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С.Гланц МЕДИКО-БИОЛОГИЧЕСКАЯ СТАТИСТИКА
McGraw-Hill, 1994; М.: Практика, 1998. — 459 с. В книге описаны все основные методы, которыми пользуется современная
статистика, как параметрические, так и непараметрические: анализ различий, связей, планирование исследования, анализ выживаемости. Просто и наглядно — при этом вполне строго — автор описывает принцип каждого метода, дает четкую схему применения, обязательно указывает на ограничения и возможные ошибки. Изящные иллюстрации и остроумный разбор примеров, взятых из медицинских публикаций, делают чтение легким и увлекательным. Врачам-практикам книга поможет грамотно, критически читать медицинскую литературу. Для врачей-исследователей книга станет руководством по планированию, проведению и обработке результатов исследований.
Оглавление Предисловие 12 1. Статистика и клиническая практика 17 Ограничение финансирования и статистика 17 Достоверность и статистическая значимость 20 Доверяй, но проверяй 22 Ошибки вечны? 25 2. Как описать данные 27 Среднее 30 Стандартное отклонение 30 Нормальное распределение 31 Медиана и процентили 32 Выборочные оценки 36 Насколько точны выборочные оценки 37 Выводы 44 Задачи 45 3. Сравнение нескольких групп: дисперсионный анализ 47 Случайные выборки из нормально распределенной совокупности 48 Две оценки дисперсии 53 Критическое значение F 56 Три примера 63 Задачи 75 4. Сравнение двух групп: критерий Стьюдента 81 Принцип метода 82 Стандартное отклонение разности 85 Критическое значение t 88 Выборки произвольного объема 96 Продолжение примеров 97 Критерий Стьюдента с точки зрения дисперсионного анализа 99 Ошибки в использовании критерия Стьюдента 101Критерий Стьюдента для множественных сравнений 104
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Критерий Ньюмена— Кейлса 108Критерий Тыоки 112Множественные сравнения с контрольной группой 113Что означает P 117Задачи 1195. Анализ качественных признаков 122Новости с Марса 123Точность оценки долей 127Сравнение долей 132Таблицы сопряженности: критерий χ2 139Точный критерий Фишера 150Задачи 1556. Что значит «незначимо»: чувствительность критерия 161Эффективный диуретик 162Два рода ошибок 166Чем определяется чувствительность? 167Чувствительность дисперсионного анализа 181Чувствительность таблиц сопряженности 184Практические трудности 186Зачем вычислять чувствительность? 187Задачи 1907. Доверительные интервалы 193Доверительный интервал для разности средних 194Интервал шире — доверия больше 200Проверка гипотез с помощью доверительных интервалов 202Доверительный интервал для среднего 205Доверительный интервал для разности долей 206Доверительный интервал для доли 211Доверительный интервал для значений 216Задачи 2198. Анализ зависимостей 221Уравнение регрессии 225Оценка параметров уравнения регрессии по выборке 227Сравнение двух линий регрессий 244Корреляция 250Коэффициент ранговой корреляции Спирмена 261Чувствительность коэффициента корреляции 266Сравнение двух способов измерения: метод Блэнда — Алтмана 270Заключение 274Задачи 2759. Анализ повторных измерений 285Парный критерий Стьюдента 286Новый подход к дисперсионному анализу 294Дисперсионный анализ повторных измерений 305
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Качественные признаки: критерий Мак-Нимара 314Задачи 31810. Непараметрические критерии 323Параметрические и непараметрические методы. Какой выбрать? 324Сравнение двух выборок: критерий Манна— Уитни 327Сравнение наблюдений до и после лечения: критерий Уилкоксона 338Сравнение нескольких групп: критерий Крускала— Уоллиса 346Повторные измерения: критерий Фридмана 354Выводы 364Задачи 36511. Анализ выживаемости 372Пассивное курение на Плутоне 373Кривая выживаемости 376Сравнение двух кривых выживаемости 386Критерий Гехана 395Чувствительность и объем выборки 396Заключение 398Задачи 39812. Как построить исследование 402Каким критерием воспользоваться 403Рандомизация и слепой метод 405Достаточно ли рандомизации? 413Кого мы изучаем 417Как улучшить положение 419Приложения А. Формулы для вычислений 423Б. Диаграммы чувствительности дисперсионного анализа 430В. Решения задач 439Предметный указатель 456
Предметный указатель α-ошибка — см. Ошибки I и II рода,
см. также Уровень значимости Берксона эффект 419 Блэнда—Алтмана метод 270-274 Бонферрони неравенство 105 Бонферрони поправка 105-107 для повторных измерений 312-314 Вариация 295 Внутригрупповая дисперсия 54 Выборочное среднее 37 Выборочное стандартное отклонение
37 Выбывание 373—376 Выживаемость 372—398
доверительный интервал 382-385 логранговый критерий 386-395 медиана 377, 381 критерий Гехана 395—396 стандартная ошибка 382-385 чувствительность 396—397
Гехана критерий 395—396 Гринвуда формула 382 Даннета критерий 116—117 Двойной слепой метод 137, 406-410 Дисперсионный анализ 47—75
условия применимости 58-59
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чувствительность 181—184, 430-438
Дисперсионный анализ повторных измерений 305-312 чувствительность 314
Дисперсия 30—31 объединенная оценка 88, 96
Доверительная область для значений 243—244 для линии регрессии 241-243
Доверительный интервал 193-219 для доли 211—216
при малой численности групп 213—216
для значений 216—219 использование для оценки статистической значимости различий 202-205 для разности долей 206—207 для разности средних 194-200 для среднего 205—206 и чувствительность 209—211
Доля 123-124 сравнение 132—134 стандартное отклонение 125-127 стандартная ошибка 129-131
Исследования: типы 64 Йейтса поправка 144—145
для критерия Гехана 396 для критерия Манна—Уитни 333 для критерия Уилкоксона 342 для логрангового критерия 394-395
Качественные признаки 122 Количественные признаки 122 Контролируемое испытание 68-69,
405-413 Корреляция 250—269
и регрессия 255—257 коэффициент 250—254
порядковых признаков — см. Спирмена коэффициент ранговой корреляции
Крускала—Уоллиса критерий 346-348
Линии регрессии, сравнение 244-250 Логранговый критерий 386-395 Мак-Нимара критерий 314-317 Манна—Уитни критерий 327-333 Медиана 32—36
выживаемости 377, 381 Межгрупповая дисперсия 55 Множественные сравнения, см. также
Эффект множественных сравнений методы 105—113 с контрольной группой 113-117
Мощность — см. Чувствительность Непараметрические критерии 141,
323-326 для множественных сравнений 350-352 чувствительность 325—326
Неравенство Бонферрони 105 Нормальное распределение 31-36
проверка на соответствие данным 326 стандартное 133, 191—192
Нулевая гипотеза 47, 117—119 Ньюмена—Кейлса критерий 108-112
повторные измерения 314 Обсервационное исследование 64 Ожидаемое число 139—142 Остаточная дисперсия 235 Остаточное стандартное отклонение
235 Ошибки I и II рода 119, 166-167 Параметр нецентральности 174, 181,
185 Параметры распределения 29
выборочные оценки 36—37 Плацебо эффект 19, 293 Повторные измерения 305-317
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Показатели процесса и результата 136, 398
Поправка Йейтса 134 Порядковые признаки 123 Признаки: количественные,
качественные и порядковые 122—123
Проспективное исследование 64 Процентили 32—36 P, определение 117—119 Ранг 324 Рандомизация 68, 405—417 Регрессии уравнение 225—227
расчет параметров 227—234 Ретроспективное исследование 64 Слепой метод 137, 293—294, 406-410 Спирмена коэффициент ранговой
корреляции 261-265 Среднее 29-30 Стандартное нормальное
распределение 133 Стандартное отклонение 30-31
доли 125-127 и стандартная ошибка среднего 42—44 разности и суммы 85—87
Степени свободы 57 Стандартная ошибка доли 128—130
среднего 37—44 Стьюдента критерий 81—108
и дисперсионный анализ 99-101 ошибки в использовании 101-104 парный 286—291
Таблицы сопряженности 139
преобразование 147—150 чувствительность 184—185
Тьюки критерий 112—113 для повторных измерений 314
Уилкоксона критерий 338—344 Уровень значимости 57 Факториал 151, 427 Фишера точный критерий 150-154 Формула Гринвуда 382 Фридмана критерий 354—357
ϕ — см. Параметр нецентральности F критерий 55 критическое значение 56-62 χ2 критерий 141—147 критическое значение 143, 148-149 поправка Йейтса 144—145
Цензурирование — см. Выбывание Центральная предельная теорема 41-
42 Чувствительность 161—190
величина различий 170—173 дисперсионного анализа 181-184 дисперсионного анализа повторных измерений 314 объем выборки 174—177 разброс значений 173—174 таблицы сопряженности 184-185 уровень значимости 168-170
Эффект множественных сравнений 101-103, 413-417
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