is carried out is conditional on the results of the first part. This sampling procedure is analogous to interim monitoring in clinical trials. For additional sequential LQAS designs, see Myatt and Bennett (2008); Olives et al. (2009) for example.

Regardless of whether a single or double sampling plan is used, “failure to achieve elimination” can be declared at any point in the survey if the number of detected NT deaths surpasses the acceptance number, and the survey can be stopped early. If a large number of NT deaths are observed early in the survey, the survey should not be stopped until enough data (we require a representative sample of at least 250 mothers of eligible live births) has been collected to assess the remaining risk factors for NT (e.g. TT coverage; proportion of deliveries in a health facility and assisted by medically-trained attendants; and use of traditional substances on the umbilical stump).

It is important to keep in mind that, when the survey is stopped early, the collected data may not be representative of the entire district (because not all clusters have been visited). On many occasions, we may not want to stop the survey, even after the sample of 250 mothers was obtained. Specifically, if clusters are visited systematically (e.g. all urban clusters are visited first), then the collected data is susceptible to selection bias. Coverage estimates from the subsample obtained before the survey was stopped are no longer generalizable to the entire population. If clusters are visited on a random basis, the coverage estimates may be representative, even if the survey is stopped early. When representative coverage estimates of the additional indicators (e.g. vaccination, cord care, and clean delivery) are of interest, program managers must carefully consider whether the collected data is a representative sample of the district. If it is unclear whether the sample is representative, sampling should continue.

from the results of a preliminary first sample if the number of NT deaths detected is very low (e.g. 0). When the number of NT deaths in the first sample is not low enough to declare elimination (and the number of NT deaths in the first sample does not exceed the acceptance number), the second sample is necessary.

To construct a double sampling survey plan, we again specify thresholds pl, pu, α, and β. We also need to specify an additional parameter, α1, which is the probability of declaring elimination after the preliminary sample, given pu. This additional parameter does not affect the overall α-level of the survey design, but instead serves as a guide to select the sample size and decision rule for the preliminary sample. Based on these parameters, we can find the minimum sample sizes for the preliminary and secondary samples, n1 and n2, and the corresponding acceptance numbers d1 and d2, to meet our survey design specifications.

The proposed double and single sampling plans are designed using identical overall survey parameters pl, pu, α, and β. Therefore, to decide between a single and double sam- pling plan, we evaluate cost-effectiveness and feasibility, and are not concerned about the statistical precision of double versus single sampling (as they have the same preci- sion). Thus the main reason that one would use a double sampling design is to reduce the amount of money/time spent conducting the survey.

Double sampling is only more cost-effective if we expect that the district has achieved elimination with some reasonable level of confidence. If the second sample is required, the total sample size required for a double sampling survey is always greater than the sample size for a single sampling survey. This result is due to the fact that we analyze the data twice during the survey period and have two different opportunities to declare elimination. In statistics, this issue is often referred to as “multiple comparisons”, and we must adjust the classification errors to account for the fact that we look at the data twice. So, to obtain the desired classification errors α and β, we must sample more individuals in the double sampling plan to account for the inflated classification errors caused by looking at the data twice. As a general rule, we want to minimize the probability that we

will need the second part of the sampling.

Note that planning a double sampling survey also requires some extra effort when contrasted to a single sampling plan. Specifically, one must decide which clusters will be included in the first and in the second sample. Clusters should be divided between the samples such that the first sample is representative of the entire target population. Otherwise, inferences about the additional indicators (vaccination coverage, clean de- livery, cord care, etc.) will not be representative of the surveyed population and will consequently be difficult to interpret. As an example, we cannot spatially partition the district to construct the first and second sample, though data collection would be much easier subsequent to such a partitioning. Additionally, one must analyze the data from the small sample, and decide whether the next sampling stage should occur. This interim analysis could be logistically challenging. Further, survey preparations are necessary for all clusters (for both the first and second sample) and may be considerable if a second part is required.

When choosing between a single versus double sampling plan, the deciding factor should be: “Is the cost/time savings that are potentially associated with double sampling worth the additional logistics that go into planning a double sampling survey and the potential extra cost of the second part?” So we need a measure of the odds that a second sample will be required. The odds of requiring a second sample decrease with the odds that the NT rate is well-below 1 in 1000 live births. If we expect that a second sample will be required in the double sampling plan (i.e. we are uncertain about whether or not elimination has been achieved), then we should choose a single sampling plan, to save both time and money. More commonly, it may simply be logistically infeasible to conduct a double sampling survey. For instance, a lack of communication equipment and/or long travel times between clusters would preclude the midpoint evaluation (to determine if the second sample is required).

In summary, the decision of whether to use a single or double sampling plan requires some prior information about the district-level NTMR and knowledge of the cost and

logistical differentials for single and double sampling plans.