Table 1 Algorithms and metrics as quality indicators of primary care

Identifying an individual’s likely PCP [12]: To find out the designated primary care physician

1) Plurality provider: Provider who billed the greatest number of Evaluation & Management (E&M) visits in a year for the beneficiary (includes specialists)

2) Majority provider: Provider who billed for the plurality of E&M visits (must be > 50% of all visits)

Process quality [15]: Quality measurement and reporting the comprehensiveness of care [7] (both the scope of services offered and the depth and breadth of conditions managed by the primary care team)

1) Appropriate-care-model composite score for preventive care [15,16,17]: The five measures were the appropriate-care-model composite measures for diabetes, medication management, and depression. (A composite measure combines the individual measures of care needed for a condition. In the case of diabetes, the composite measure includes the receipt of cholesterol screening, eye exams, urine protein screening, and an HbA1c test, which measures blood glucose.)

2) First contact [18, 19]: Time from discharge to the first PCP visit

3) Negligent adverse events [68]: Determinations of negligence were based on peer reviews

4) Documentation of lifestyle counselling from PCP notes in EHR [13]: Settled claims for negligent adverse events are an expression of patients’ experiences of medical errors and provide a useful insight into errors in primary care

5) Medication intensification [13]: Defined as initiation of a new medication or an increase in the dose of an existing medication

6) Duration of consultation time [20, 69]

7) “No-shows” and “same-day” cancellations, “after-hours” care availability [34]

8) Prevention Quality Indicators (PQI) [70]: episodes that may be potentially avoided through the timely receipt of primary or preventive care, including diabetes short-term complications admission rate, perforated appendix admission rate, diabetes long-term complications admission rate, etc

9) Care density [70] measures the extent of ‘patient-sharing’ among an individual’s ambulatory providers. The numerator of care density is the sum of shared patients among each pair of a patient’s outpatient doctors, and the denominator is the total number of pairs of outpatient doctors that a patient sees

10) Geographic accessibility to primary care providers [30, 31]: spatial accessibility to primary care service (i.e., PCPs/10,000 population, availability of PCPs within a global service catchment of 30-min drive time)

Continuity index [41]: Degree of coordination required between different providers during an episode or

1) Continuity of Care (COC) index [71]:\(COC-\frac{\sum_{i=1}^Pn_i^2-N}{N\left(N-1\right)}\) , P = total number of providers, P = total number of providers, N = total number of visits, n_i = number of visits per provider i., ni = number of visits per provider i. This index weights both the frequency of visits to each caretaker and the dispersion of visits between caretakers. Index values range from 0 (each visit made to a different physician) to 1 (all visits made to a single physician)

2) Number of Providers Seen (NOP) [72]: Number of providers with whom the patient had contact in a defined time interval (e.g., one year)

3) Sequential Continuity Index (SECON) [44, 73]: Measures the number of visits made to the caretaker whom the patient saw in the most recent visit. This index is useful for assessing the need to share information among caretakers. Index values range from 0 (every visit made to a physician other than the physician seen in the previous visit) to 1 (all visits made to a single physician): \(SECON=\frac{\varnothing 1+\dots +\varnothing n-1}{N-1}\), where ∅ = 1 if visit i & i + 1 are to the same provider and ∅ = 0 if otherwise, and N = total number of visits

4) Likelihood of Sequential Continuity Index (LISECON) [74]: the likelihood that SECON is greater than would occur if distribution of practitioners across sequential visits were random

5) Likelihood of Continuity Index (LICON) [75]=\(1-\sum_{i=1}^{k}{p}_{n}i+\frac{i}{M}{p}_{n-1} (i)\) where \({p}_{n}i=\frac{M-\left[I-1\right]}{M}{p}_{n-1}\left(i-1\right)+\left(\frac{i}{M}\right){p}_{n-1}i;\) N = total number of visits; n_i = number of visits to i-th provider and Pn(k) if the probability of seeing k different providers in n visits; M = total number of providers

6) Herfindahl Index (HI) [76]=\(\sum_{i=1}^{p}{(\frac{ni}{n})}^{2},\) where p = total number of providers, n = total number of visits during episode ni = number of visits to provider i,cj = indicator of sequential visits to same providers; equal to 1 if visits j and j + 1 are to the same provider, 0 otherwise

7) Modified Continuity Index (MCI) [77] = \(\frac{\sum_{i=1}^{k}ni /k}{\sum_{i=1}^{k}pi /k}\), where n_i = no of visits and p_i = total number of providers seen by patient i in population k during a defined time interval

8) Modified, Modified Continuity Index (MMCI) [78]: \(MMCI=\frac{1-\left({\displaystyle\frac P{N+0.1}}\right)}{1-\left(\frac1{N+0.1}\right)}\), where P = total number of providers, N = total number of visits, n_i = number of visits per provider iAnalysed in quartiles with 1 = least continuous, 4 = most continuous

9) Usual Provider Continuity UPC index [73]: Ratio of the number of visits to the most frequently seen provider to the total number of visits to all providers

10) Duration of (established PCP-patient) relationship [79]

11) Rate of provider turnover [80]: the rate of a PCP leaves a clinical practice or retires

12) Most frequent provider continuity (MFPC): \(MFPC=\frac{Max\left(n_1,n_2,\cdots,n_p\right)}N\). The proportion of outpatient visits that a patient has with his/her most frequent provider

13) Bice-Boxerman Continuity of Care [BB-COC]: \(\frac{\left({\sum }_{i=1}p {n}_{i}^{2}\right)-n}{n(n-1)}\), where p = total number of providers n = total number of visits during episode ni = number of visits to provider i cj = indicator of sequential visits to same providers; equal to 1 if visits j and j + 1 are to the same provider, 0 otherwise [81]

14) Days out of PCP cover (DOC) were calculated by subtraction of the pre-defined optimal maximum time interval (updated according to diabetes severity level) from the actual time interval between a PCP service and the next healthcare service (either PCP or hospital admission)

15) Cover [82] shows a time-limited protective effect of primary care. The cover index  = [∑ascertainment days—∑DOC] / ∑ascertainment days] was calculated for each individual annually. As the optimal maximum time interval was identified as a range of values from the threshold effects model, the cover index was calculated with low, middle and upper values bounds corresponding to low, middle and upper values of the optimal maximum time interval identified for each complication cohort

Regularity index [50, 51]: Measures how well distributed the PCP service utilisation is, not how often

1) Interval index [51] was based on with annual regularity of PCP contact defined as an ordinal variable with contacts over a 1-year period as none, any, annual, or semi-annual (at least one visit in each half of both years), or quarterly. For example, expressed as the percentage of PCP visits occurring in each quarter (0%, 25%, 50%, 100%)

2) Variance index [51]: \(VI=\frac1{1+var\left(days\right)}\), where days are the number of days between consecutive PCP visits. Analysed in quartiles with 1 = least regular4 = most regular

3) Relative variance index (RVI): \(RVI=1/\left(1+\left(\frac{sd\left(days\right)}{mean\left(days\right)}\times100\right)\right)\) where days are the number of days between consecutive PCP visits. Analysed in quartiles with 1 = least regular, 4 = most regular Differs from the variance index in that the coefficient of variation in the days between PCP contacts is used rather than the variance. At least two PCP contacts per year required to calculate. The modified index produces a unitless measure of variation, which is less correlated with frequency compared with previous measures [51]