Optimum allocation for a dual-frame telephone survey 5. Example: National Immunization SurveyOptimum allocation for a dual-frame telephone survey 5. Example: National Immunization Survey

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5.1 Introduction

CDC has sponsored the National Immunization Survey (NIS) since 1994 to monitor the vaccination status of young children age $19-35$  months. The NIS uses two phases of data collection: a dual-frame RDD telephone survey of households with age-eligible children, followed by a mail survey of the vaccination providers of these children, which obtains vaccination histories for the children for each recommended vaccine. Each such child’s provider-reported number of doses is compared to the recommended number of doses to determine whether the child is up-to-date (UTD). Information about the NIS is available in Smith, Hoaglin, Battaglia, Khare and Barker (2005) and the 2011 Data User’s Guide (CDC 2012).

We will discuss the NIS as it was conducted in 2011. The main interview consisted of six sections, beginning with Section S, which is a brief questionnaire module that determines whether the household has age-eligible children. The interview is then terminated for ineligible households. For eligible respondents with an available vaccination record (shotcard), Section A obtains the child(ren)’s household-reported vaccination history. For all other respondents, Section B obtains a more limited and less specific amount of information about the child(ren)’s vaccinations. Section C collects demographic characteristics of the child(ren), the mother, and the household. Section D collects the names and contact information for the child(ren)’s vaccination providers and requests parental consent to contact the providers, while Section E collects information regarding current health insurance coverage.

5.2 Optimum allocation for NIS

The NIS is designed to produce estimates at the national level and for 56 non-overlapping estimation areas, consisting of 46 whole states, 6 large urban areas, and 4 rest-of-state areas. Each of these areas is a sampling stratum in the NIS design. For each of these areas, NIS is designed to minimize the cost of the survey subject to a constraint on variance: the coefficient of variation (CV) of the estimator of the vaccination coverage rate (UTD children as a proportion of all eligible children) is to be 7.5 percent at the estimation-area level, when the true rate is 50 percent.

Given the take-all protocol, the six-part survey interview is administered to all respondents in both sample. Given the screening protocol, the survey interview is administered to all respondents in the landline sample, while in the cell-phone sample, the overall interview is now in two parts: (i) the brief screener to determine telephone status and (ii) the aforementioned six-part survey interview. Dual users are screened out of the cell-phone sample.

To illustrate the optimum allocation, we take the per-unit costs to be proportional to the following values: ${c^{\prime }}_B=0.06,$ ${c^{″}}_B=2.03,$ $c_B=1.96,$ and $c_A=\mathrm{1.00.}$ Cell-phone interviews require roughly twice as many labor hours as landline interviews. We assume the following population proportions for age-eligible children by telephone status: $W_A= 0.59,$ $W_a=0.08,$ $W_{ab}=0.51,$ $W_b=0.41,$ $W_B=0.92,$ $\alpha =0.86,$ and $\beta =\mathrm{0.55.}$ We calculated these proportions using data from the January $–$ June 2010 National Health Interview Survey.

To estimate a vaccination coverage rate given the take-all approach, we work with the variable

$$Y_i=\{\begin{array}{l}1, \text{ if the }{i}^{\text{th}}\text{ case is an age-eligible child who is UTD}\hfill \\ 0,\text{ otherwise}\text{.}\hfill \end{array}$$

Then, the estimated vaccination coverage rate is $\ddot{Y}/N_e,$ where $N_e$ signifies the number of age-eligible children in the population (assumed known from vital statistics and related records). In accordance with the variance constraint, we take ${\overline{Y}}_{ae}={\overline{Y}}_{abe}={\overline{Y}}_{be}=0.5,$ where the subscript $e$ signifies the mean of the age-eligible cases within the corresponding telephone status domain. Then, ${\overline{Y}}_d={\overline{Y}}_{de}{P}_{de}$ and $S_d^2={\overline{Y}}_d\left(1-{\overline{Y}}_d\right),$ where $d=a, ab, b$ designates the three telephone status domains and $P_{de}=N_{de}/N_d$ signifies the age-eligibility rate within domain $d.$ Based on NIS experience, we take $P_{ae}=0.015,$ $P_{abe}=0.03,$ and $P_{be}=0.05,$ reflecting an increasing eligibility rate across the telephone status domains; that is, young child-bearing families tend to have a cell phone and further tend to be CPO. By definition, the variance is the square of the coefficient of variation times the square of the population proportion. Thus, the variance constraint is $\text{Var}\left\{\ddot{Y}/N_e\right\}={0.075}^2\times {0.5}^2.$

To estimate a vaccination coverage rate given the screening design, we work with the variable

$$Y_i=\{\begin{array}{lll}1,\hfill & \text{if }i\in s_A,\hfill & \text{and is an age-eligible child who is UTD}\hfill \\ 0\text{,}\hfill & \text{if }i\in s_A\text{,}\hfill & \text{and is not an age-eligible child or is not UTD}\hfill \\ 1,\hfill & \text{if }i\in s_B,\hfill & \text{and is CPO and is an age-eligible child who is UTD}\hfill \\ 0\text{,}\hfill & \text{if }i\in s_B\text{,}\hfill & \text{and is not CPO or is not an age-eligible child or is not UTD}.\hfill \end{array}$$

Given these assumptions, the values of the efficiency ratio $E$ lie below 1.0 for all values of $p$ and from this we conclude that the screening design may be relatively less costly than the take-all design. The optimum value of $p$ is about 0.39. However, $E$ is quite flat in a neighborhood of the optimum and thus values of $p$ in this neighborhood would produce similar total cost.

Given our assumptions, the optimum allocation for the take-all protocol at the optimum $p$ is $n_A=\text{3,069}$ and $n_B=\text{7,437,}$ which equates to 86 NIS interviews on behalf of age-eligible children in the landline sample and 289 interviews on behalf of age-eligible children in the cell-phone sample. For the screening protocol, the optimum allocation is $n_A=\text{5,858}$ and $n_B=\text{8,432,}$ which we expect to yield 164 NIS interviews on behalf of age-eligible children in the landline sample and 188 NIS interviews of CPO households on behalf of their age-eligible children. These allocations apply to a single typical estimation area. Table 5.1 displays the expected sample sizes by telephone status domain given the optimum allocations. Given the screening protocol, the cell-phone sample yields an expected 4,674 dual users, which in turn reflect an expected 140 age-eligible children (who are not to be interviewed and thus are not included in the table).

We developed the optimum allocations revealed here under ideal conditions in which there is no nonresponse. To prepare a sample for actual use in the NIS (or any real survey), the allocation must be adjusted by the reciprocals of the expected survey cooperation rates and by the expected design effect due to weighting and clustering.

While the extant evidence shows that the screening protocol is slightly less costly than the take-all protocol, given that both achieve the same fixed variance constraint, the take-all protocol actually provides the NIS an ongoing platform for testing and comparing both protocols. The authors continue to monitor the achieved sample composition and to conduct other specialized studies of response and nonresponse error.

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